The Relationship between the Hybrid New Keynesian Phillips Curve and the NAIRU over Time

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2 The Relaionship beween he Hybrid New Keynesian Phillips Curve and he NAIRU over Time Lena Vogel * Ocober Absrac New Keynesian models of he Phillips curve in he spiri of Galí and Gerler (999) generally assume a shor-run rade-off beween inflaion and a measure of excess demand due o nominal rigidiies, while in he long run inflaion is consan a he Non- Acceleraing Inflaion Rae of Unemploymen (NAIRU). By conras, Gordon (997) in his riangle model of inflaion models a ime-varying NAIRU. We combine boh approaches and esimae sae-space models of he hybrid New Keynesian Phillips curve (NKPC), where excess demand is measured by he unemploymen gap and he NAIRU is allowed o vary over ime as in Gordon (997). Moreover, inflaion expecaions are measured direcly from surveys on household s inflaion expecaions and no insrumened for. Our model is esimaed for he US, he UK, Ialy and Spain and we find considerable variaion in he NAIRU over ime wih NAIRU esimaes significanly differen from HP-filer derived measures such as usually employed in dynamic sochasic general equilibrium (DSGE) models. In conras o GMM resuls for he hybrid NKPC, we find ha backward looking behaviour generally seems o be quaniaively more imporan for inflaion han forward looking behaviour. JEL classificaion: C3, E3 Keywords: Hybrid New Keynesian Phillips curve, ime-varying NAIRU, sae-space models * Universiy of Ken, UK, and Universiy of Hamburg, Germany. Conac auhor: Lena.Vogel@wiso.unihamburg.de. The auhor would like o hank Miguel Léon-Ledesma and Ulrich Frische for very helpful discussions and suggesions on earlier versions of his paper. Remaining errors are mine, of course.

3 . Inroducion The mos commonly used model of he Phillips curve in modern macroeconomics is he hybrid New Keynesian Phillips curve (NKPC) as developed in Galí and Gerler (999), relaing he inflaion rae o lagged inflaion, inflaion expecaions and a measure of excess demand, saing a shor-run rade-off beween inflaion and unemploymen and long-run equilibrium wih consan inflaion a he NAIRU. However, he NAIRU may change over ime if he marke characerisics underlying he equilibrium relaion beween inflaion and unemploymen change (Friedman, 9, and Phelps, 9). Feedback effecs beween labour produciviy and unemploymen as in Phelps (99) srucural slumps and, accordingly, hyseresis of unemploymen (e.g. Sigliz, 997) may also cause he underlying naural rae of unemploymen o shif. Wih a imevarying NAIRU, he unemploymen rae ha will keep inflaion consan changes so ha knowledge of hese movemens is of grea imporance for efficien moneary policy argeing. In his paper, we invesigae he relaionship beween he hybrid NKPC and a imevarying NAIRU for he US, he UK, Ialy and Spain. We esimae sae-space models of he hybrid New Keynesian Phillips curve, where he ime-varying NAIRU is esimaed as an unobserved componen. Thus, we can analyse changes in he NAIRU wihin he heory-based sysem of he hybrid NKPC, aking accoun of he inerdependencies beween inflaion, inflaion expecaions and he unemploymen gap when deermining changes in he naural unemploymen rae. We conras our esimaes of he imevarying NAIRU from he sae-space model wih mechanically calculaed seady-sae unemploymen from an HP-filer, such as usually employed in dynamic sochasic general equilibrium (DSGE) models (Dees e al., ). Mos empirical sudies of he hybrid NKPC make use of he Generalized Mehod of Momens (GMM), insrumening for inflaion expecaions wih he oupu gap, he ineres rae and addiional lags of inflaion. These models generally find ha while backward looking behaviour wih regard o inflaion is saisically significan, forward looking behaviour is quaniaively more imporan. If excess demand is measured by he oupu gap, i is ofen found insignifican; herefore, Galí and Gerler (999) propose For examples of GMM esimaes of he hybrid NKPC for he US see Galí/ Gerler (999) and Galí/ Gerler/Lopez-Salido (, 3, 5).

4 o use real marginal cos insead. Proxying his wih uni labour cos, mos sudies find a significan and correcly signed coefficien. However, he GMM approach may be biased due o idenificaion problems and weak insrumen bias wih regard o inflaion expecaions ha impede he recovery of unique srucural coefficiens (e.g. Lindé, 5; Rudd and Whelan, 5, and Dees e al., ). We avoid his problem by using direc survey measures for households inflaion expecaions from he Universiy of Michigan s Surveys of Consumers for he US and he EC Consumer Survey for he European economies in our esimaions. Overall, our sae-space model of he hybrid NKPC hus avoids he idenificaion problems encounered in sandard GMM models and obains ime-varying esimaes of he NAIRU wihin he heory-based sysem, where he resricions on coefficiens of he model can be esed direcly. We find significan changes in he NAIRU over ime in all he counries under invesigaion, which seem o move closely wih acual unemploymen raes. The paper is srucured as follows: A shor discussion of heories of he Phillips curve is given in secion, while secion 3 presens he model and mehodology used for he economeric esimaions. Secion presens he resuls from our esimaions of he saespace models of he ime-varying NAIRU in a hybrid NKPC seing. Finally, secion 5 summarises and concludes.. Theories of he Phillips Curve The New Keynesian Model of he Phillips Curve Assuming Calvo (93) pricing wih sicky prices and raional firms, he New Keynesian Phillips curve (NKPC) 3 is a funcion of expeced inflaion Eπ and a measure of excess demand y, which according o he heory of profi-maximising firms Oher empiricial sudies of he New Keynesian Phillips curve ha employ survey measures of inflaion expecaions are, e.g., Robers (995, 997), Adam/Padula (3) and Paloviia (). 3 An exensive summary of he lieraure on New Keynesian heories of moneary policy is given in Clarida/Galì/Gerler (999). Robers (995, 997) and Mankiw/Reis (a), iner alia, provide empirical esimaes of he sicky-prices New Keynesian Phillips curve. 3

5 is represened by he percenage deviaion of firms real marginal cos from heir seadysae value (Galí and Gerler, 999): () π = λy βeπ u, where denoes he inflaion rae (p p - ), u is an i.i.d. disurbance erm and λ ( θ )( βθ ) / θ is a funcion of he probabiliy of price adjusmen ( - θ) and he subjecive discoun facor β. Wih raional expecaions, unexpeced movemens in inflaion will only have shor-run real effecs, since inflaion expecaions will adjus and influence curren inflaion. Ieraing equaion () forward gives he following closed form of he NKPC: j () π = λ β E y j j= Inflaion should hus equal fuure discouned expeced marginal coss. More recenly, New Keynesian models of he Phillips curve have incorporaed a lagged inflaion erm o accoun for he srong persisence of inflaion ypically observed in empirical daa. Firs inroduced by Galí and Gerler (999) 5, i is assumed ha of he firms who are able o adjus prices in any period, only a fracion adjuss o heir opimal prices, while he ohers updae las period s opimal prices wih lagged inflaion as a rule of umb. This resuls in he so-called hybrid NKPC: (3) π φπ φ) E( π γy ε, = ( ) wih φ and ε IID(, σ² ε ). The hybrid NKPC presened in equaion (3) hus incorporaes sicky prices as well as inflaion ineria and has become he workhorse of modern macroeconomics. The lagged inflaion erm migh also be explained by sicky informaion as in Mankiw and Reis Sudies previous o Galí/ Gerler (999) usually employed he oupu gap as he measure of excess demand. However, Galí/ Gerler (999) as well as Galí e al. (5) sress he imporance of using real marginal cos (which, assuming a Cobb-Douglas producion funcion, can be proxied by he labour share) insead of he oupu gap for empirical esimaion of he NKPC. 5 Fuhrer/ Moore (995) also observe he missing persisence in inflaion in sandard New Keynesian models of he Phillips curve wih saggered conracs à la Taylor (9) and presen a model similar o he hybrid NKPC, he so-called relaive conracing model, where agens negoiae wages relaive o exising wage conracs during he ime heir wage conrac will be in effec. This inroduces persisence boh in inflaion and excess demand and he auhors show ha he dynamics of he model mach acual dynamics in inflaion quie closely.

6 (, a, b) which could be due o raional inaenion (Sims, 3, and Reis, ) relaed, for insance, o media coverage on inflaion (Carroll,, 3). Mos empirical sudies of he hybrid NKPC in he lieraure obain esimaes of he coefficiens of he model using he Generalized Mehod of Momens (GMM). By assuming raional expecaions and i.i.d. errors, he forecas error of inflaion mus be uncorrelaed wih variables daed and earlier, providing he following orhogonaliy condiion: E ( π y z =, () { λ βπ ) } where z is a vecor of variables daed and earlier. Galí and Gerler (999) as well as Galí, Gerler and Lopez-Salido (, 3, 5) amongs many ohers presen GMM esimaes of he hybrid NKPC for he US. While hey find a significan impac of inflaion ineria on curren inflaion, he effec of forward-looking behaviour, i.e. inflaion expecaions, on inflaion seems o be quaniaively more imporan. The coefficien on excess demand is usually found significan and correcly signed. However, Lindé (5), Rudd and Whelan (5) and Dees, Pesaran, Smih and Smih () argue ha he GMM approach o he hybrid NKPC ofen suffers from idenificaion problems and weak insrumen bias: As is common pracice in mos papers in he lieraure, apar from he oupu gap and he ineres rae, addiional lags on inflaion are used o insrumen for inflaion expecaions. However, Dees e al. () show ha his is only appropriae if he oupu gap depends on pas values of inflaion, eiher direcly or indirecly. If his is no he case, insrumens do no fulfil he rank condiion and resuls may be seriously biased due o he weak insrumens. Lindé (5) proposes he use of full informaion maximum likelihood esimaors (FIML) o avoid he possible bias in GMM single equaion esimaions. Nason and Smih (5) also acknowledge he idenificaion problems of GMM mehods. They presen an alernaive idenificaion mehod where a srucural vecor auoregressive (SVAR) sysem of he hybrid NKPC is esimaed, inroducing an addiional errorcovariance resricion beween he wo equaions in he sysem: The oupu gap is assumed o follow a firs-order auoregressive process and does no depend on curren inflaion, which is described by he hybrid NKPC. However, pas lags of inflaion are 5

7 allowed o affec he oupu gap, so ha he idenificaion problem menioned by Dees e al. () is no solved. Baini, Jackson and Nickell (5) furhermore address he problem of a possible omied variable bias of he sandard NKPC for he case of an open economy such as he UK, including proxies for maerial inpu prices, foreign compeiion and employmen adjusmen coss. They find ha marginal cos is inaccuraely proxied by he labour share if employmen adjusmen coss are no accouned for and ha inflaion in he UK is significanly explained by shifs in real impor prices and foreign compeiion. Bjørnsad and Nymoen () also discuss a possible omied variable bias for NKPC esimaions, namely a linear combinaion of uni labour coss and he real exchange rae, since he NKPC is encompassed by imperfec compeiion models of inflaion bu no vice versa. They esimae he NKPC wih a panel model for OECD counries and find ha expeced inflaion and marginal cos in he model provide replacemens for equilibrium correcion erms in he imperfec compeiion model. Anoher empirical approach o he hybrid NKPC is developed by Sbordone (, 5) who esimaes he closed form of he NKPC in equaion (). The NKPC is esimaed in a wo-sep procedure: Firs, uni labour coss (ulc) as a proxy for nominal marginal cos are forecased in an unresriced VAR. Second, aking he forecas as given, he disance beween he pah of he price/ulc raio implied by he model and ha of he real dynamic daa is minimised in order o gain esimaes of he srucural parameers of he model. Similar o Galí and Gerler (999) and subsequen papers, Sbordone (, 5) finds ha while backward looking behaviour wih regard o inflaion is significan, forward looking behaviour is relaively more imporan. Her approach has been criicised by Kurmann (5): Kurmann s (5) paper analyses he fi of he inflaion pah derived from he closed form NKPC wih respec o acual inflaion and concludes ha while he fi of he model seems impressive, he confidence inerval around he poin esimaes is relaively large so ha i remains uncerain wheher backward looking or forward looking behaviour dominaes. In ha sense, his criique applies also o Galí and Gerler (999). There exis several oher sudies of he New Keynesian Phillips curve ha employ direc survey measures of inflaion expecaions insead of insrumens: Robers (995, 997)

8 uses he Michigan survey of households inflaion expecaions and he Livingson survey of professional forecasers inflaion expecaions for he US in his sudy of he NKPC. He finds ha expecaions are no perfecly raional and here is evidence of a role for lagged inflaion in explaining curren inflaion. Similarly, Adam and Padula (3) analyse he NKPC for he US wih daa from he Survey of Professional Forecasers (SPF). Like Robers (995, 997), hey find ha survey daa of inflaion expecaions do no confirm he raionaliy hypohesis needed for he orhogonaliy assumpion of forecas errors wih respec o oupu, so ha esimaions insrumening for expecaions may be severely disored. Furhermore, hey find ha lagged inflaion eners he hybrid NKPC significanly. Finally, Paloviia () esimaes differen models of he Phillips curve for European economies using survey daa from Consensus Economics for inflaion expecaions. While she finds ha he NKPC fis he daa adequaely, he New Classical and Hybrid NKPC model perform beer and even when allowing for possible non-raionaliy of expecaions, he lagged inflaion erm sill eners significanly. Thus overall, here seems o be a srong case for including lagged inflaion in he hybrid NKPC and using survey daa o accoun for possible disorions due o non-raionaliy of expecaions. Modelling he NAIRU over Time Gordon (997) proposes a differen model of he Phillips curve in his Triangle Model, where inflaion depends on inflaion ineria in he form of lagged values of inflaion, presen and pas measures of excess demand (D) as well as presen and pas supply shocks (z) (Gordon, 997): (5) π = α( L) π β ( L) D γ ( L) z ε, where (L) sands for he lag operaor. Excess demand D is normalised o zero and can be represened by he oupu gap or he unemploymen gap, which is defined as he gap beween he curren unemploymen rae and is naural value (U U N ). If he sum of he α-coefficiens equals exacly uniy, i can be shown ha here exiss a naural rae of unemploymen consisen wih consan inflaion, hence a NAIRU. Long-run seadysae unemploymen is hus explicily modelled in equaion (5). The noion of changes in he NAIRU aribuable o changes in he microeconomic relaions governing he produc and labour markes was acknowledged by Friedman and 7

9 Phelps already in 9 and laer ascribed for example o srucural slumps (Phelps, 99) or hyseresis of unemploymen (e.g. Sigliz, 997). Neverheless, mos empirical approaches o he Phillips curve es he performance of an assumed fixed value for he NAIRU. Gordon (997) resigns from his approach and insead esimaes a ime-varying NAIRU in equaion (5), specifying i as an unobserved componen following a simple random walk (Gordon, 997, p. ): N () π = a L) π b L U U c L z e wih e IID (, σ² e ) ( )( ) ( ) ( N N (7) U U ν wih ν IID (, σ² ν ) = The NAIRU is allowed o vary over ime according o he sae-equaion in (7) and exiss if he sum of he a-coefficiens equals one and he sum of he b-coefficiens is significanly negaive. Thus, by using he unobserved componens approach in a saespace model of he Phillips curve, Gordon (997) employs a specific economeric echnique o esimae changes in he NAIRU over ime wihin he sysem se ou by he riangle model, hereby providing esable esimaes of hose changes. Gordon (997) finds for he US in he ime-period 955(q) 99(q) ha he NAIRU or long-run Phillips curve has varied significanly beween 5.3% and.5%, conrary o he exbook assumpion of a consan NAIRU a % for he US afer 97. In a recen paper, Harvey (7) uses he unobserved componen approach o model a hybrid NKPC, where lagged inflaion π - is subsiued for a random walk µ * : * * * () π γ ) µ γe ( π ) β x ε wih ε * IID (, σ² ε* ), = ( (9) µ = µ η wih η * IID (, σ² η* ), * * * where γ and x represens he oupu gap in period. Since inflaion π is mos commonly found o be inegraed of order one, bu he oupu gap x is saionary by consrucion, he unobserved componen µ * capures he long-run forecas of π and can hus be regarded as a measure of core inflaion. Harvey (7) hen shows ha in seady-sae, a reduced form of () can be derived as Saiger/Sock/Wason (997) use a similar model o esimae a ime-varying NAIRU for he US over he ime period 9(q) 99(q). However, hey solve he model o include he NAIRU in he consan erm, which is hen esimaed wih a flexible polynomial ( spline ). The auhors find esimaes of he NAIRU or long-run Phillips curve in a 95% confidence inerval beween 5% and.5%.

10 j () π ~ * * = µ γβ γ E ( x j ) β x ~ ε wih ~ ε IID (, j= σ ~ε ), () ~ µ = ~ µ ~ η wih ~ η IID (, σ ). ~η However, assuming ha x is driven by an AR() process wih roo φ <, equaion () becomes: * β () π = ~ µ x ~ ε. φγ The model of he hybrid NKPC hus revers back o a simple Phillips curve wihou expecaions or dynamics and idenificaion of γ is no possible unless he oupu gap follows a higher order AR(p) process wih p. The unobserved componen µ ~ capures boh core inflaion and inflaion expecaions, making a direc inerpreaion difficul. 3. Model and Mehodology The model used in his paper combines he hybrid NKPC as developed by Galí and Gerler (999) and he unobserved componens approaches by Gordon (997) and Harvey (7). The hybrid NKPC is chosen as he baseline model because i has become he mos widely used model of he Phillips curve in recen years and incorporaes boh nominal rigidiies in he form of sicky prices and inflaion ineria which migh be due o some form of sicky informaion. Neverheless, as in he original model developed by Friedman (9) and Phelps (9), he assumpion of a verical long-run Phillips curve a he NAIRU, hence no long-run rade-off, is reained, bu he NAIRU may vary over ime if srucural characerisics of he labour and commodiy markes change. I hus seems o be a good saring poin for he analysis of he relaionship beween he shor-run New Keynesian Phillips curve and he NAIRU over ime. As in Gordon (997), he NAIRU is modelled direcly by subsiuing he oupu gap for he unemploymen gap and modelling he ime-varying NAIRU as an unobserved componen in a sae-space represenaion. In order o ensure ha he unobserved componen measures he ime-varying NAIRU and o avoid he idenificaion problem in Harvey (7), we include survey measures of inflaion expecaions direcly in he model. This gives he following model of he ime-varying 9

11 NAIRU in a hybrid NKPC seing, aking full accoun of sicky prices and inflaion ineria: survey N (3) π απ α) E ( π ) β ( U U ε wih ε IID (, σ² ε ) () N N U U ν wih ν IID (, σ² ν ), where < α <. By allowing he naural rae of unemploymen, or NAIRU, o vary over ime according o he sae equaion in (), we can esimae changes in equilibrium unemploymen wihin he sysem of he hybrid NKPC, conrolling for he inerdependencies beween inflaion, inflaion expecaions and unemploymen. Thus, raher han assuming a fixed value of he NAIRU and esing is empirical performance, his approach provides economerically esable esimaes of srucural changes in he NAIRU over ime. = ( ) = The sae-space model of he hybrid NKPC presened in equaion (3) has a number of advanages over oher specificaions and esimaion mehods found in he lieraure: Our model in equaions (3) and () avoids he possible weak idenificaion bias of GMM esimaions of he hybrid NKPC described above by using independen survey measures of inflaion expecaions insead of IV procedures using furher lags of inflaion as insrumens. Thus, survey measures of household s inflaion expecaions provide raw daa ha does no depend on any underlying economeric mehodology. A furher advanage of he model given in equaions (3) and () is ha i allows he ime-varying NAIRU o be esimaed wihin he sysem se ou by he hybrid NKPC. The inerdependencies beween inflaion, inflaion expecaions and unemploymen are used o deermine seady-sae unemploymen over ime as given by he sae-variable U N. The sysems approach hus provides esimaes of he ime-varying NAIRU ha are grounded in macroeconomic heory raher han mechanically obained as HP-filered seady-sae measures, such as usually applied in DSGE models (Dees e al., ). Finally, he esimaes of he unobserved componen of he ime-varying NAIRU can be compared o mechanically derived seady-saes measures of unemploymen, such as HP-filered rend unemploymen. Furhermore, he significance of he resricion

12 imposed on he coefficiens of lagged and expeced inflaion in (3) ( α β = α ( α) = ) can be esed wihin he model. Overall, he sae-space represenaion of he hybrid NKPC avoids idenificaion problems of GMM approaches and provides a flexible and esable esimaion mehod boh for he sandard shor-run hybrid NKPC and he ime-varying NAIRU.. Empirical Resuls Descripion of he Daa The model of he hybrid NKPC presened above was esimaed for he US for he ime period 9(q) o 7(q3), for he UK and Ialy for he ime period 95(q) o 7(q3) and for Spain for he period 9(q3) o 7(q3). The shorer esimaion period for he European counries was due o shorer ime series of survey daa of household s inflaion expecaions. We used quarerly daa for consumer prices, he unemploymen rae and inflaion expecaions. Daa for he consumer price index (CPI) for all iems and he sandardised unemploymen rae were aken from he OECD Main Economic Indicaors (MEI) (OECD, ) daabase. The inflaion rae was hen calculaed as he annual growh rae of he CPI. Survey measures of households inflaion expecaions in he Unied Saes were provided by he Universiy of Michigan s Surveys of Consumers (SCA), while for he European economies in our sample we employed survey daa from he Consumer Survey of he Join Harmonised EU Programme of Business and Consumer Surveys direced by he European Commission. 7 While he Michigan Survey asks direcly for a quaniaive esimae of expeced inflaion, he EC Survey uses a qualiaive measure of inflaion expecaions, asking inerviewees abou he direcion of he expeced price movemen, raher han a specific poin esimae. In order o derive a quaniaive ime series of inflaion expecaions, he qualiaive answers were convered wih he probabiliy mehod of Carlson and Parkin (975), scaling inflaion expecaions wih one-period lagged inflaion, recursive mean inflaion unil las period, recursively HP- 7 Alhough he surveys are conduced by counry-specific insiues, he quesionnaire and iming of he survey are idenical across European counries and sample sizes are similar, so ha he daa are consisen over ime and across counries. Papers using he EC Consumer Survey daa include Nielsen (3) and Döpke e al. ().

13 filered inflaion and he recursively fied values obained from an ARMA(,)-model of inflaion ha were also filered wih an HP-filer as in Döpke e al. (). Figure : Inflaion and expeced inflaion for he US CPI inflaion expeced inflaion Source: OECD and SCA daa, own calculaions and graphs. As can be seen from Figure, households inflaion expecaions mach acual inflaion for he US relaively well, especially during he oil price shocks of he 7s and s. Afer a period of overshooing during he 9s, inflaion expecaions seem o have sabilised a around 3 % since he beginning of he new millennium in line wih acual inflaion. Figure presens he resuling ime series of expeced inflaion for he UK, Ialy and Spain. The graph for he UK also shows he ime series of expeced inflaion of he Inflaion Aiudes Survey by he Bank of England for he ime period 999(q) 7(q3). The ime series of expeced inflaion derived wih he probabiliy mehod are generally quie close for he hree counries analysed here: Deails of boh surveys and on he probabiliy mehod o exrac a quaniaive measure of inflaion expecaions from he qualiaive survey of he EC are given in Appendix.

14 Figure : Inflaion and Expeced Inflaion for he UK, Ialy and Spain 9 UK 9 Ialy CPI inflaion exp inflaion ARMA exp inflaion BoE exp inflaion HP exp inflaion mean exp inflaion lagged infl CPI inflaion exp inflaion ARMA exp inflaion HP exp inflaion mean exp inflaion lagged infl Spain CPI inflaion exp inflaion ARMA exp inflaion HP exp inflaion mean exp inflaion lagged infl Source: OECD, BoE and EC Consumer Survey daa, own calculaions and graphs. Time series of expeced inflaion for he UK fi acual inflaion relaively closely, only expecaions scaled wih recursive mean inflaion overshoo from 99 onwards, bu converge owards acual inflaion raes owards he end of he sample period. Furhermore, hey are found very close o he series of expeced inflaion published by he Bank of England. Inflaion expecaions in Ialy mach acual inflaion raes quie closely unil 995; hereafer inflaion expecaions scaled wih recursive mean inflaion overshoo acual inflaion raes unil. This maches he observaion by several sudies ha inflaion was severely overesimaed during he ime of he Euro inroducion. 9 The remaining ime series of expeced inflaion for Ialy are below acual 9 See Malgarini () for a summary of sudies on Ialian inflaion expecaions. 3

15 inflaion afer. In Spain, inflaion expecaions seem o have generally underesimaed acual inflaion up unil he mid-9s. Afer a considerable drop in inflaion raes, expeced inflaion raes approach acual raes in he second half of he sample period. To discriminae more formally beween he differen series of inflaion expecaions derived from he probabiliy mehod, we calculaed he roo mean squared error (RMSE) of he inflaion expecaions series wih respec o acual inflaion four quarer ahead: (5) RMSE = n i= ( π π e ) n The RMSE hus gives a measure of forecasing accuracy of inflaion expecaions. Table presens values of he RMSE for differen scaling facors of expeced inflaion for he UK, Ialy and Spain. < Table here > The lowes forecasing error is achieved wih he HP-filered fied values for inflaion from he ARMA-model (infl_exp_arma) in all hree counries under invesigaion here, alhough RMSEs of expeced inflaion wih oher scaling facors are quie close in he case of Ialy and Spain. We hus decided o use infl_exp_arma in our model of he hybrid NKPC. Tesing for Uni Roos Before we carried ou any esimaions, all ime series in he model were esed for uni roos wih he augmened Dickey-Fuller es (ADF es, Dickey and Fuller, 9). Inflaion and is expecaions seem o be non-saionary in all he counries under invesigaion here (Table A in he Appendix). In he case of he US for he sample 9(q) 7(q), his migh be due o a srucural break in inflaion afer he oil price shocks, when inflaion raes in he US were sabilised subsanially. Inflaion raes of he European counries for he shorer sample from 9(q) 7(q3) seem o have sabilised afer he urbulences of he ERM currency crisis While he unemploymen rae for he US was found o be saionary, he ADF ess could no

16 rejec he null of a uni roo for he UK, Ialy and Spain. This migh be due o he significan fall in unemploymen raes in he European counries from he mid-9s onwards. As menioned by Fanelli (7), mos empirical sudies on he hybrid NKPC fail o acknowledge he non-saionariy of inflaion and inflaion expecaions. The auhor argues ha non-saionariy may originae from he aggregaion of secoral and regional/naional Phillips curves, wih saionary variables a he firm level as assumed in heory. To rule ou spurious resuls, we esimaed simple OLS models of he hybrid NKPC wih HP-filer derived oupu and unemploymen gaps and esed he residuals for saionariy using special criical values from MacKinnon (99). For all he models, residuals were saionary a he % level, suggesing coinegraion of he variables. Sae-Space Models of he Time-Varying NAIRU The sae-space model of he hybrid NKPC presened in equaions (3) and () was esimaed in wo differen models: In he firs specificaion, he coefficiens of lagged inflaion and expeced inflaion were esimaed freely, while in he second specificaion hey were resriced o sum o exacly one. We hen exraced esimaes of he imevarying NAIRU wih he Kalman filer (Kalman, 9). This enabled us o es for he significance of he resricionα β = on he coefficiens of lagged and expeced inflaion and compare he esimaes of he ime-varying NAIRU from he wo models. In order o enable convergence, he variances of he observaion equaion and he sae equaion had o be resriced. Variances of he observaion equaion vary wih each model, bu he variance of he sae equaion was se uniformly o σ² v =. in accordance wih Gordon (997). To provide saring values for he ieraions, he esimaion periods were shorened, usually by quarers. Fi of he Models The esimaed coefficiens of he observaion equaion for boh he resriced and he unresriced model for he US, he UK, Ialy and Spain are given in Tables A A9 in he Appendix. Surprisingly, in conras o he resuls of Galí and Gerler (999), Galí e al. (, 3, 5) and Sbordone (, 5), we find ha he coefficien on We omi he resuls from he OLS models for reasons of space limiaion, bu hey can be obained from he auhor upon reques. 5

17 lagged inflaion is larger han ha on expeced inflaion for all counries in our sample, wih he noable excepion of Spain. The reason for his finding migh be he differen esimaion mehod employed here, where we use survey measures of inflaion expecaions insead of insrumens and he differen specificaion wih he unemploymen gap insead of real marginal cos. The unemploymen gap generally eners he hybrid NKPC wih a highly significan coefficien. For he US and he UK, he coefficien is negaively signed, as expeced, bu for Ialy and Spain we find a significanly posiive coefficien. This migh be due o he esimaion period used here, where a simulaneous drop in boh inflaion and unemploymen occurred in he wo counries in he laer half of he sample period. This was caused by moneary policies aimed a joining he EMU as well as labour marke reforms and a boom ha boosed employmen in Ialy and Spain. Figure 3: Unemploymen and Inflaion in Ialy and Spain Ialy Spain Unemploymen rae Inflaion rae Unemploymen rae Inflaion rae Source: OECD daa, own calculaions and graphs. Neverheless, a Phillips curve relaion beween inflaion and unemploymen is sill visible a leas in he firs half of he sample period (Figure 3). In order o check for misspecificaion, we esed he residuals of all models for normaliy and saionariy. The ADF es rejeced he null of a uni roo for he residuals a he % level for all models, whereas he Anderson-Darling es for normaliy (Anderson and Darling, 95, 95) could no rejec he null of a normal disribuion for all models excep hose for he UK, where wo large ouliers (99/99) disored he oucome.

18 Fied values of he unresriced and he resriced model (where coefficiens on lagged and expeced inflaion were resriced o sum o one), as well as he residuals, are ploed in Figures and 5, respecively. Figure : Fied Values from he Unresriced Model of he Hybrid NKPC US 5 UK Infl Infl_fied /- s.e. residuals Infl Infl_fied /- s.e. residuals Ialy Spain Infl Infl_fied /- s.e. residuals Infl Infl_fied /- s.e. residuals Source: OECD, EC Consumer Survey and SCA daa, own esimaions, own graphs. In mos of he counries under invesigaion here, fied values from he unresriced and he resriced model differ only marginally, and he fi of he model generally seems very close wih respec o acual inflaion raes. Only in he case of he US i seems ha he fi from he unresriced model is igher, wih excepionally low sandard errors. Neverheless, fied values from he resriced model for he US sill fi acual inflaion raes very closely. As indicaed by he ess for saionariy and normaliy, he residuals ploed in Figures and 5 generally seem o follow whie noise processes around mean zero. 7

19 Figure 5: Fied Values from he Resriced Model of he Hybrid NKPC US UK Infl Infl_fied /- s.e. residuals Infl Infl_fied /- s.e. residuals.... Ialy Spain Infl Infl_fied /- s.e. residuals Infl Infl_fied /- s.e. residuals Source: OECD, EC Consumer Survey and SCA daa, own esimaions, own graphs. Time-varying NAIRU Esimaes From he sae-space model of he hybrid NKPC as in equaions (3) and () we derived smoohed esimaes of he ime-varying NAIRU wih he Kalman filer. Figure presens he ime-varying NAIRU esimaes for he US, he UK, Ialy and Spain from he unresriced model.

20 Figure : Time-Varying NAIRUs from he Unresriced Model US UK SV /- s.e. Unemploymen rae SV /- s.e. Unemploymen rae Ialy Spain SV /- s.e. Unemploymen rae SV /- s.e. Unemploymen rae Source: OECD, EC Consumer Survey and SCA daa, own esimaions, own graphs. Generally, unresriced NAIRU esimaes for he four counries under invesigaion here show considerable variaion, usually in line wih acual unemploymen raes, wih he noable excepion of he UK, where NAIRU poin esimaes seem relaively sable. For he US and he UK, he unresriced model yields raher implausible values of he NAIRU, suggesing ha unemploymen was significanly above is naural rae in he US over he whole esimaion period, albei wih very large confidence bands. By conras, NAIRU esimaes for Spain show a igh confidence band and are found close o acual unemploymen raes, implying ha unemploymen was above is naural rae only a he peak in 99/95 and below in. A similar resul applies for Ialy, wih a 9

21 NAIRU close o acual unemploymen from 99 onwards, and unemploymen below is naural rae from 99 o 99. Figure 7: Time-Varying NAIRUs from he Resriced Model US UK SV /- s.e. Unemploymen rae SV /- s.e. Unemploymen rae Ialy Spain SV /- s.e. Unemploymen rae SV /- s.e. Unemploymen rae Source: OECD, EC Consumer Survey and SCA daa, own esimaions, own graphs. Conrasing ime-varying esimaes of he NAIRU from he resriced models wih hose from he unresriced model, he improvemen in significance and variaion of he NAIRU is remarkable. Especially for he US and he UK we now find highly significan NAIRU esimaes wih low sandard errors close o acual unemploymen raes. While we find for he UK ha unemploymen was below he naural rae only in and in he las years of he sample period, in he US unemploymen seems o flucuae around he NAIRU, wih he NAIRU leading acual unemploymen during he period of

22 oil price shocks in he 7s and s. In he case of Ialy, he picure seems mosly unchanged compared o he unresriced model, wih being he only years where confidence bands of he NAIRU are above acual unemploymen. For Spain, he fi of he ime-varying NAIRU is again remarkable, bu we now find ha unemploymen was above is naural rae for mos of he sample period. Comparison of he Models Finally, we compare he Kalman-filered smoohed esimaes of he ime-varying NAIRU from he unresriced and he resriced model of he hybrid NKPC o each oher and o a mechanically calculaed NAIRU derived wih he HP-filer, shown in Figure. Figure : Comparison of NAIRU Esimaes US UK Unemploymen rae HP-filered NAIRU NAIRU unresriced model NAIRU resriced model Unemploymen rae HP-filered NAIRU NAIRU unresriced model NAIRU resriced model 3 Ialy Spain Unemploymen rae HP-filered NAIRU NAIRU unresriced model NAIRU resriced model Unemploymen rae HP-filered NAIRU NAIRU unresriced model NAIRU resriced model Source: OECD, EC Consumer Survey and SCA daa, own esimaions, own graphs.

23 Overall, we find hree main resuls: Firs, as already noed above, NAIRU esimaes from he resriced model of he hybrid NKPC generally seem more plausible in relaion o acual unemploymen and in he case of he US and he UK yield significanly differen esimaes. Second, all NAIRU esimaes derived from he sae-space models are significanly differen from he mechanically derived HP-filered NAIRUs, suggesing ha esimaing he NAIRU in a heoreically grounded macroeconomic model, aking accoun of he ineracion of inflaion, inflaion expecaions and he unemploymen gap, yields significan new insighs. Third, all NAIRU esimaes from he sae-space models of he hybrid NKPC imply a drop in naural unemploymen raes in he second half of he 9s, which in he case of Ialy exends unil he end of he esimaion period. For he US, Ialy and Spain, he drop in naural unemploymen raes is even more pronounced han he fall in acual unemploymen raes, suggesing ha unemploymen remained above is naural value in his period. As noed above, in he case of he US and he UK he unresriced model gives implausibly low values of he NAIRU, suggesing ha acual unemploymen was always significanly above is naural value. These resuls are no in line wih hose found in he lieraure for he US (e.g. Gordon, 997, and Saiger e al., 997). By conras, ime-varying esimaes of he NAIRU from he resriced model imply a mean naural unemploymen of 5.5% (7.5%) for he US (UK), close o acual mean unemploymen of 5.% (7.37%). Noe ha average naural unemploymen is sill esimaed o be lower han average acual unemploymen. For Ialy, esimaes of he NAIRU from he sae-space models differ mosly in he firs half of he sample period, where he NAIRU implied by he resriced model is lower. Overall, he resriced NAIRU (9.3%) has a mean closer o average acual unemploymen raes in Ialy (9.39%) han he unresriced NAIRU (.%). By conras, in he case of Spain he ime-varying NAIRU from he unresriced model (mean: 3.3%) seems o be closer o acual unemploymen (mean: 3.9%) han he ime-varying NAIRU from he resriced model (mean:.%). In order o discriminae more formally beween he unresriced and he resriced model of he hybrid NKPC, we analysed he informaion crieria and conduced a Wald es on This resul is in line wih hose in Gordon (997) and Saiger e al. (997) for he US.

24 he resricion α β =. Furhermore, since he unresriced model encompasses he resriced one, we could run a likelihood raio es according o he formula () [(θ) - (θ*)] ²(m), where (θ) is he log likelihood of he unresriced model, (θ*) he log likelihood of he resriced model and m he number of resricions, which here equals one. The informaion crieria of he models are found in Tables A A9 in he Appendix, and es values for he Wald es and he likelihood raio es are shown in Table. < Table here > Generally, coefficiens on lagged and expeced inflaion summed closely o one in all he unresriced models of he hybrid NKPC, so ha he Wald es could no rejec he null hypohesis of he resricion α β = in all counries excep for he US. However, he informaion crieria and he likelihood raio es are less conclusive: While boh also favour he resriced model in he case of Ialy; for he US, he UK and Spain informaion crieria are smaller for he unresriced model and he likelihood raio es rejecs he null of he validiy of he resricion. In he case of he UK his migh be due o he non-normaliy of he residuals which violae a condiion for a valid likelihood raio es. Judging from he very igh fi of he model for he US, i migh be he case ha he unresriced sae-space model assigns oo much of he variabiliy in he daa o he coefficiens of he model, leading o he implausible esimae of he NAIRU. Finally, in he case of Spain, esimaes of he NAIRU from boh models are very close so ha he resricion migh no be necessary. 5. Conclusion Mos models of he Phillips curve assume ha here is no long-run rade-off beween inflaion and unemploymen or oupu due o raional expecaions of agens and ha he long-run Phillips curve is hence verical a he naural rae of unemploymen or NAIRU. Pioneered by Friedman (9) and Phelps (9), his concep is by now well acceped and embodied in he mos commonly used model of he Phillips curve, he hybrid New Keynesian Phillips curve (NKPC) derived by Galí and Gerler (999). See Hamilon (99). 3

25 Inroducing addiional rigidiies such as informaion sickiness (Mankiw and Reis,, a, b) yields a much slower adjusmen process of expecaions, more ineria in inflaion and, hus, a longer-lived rade-off beween inflaion and unemploymen. We esimaed he shifs in he naural rae of unemploymen or NAIRU as an unobserved componen in a sae-space model of he hybrid NKPC, combining approaches of Gordon (997) and Harvey (7). Using direc survey daa for inflaion expecaions from he Universiy of Michigan s Surveys of Consumers and he EC Consumer Survey o avoid he problems of weak insrumen bias ofen encounered in sandard GMM approaches, he model was esimaed for he US, he UK, Ialy and Spain. Boh he models for he US and he UK showed a significan shor-run rade-off beween inflaion and oupu or unemploymen, whereas in he case of Ialy and Spain, we found a significanly posiive coefficien. Neverheless, in he firs par of he esimaion period, a Phillips curve relaion beween inflaion and unemploymen is also visible in he laer wo counries. As expeced, coefficiens on lagged and expeced inflaion summed closely o one in all he counries and he resricion α β = could no be rejeced excep in he model for he US. The Kalman-filered smoohed esimaes of he ime-varying NAIRU all showed considerable variaion over ime, usually in line wih variaion in unemploymen raes. Comparing esimaes from an unresriced and a resriced hybrid NKPC model, esimaes from he resriced model generally gave more plausible values, alhough formal ess preferred he unresriced model for he US, he UK and Spain. Furhermore, all esimaes of he ime-varying NAIRU differed significanly from seady-sae measures of unemploymen calculaed from he HP-filer, implying ha a heory-based sysems approach yields imporan new informaion. I is hus suggesed for all counries invesigaed here ha he NAIRU has shifed considerably wih he business cycle and economic shocks during he esimaion period, wih acual unemploymen raes flucuaing around heir naural rae. This has imporan implicaions for moneary policy, since inflaion argeing and sabilisaion will be he more accurae, he beer he knowledge of he NAIRU a any given poin in ime. Sill furher quesions remain for fuure research: Wha is he direcion of causaliy beween changes in unemploymen and changes in he NAIRU is i unemploymen

26 ha coninually adjuss o a changing naural unemploymen rae or is he opposie he case? And how do changes in he NAIRU feed back ino unemploymen and inflaion?. Bibliography Adam, K. and Padula, M. (3): Inflaion dynamics and subjecive expecaions in he Unied Saes, in: ECB Working Paper Series, Working paper no.. Anderson, T. W. and Darling, D. A. (95): Asympoic Theory of Cerain Goodness of Fi Crieria Based on Sochasic Processes, in: Annals of Mahemaical Saisics, vol. 3, no., pp Anderson, T. W. and Darling, D. A. (95): A Tes of Goodness of Fi, in: Journal of he American Saisical Associaion, vol. 9, no., pp Bank of England (): Inflaion Aiudes Survey, hp:// Bachelor, R.A. and Orr, A.B. (9): Inflaion Expecaions Revisied, in: Economica, vol. 5, no. 9, pp Baini, N.; Jackson, B. and Nickell, S. (5): An open-economy new Keynesian Phillips curve for he U.K., in: Journal of Moneary Economics, vol. 5, no., pp. 7. Berola, G. and Garibaldi, P. (3): The Srucure and Hisory of Ialian Unemploymen, in: CESifo Working Paper Series, Caegory : Labour Markes, Working paper no. 97. Bjørnsad, R. and Nymoen, R. (): The New Keynesian Phillips curve esed on OECD panel daa, in: Economics Discussion Papers, Discussion Paper. Calvo, G. (93): Saggered Prices in a Uiliy-Maximizing Framework, in: Journal of Moneary Economics, vol., no. 3, pp Carlson, J.A. and Parkin, M. (975): Inflaion Expecaions, in: Economica, vol., no., pp

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28 Fuhrer, J. and Moore, G. (995): Inflaion Persisence, in: The Quarerly Journal of Economics, vol., no., pp Galí, J. and Gerler, M. (999): Inflaion dynamics: a srucural economeric analysis, in: Journal of Moneary Economics, vol., no., pp. 95. Galí, J.; Gerler, M. and Lopez-Salido, J.D. (): European Inflaion Dynamics, in: European Economic Review, vol. 5, no. 7, pp Galí, J.; Gerler, M. and Lopez-Salido, J.D. (3): Erraum o European Inflaion Dynamics, in: European Economic Review, vol. 7, no., pp Galí, J.; Gerler, M. and Lopez-Salido, J.D. (5): Robusness of he Esimaes of he Hybrid New Keynesian Phillips Curve, in: Journal of Moneary Economics, vol. 5, no., pp. 7. Gordon, R.J. (997): The Time-Varying NAIRU and is Implicaions for Economic Policy, in: Journal of Economic Perspecives, vol., no., pp. 3. Hamilon, J.D. (99): Time Series Analysis, Princeon Universiy Press, Princeon, New Jersey. Harvey, A. (7): Modeling he Phillips curve wih unobserved componens, Working paper, Faculy of Economics, Cambridge Universiy. Kalman, R.E. (9): A new approach o linear filering and predicion problems, in: Journal of Basic Engineering, Transacions ASMA, Series D, vol., March, pp Kurmann, A. (5): Quanifying he uncerainy abou he fi of a new Keynesian pricing model, in: Journal of Moneary Economics, vol. 5, no., pp Lindé, J. (5): Esimaing New-Keynesian Phillips curves: A full informaion maximum likelihood approach, in: Journal of Moneary Economics, vol. 5, no., pp

29 MacKinnon, J.G. (99): Criical Values for Co-Inegraion Tess, in: Engle, R.F. and Granger, C.W.J. (eds., 99): Long-Run Economic Relaionships, Oxford Universiy Press, Oxford, pp MacKinnon, J.G. (99): Numerical Disribuion Funcions for Uni Roo and Coinegraion Tess, in: Journal of Applied Economerics, vol., no., pp. -. Malgarini, M. (): Quaniaive Inflaion Percepions and Expecaions of Ialian Consumers, in: ISAE Working Papers Series, Working paper no. 9. Mankiw, N.G. and Reis, R. (): Sicky Informaion: A Model of Moneary Nonneuraliy and Srucural Slumps, in: NBER Working Paper Series, Working Paper. Mankiw, N.G. and Reis, R. (a): Sicky Informaion versus Sicky Prices: A Proposal o Replace he New Keynesian Phillips Curve, in: The Quarerly Journal of Economics, vol. 7, no., pp Mankiw, N.G. and Reis, R. (b): Wha Measure of Inflaion Should a Cenral Bank Targe?, in: NBER Working Paper Series, Working Paper Nason, J.M. and Smih, G.W. (5): Idenifying he New Keynesian Phillips Curve, in: Federal Reserve Bank of Alana Working Paper Series, Working paper no.. Nielsen, H. (3): Inflaion Expecaions in he EU Resuls from Survey Daa, Discussion Paper No. 3, Sonderforschungsbereich 373, Humbold Universiä zu Berlin. OECD (): Main Economic Indicaors, obained via EcoWin. Paloviia, M. (): Comparing alernaive Phillips curve specificaions: European Resuls wih survey-based expecaions, in: Applied Economics, vol., no. 7, p Phelps, E.S. (9): Money-Wage Dynamics and Labor-Marke Equilibrium, in: The Journal of Poliical Economy, vol. 7, no., pp. 7 7.

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31 7. Appendix Appendix : Survey Daa of Expeced Inflaion and he Probabiliy Mehod The SCA of he Universiy of Michigan asks inerviewees specifically abou heir inflaion expecaions over he nex monhs: By abou wha percen do you expec prices o go (up/down), on he average, during he nex monhs? 3 The Survey hence provides a direc quaniaive measure of annual inflaion expecaions, which is published online on a quarerly basis from 9(q) 7(q3). Survey measures of household s inflaion expecaions for he European counries in his paper are provided by he Consumer Survey of he European Commission (EC, ), which is inegraed ino he Join Harmonised EU Programme of Business and Consumer Surveys. Daa on households inflaion expecaions are available from January 95 onwards, in he case of Spain from June 9 onwards. Unforunaely, he EC Consumer Survey only provides a qualiaive measure of households inflaion expecaions insead of asking for a quaniaive esimae of expeced inflaion as in he Michigan Survey. Inerviewees are asked in quesion of he Consumer Survey: By comparison wih he pas monhs, how do you expec ha consumer prices will develop in he nex monhs? They will... increase more rapidly increase a he same rae = increase a a slower rae - say abou he same -- fall The EC Consumer Survey on households inflaion expecaions is hus a penachoomous qualiaive survey, which needs o be ransformed in order o recover a quaniaive ime series of expeced inflaion. 3 See Universiy of Michigan (b): Survey Descripion, p. 5, hp:// See European Commission (7), p., hp://ec.europa.eu/economy_finance/indicaors/business_consumer_surveys/userguide_en.pdf. 3