Measuring the UK Short-Run NAIRU

Transcription

1 p Exernal UNIT ime Discussion Paper No.12 Measuring he UK Shor-Run NAIRU by Nicolea Baini and Jennifer Greenslade

2 Exernal MPC Uni Discussion Paper No. 12* Measuring he UK Shor-Run NAIRU By Nicolea Baini and Jennifer Greenslade April 2003 ISSN: Copyrigh Bank of England 2003 (*) Disclaimer: These Discussion Papers repor on research carried ou by, or under supervision of he Exernal Members of he Moneary Policy Commiee and heir dedicaed economic saff. Papers are made available as soon as pracicable in order o share research and simulae furher discussion of key policy issues. However, he views expressed are hose of he auhors and do no represen he views of he Bank of England or necessarily he views of Exernal Members of he Moneary Policy Commiee.

3 Measuring he UK Shor-Run NAIRU 1 April 2003 Absrac This paper derives alernaive measures of he shor-run NAIRU (SRN) for he UK, he rae for unemploymen a which inflaion will neiher increase nor decrease in he shor-run. We esimae he NAIRU joinly wih price equaions by using he Kalman filer. Our work suggess ha boh srucural changes in he labour marke and favourable supply shocks may have had a beneficial impac on RPIX inflaion over he las few years. We show ha deviaions of unemploymen from he shor-run NAIRU measures prove helpful in predicing inflaion and we demonsrae heir usefulness in Taylor-ype policy rules for he ineres rae. JEL classificaion: E24, E31, E50 Keywords: equilibrium unemploymen, ime-varying NAIRU, shor-run NAIRU, Phillips curve, supply shocks (1) We hank Seve Nickell for many helpful commens and suggesions on his paper as i progressed and Kae Barker, Marian Bell and seminar paricipans a he Bank of England for commens on an earlier draf. 1

4 Lis of Conens Absrac 1. Inroducion 2. Three alernaive measures of he shor-run NAIRU (SRN) 2.1 Mehodology 2.2 SRNs compared SRN based on a quasi-consan longer-run NAIRU (LRN) SRNs based on ime varying LRNs 3. The informaion conen of he unemploymen/srn gaps in predicing inflaion Applicaions 4.1 Alernaive supply shock scenarios 4.2 Taylor rules based on shor-run NAIRU gaps Conclusions References Daa Appendix 2

5 1. Inroducion The second half of he 1990s and he early 2000s has been a period of remarkably low levels of unemploymen wihou subsanial wage and price inflaion in he UK. This phenomenon is rue also of he US, where inflaion did no rise despie he fall in unemploymen below levels ha were believed o be compaible wih sable inflaion. Chars 1a and 1b below emphasise his poin by showing he benign profile of GDP deflaor inflaion (as well as RPIX and PCE inflaion for he UK and he US, respecively) and unemploymen in he UK and he US since Char 1a: UK Inflaion and Unemploymen Char 1b: US Inflaion and Unemploymen Level Percenage change on a year earlier Level Percenage change on a year earlier li RPIX (rhs) GDP deflaor (rhs) LFS unemploymen rae (lhs) PCE deflaor (rhs) GDP deflaor (rhs) Unemploymen rae (lhs) One of he explanaions for his happy sae of affairs is ha in boh counries he NAIRU has fallen in recen years (see Cassino and Thornon (2002), Driver, Greenslade and Pierse (2003), Greenslade, Pierse and Saleheen (2003) for he UK. For he US see, among ohers, Saiger e al (1997a, 1997b), Gordon (1997, 1998), Sock (1998), Sock and Wason (1998), Kaz and Krueger (1999), and Ball and Moffi (2001)). Oher explanaions include he success of moneary policy in boh counries o anchor inflaion expecaions; or he incidence of a series of favourable supply shocks, noably, exchange rae appreciaions in boh counries which have driven down he cos o firms of inermediae impored goods and boosed workers real consumpion wages; and a shif owards a more rapid rae of produciviy growh in he US which has offse he inflaionary impac of rising wage demands in he face of falling unemploymen. 3

6 In his paper we invesigae furher wo of hese explanaions for he low inflaion-low unemploymen oucomes in he UK case, namely, shifs in he unemploymen level associaed wih sable inflaion and he impac of shocks o inflaion. For his purpose we derive alernaive measures of he shor-run or effecive NAIRU (SRN). This is a reference rae for unemploymen ha reflecs inflaionary pressures over a shor-run horizon. I can be hough of as he rae for unemploymen a which inflaion will neiher increase nor decrease in he shor-run, aking accoun no jus of shifs in he longer-run NAIRU (LRN) i.e. he rae of unemploymen consisen wih seady sae inflaion when he economy has fully adjused o any shock or when here are no shocks bu also of emporary supply side shocks, like shorrun shocks o oil prices or impor prices. 1 Over he policy horizon ha maers for moneary policy, inflaion is influenced by changes in inflaion expecaions and shocks o labour and/or oher inpu cos variables in addiion o shifs in he gap beween unemploymen and he longer-run NAIRU (LRN). So focussing on deviaions of unemploymen from his shorer-run NAIRU concep may help explain why he oulook for UK inflaion has been so benign, despie hisorically low levels of unemploymen. The paper is organised as follows. Secion 2 derives measures of he shor-run NAIRU by esimaing hree differen models of price dynamics on UK daa. The firs assumes a quasiconsan longer-run NAIRU, while he oher wo allow i o be ime-varying. In all cases we esimae he longer-run NAIRU joinly wih he price equaions by using he Kalman filer. 2 In secion 3 we examine he informaion conen of he unemploymen/srn gaps we have derived in predicing inflaion and analyse he role of recen supply side shocks in explaining he presen low inflaion-low unemploymen environmen in he UK. The informaion conen of our measures of he shor-erm unemploymen gap, as well as heir performance as feedback variable in policy rules à la Taylor is examined in secion 4. Finally secion 5 discusses policy implicaions and offers some concluding remarks. A Daa Appendix describes he daa ha we have used hroughou he paper. 2. Three alernaive measures of shor-run NAIRU As firs discussed by Friedman (1968) and Phelps (1968), in he long run he relaionship beween inflaion and unemploymen is verical a he equilibrium or naural rae of unemploymen, ha is, here is no long-run rade-off beween inflaion and unemploymen. 1 Oher emporary supply shock variables include shor-run shocks o produciviy and axes. 2 See Kalman (1960) and Kalman and Bucy (1961). 4

7 This is because in he long run, expecaions of wages and prices are fully realised by he associaed rae of inflaion. In such circumsances, any fiscal or moneary simulus aimed a moving he economy o a lower rae of unemploymen is unsuccessful, as i ends up increasing expecaions and hence pushing up prices and wages, which ulimaely shifs he unemploymen rae back o he naural rae he long-run dichoomy proposiion. In pracice, he naural rae is deermined by he inersecion of labour supply and demand curves. So, essenially, i is driven by srucural labour marke facors. These include, for insance, shifs in he exogenous separaion rae of unemploymen, in he degree of mismach, in he level of benefis relaive o pos-ax earnings, in he marke power of wage bargainers or in he elasiciy of produc demand facing he firm. Oher facors include he effec of axes, he exen of labour marke insecuriy and ha of acive labour marke measures. 3 As hese facors end o vary slowly, he naural rae of unemploymen ypically changes only gradually over ime. When unemploymen converges o is naural rae, and here are no supply shocks, inflaion is consan. For his reason he naural rae of unemploymen is also referred o in he lieraure as he Non-Acceleraing Inflaion Rae of Unemploymen (NAIRU). 4 The consancy of inflaion when unemploymen is a is NAIRU level and supply shocks are absen can be illusraed by looking a a simple expecaions-augmened Phillips curve à la Gordon 5 like equaion (1) below, where inflaion is modelled as a funcion of inflaion ineria (ie backwardlooking expecaions), demand and supply shocks: ( L) 1 ( L)( u u ) ( L) z (1) * In equaion (1), denoes inflaion a ime, 6 u is he he acual unemploymen rae, z is a vecor of supply side shocks such as changes in he value of he real oil price or in he value 3 For a discussion of he deerminans of he equilibrium rae of unemploymen see, among ohers, Nickell and Layard (1999) and Coulon and Cromb (1993). 4 In pracice he NAIRU is disinc from he naural rae of unemploymen. This is because he naural rae concep capures he long-run real equilibrium deermined by he srucural characerisics of he labour and produc markes. Whereas he NAIRU is defined solely in relaion o he level of unemploymen ha is consisen wih a sable rae of inflaion and so may i be affeced by he adjusmen of he economy o pas economic shocks. As he effecs of adjusmen o shocks fade away, he NAIRU will end owards he naural rae. See Carlin and Soskice (1995: 157). 5 See Gordon (1997) and Saiger e al (1997a, 1997b). 6 In (1) i is assumed ha he inflaion rae is inegraed of order zero, so ha is saionary. If inflaion is insead assumed o be inegraed of order one, hen will be saionary. 5

8 of he relaive impor price deflaor. These have direc price effecs because hey affec direcly he price of impored inermediae and final goods. L is a polynomial in he lag operaor, and is he difference operaor. Demand shocks are capured by he deviaion of u from u * or he long-erm unemploymen gap he NAIRU u * being here he labour marke equivalen o susainable capaciy uilisaion in he goods marke. 0, which implies ha posiive unemploymen gaps (acual above NAIRU) have a deflaionary impac and vice versa. In equaion (1), inflaion expecaions are modelled as a purely backward-looking (inerial) process and so are approximaed by a disribued lag on pas inflaion. Finally, is a serially uncorrelaed disurbance. If he sum of he coefficiens (L) is equal o one, here will be a unique equilibrium or naural rae level of u *, such ha when u = u * and z = 0, inflaion will be consan. So in his conex, he NAIRU is he value of u a which boh inflaion and unemploymen are sable. We call his value of unemploymen longer-run NAIRU (LRN) o disinguish i from he concep of a shor-run NAIRU (SRN) ha we discuss below. Use of he naural rae of unemploymen o inform policy decision in pracice is complicaed on concepual and pracical grounds. Concepually, as eviden from equaion (1), i may no be sensible o aemp o sabilise inflaion by driving u o u* in every period. As he unemploymen gap is only one deerminan of inflaion, his may no be sufficien in iself o sabilise inflaion. By he same oken, i would be highly subopimal o compensae for desabilising supply shocks or ineria in inflaion by manoeuvring u above or below u*, as he unemploymen and oupu coss of doing so could be poenially huge. Imporanly, u* is he equilibrium level of unemploymen in he (very) long run and i is no obvious ha i will be a all possible o drive unemploymen owards his disan-horizon naural level so as o hi a arge for price sabiliy defined over a much shorer policy horizon. So alhough, undoubedly, knowledge abou he naural rae of unemploymen is informaive because i ells us abou he seady-sae properies of he economy, here may be some difficulies when focussing on i for pracical, day-o-day policy decisions. Empirically, he longer-run NAIRU is unobservable. However, because i is one of he deerminans of inflaion in he long run, knowledge of is level can be relevan for policy purposes, and so here have been numerous aemps o measure i boh in he UK and in he 6

9 US. Sandard ways of deriving measures of he LRN include fiing he daa o differen ypes of models. Usually hese assume ha he LRN is consan over ime; or ha i can be capured by a linear ransformaion of some sep funcion or spline; or ha i follows a sochasic random walk. In general, esimaes of he LRN end o be raher imprecise, as uncerainies abou he specificaions of he wage-price sysems or abou measuremen of srucural labour marke facors which underlie he LRN compuaion carry over o he laer. Perhaps a more ineresing concep of equilibrium for unemploymen o use in policy is ha of a shor-run NAIRU (see Braun (1984), Layard and Bean (1989), Esrella and Mishkin (1999) and Meyer (2000)). This is he unemploymen rae a which here is no endency for inflaion o rise or fall over a shor o medium erm policy horizon (one ha is consisen wih inflaion sabilisaion a ime in pracice). In his sense i can be hough of as he longer-run NAIRU adjused for supply shocks and inflaion expecaions, ie for all he deerminans of inflaion in he simple Phillips curve model oulined in equaion (1). Unsurprisingly, as many oher variables oher han he unemploymen gap drive inflaion over shorer horizons, he SRN can be quie differen from he LRN or naural rae of unemploymen, u*. And because i is a funcion of a variey of supply side shocks, he SRN will end o bounce around much more han he gradually-moving LRN, which is insead uniquely driven by srucural labour marke facors. However, inasmuch as i provides a reference rae for unemploymen ha keeps rack of he impac on inflaion of cumulaed shifs in LRN, supply shocks and expecaions, he SRN is presumably more germane for policy in pracice as i is for predicing inflaion. Of course, from an empirical poin of view, he SRN is also unobservable, so is derivaion will be subjec o uncerainies of various kinds, as in he case of he LRN. 2.1 Mehodology Below we consruc hree differen measures of he SRN for he UK. Our approach consiss of wo seps. Firs we derive an esimae of he LRN. Second we obain a measure of he SRN based on our LRN esimaes. In wha follows we describe boh seps in more deail Sep 1: Deriving he LRN Since he LRN canno be observed direcly, we follow Greenslade, Pierse and Saleheen (2003) and model i as an unobserved sochasic random walk process. We hen esimae i 7

10 joinly wih a reduced-form model of RPIX price dynamics wih quarerly UK daa from 1973 Q1 o 2001 Q4 by using he Kalman filer. In general, exracion of he LRN via mulivariae filering appears preferable o eiher use of univariae esimaes as he former allows more informaion o be encompassed han univariae mehods as well as o mehods involving esimaes of srucural wage-price sysems and his mehod side-seps various modelling problems which are encounered when esimaing a heoreical model of he NAIRU. 7 We follow a commonly used approach and esimae he model in firs differences of inflaion as his is a way of imposing dynamic homogeneiy (see for example, Saiger, Sock and Wason (1997a)). 8 The approach generally used in he Kalman filer lieraure assumes ha inflaion expecaions are implici in he inflaion dynamics, raher han being explicily idenified. Separae work suggess ha inflaion expecaions play some role in deermining inflaion in he UK, hough he evidence is no ye conclusive (see Driver, Greenslade and Pierse (2003)). I is possible ha our NAIRU esimaes are indirecly picking up any such changes (which could be relaed o changes in he UK moneary policy regime). The resuling price sysem ha we esimae is hen: ( L) 1 ( L)( u u ) ( L) z ~ N (0, 2 ) (2) * u * = u 1 * + ~ N (0, 2 ), cov(, ) = 0 (3) where, relaive o equaion (1), we now assume ha RPIX inflaion depends on is own firs lag (absracing from he unemploymen gap and supply side shocks) wih a coefficien ha we consrain o be exacly uniy o ensure long-run neuraliy plus lags of is firs difference. As explained in Greenslade, Pierse and Saleheen (2003), esimaing he LRN in conjuncion wih equaion (3) gives a measure of equilibrium unemploymen ha works bes in he reduced-form dynamic equaion for prices and so provides a quie inuiive esimae of he level of he NAIRU in he long run. Though he variabiliy of he NAIRU can in principle be esimaed from he daa, he exen o which he NAIRU can move around from quarer o quarer is usually resriced in he academic lieraure, reflecing he assumpion ha he 7 See Cassino and Thornon (2002) for a discussion of he problems wih finding UK labour marke variables necessary for modelling he LRN as a funcion of labour marke or demographic rends. 8 Dynamic homogeneiy is imporan as i ensures a meaningful NAIRU. Anoher way in which i can be imposed is o model inflaion bu impose he sum of lagged inflaion erms o be equal o one. In erms of he RPIX models considered here, he NAIRU esimaes do no appear o be very sensiive o such a choice of specificaion (see Driver, Greenslade and Pierse (2003) for deails of models esimaed using his laer approach). 8

11 NAIRU is deermined by srucural facors ha evolve gradually over ime. Obviously, he choice of his resricion (he signal-o-noise raio) is o some degree arbirary and here is no universally acceped rule as o how o impose i. The NAIRU profiles are influenced by his resricion and we shall show he sensiiviy of he NAIRU profiles o wo values for he signal-o-noise raio. 9 In his simple se-up, inflaion changes eiher because he unemploymen gap changes or because he z vecor changes or because is non-zero a ime, in oher words, a random shock pus upward or downward pressure on he growh rae of inflaion. In urn, changes in he unemploymen gap can originae from shifs in u *, he longer-run NAIRU. Assuming ha sysem (2)-(3) is Gaussian (i.e. ha, and u 0 * are normally disribued), we can evaluae is sample log-likelihood funcion via he Kalman filer and hen find he maximum likelihood esimae of he vecor of parameers (L), (L) and (L) in he sysem ogeher wih a profile for he NAIRU (u *) by using a sandard numerical opimisaion algorihm. Throughou we concenrae on smooh Kalman filer esimaes (i.e., opimal esimaors of he sae vecor given all he informaion ha is available in he sample), raher han he filered esimaor ha only uses informaion available period by period. We derive hree differen measures of he LRN by esimaing hree separae paramerisaions of sysem (2)-(3). More precisely, o derive he firs LRN measure we resric he noise-osignal raio, i.e. he raio of he variance in he longer-run NAIRU ( 2 ) relaive o he variance of changes in inflaion ( 2 ), o a very small number (0.002). 10 This implies ha he ensuing LRN is almos consan. The second NAIRU measure adops he same mehodology as above, bu imposes a signal-o-noise raio of 0.16, which implies more volaile measures of he longer-run NAIRU. This raio is more consisen wih empirical priors in he UK (see Driver, Greenslade and Pierse (2003), Greenslade, Pierse and Saleheen (2003) and Cassino and Thornon (2002) among ohers) and produces NAIRU esimaes ha are in line wih oher empirical esimaes (see Coulon and Cromb (1994)). 11 Because he choice of he noiseo-signal raio is somewha arbirary, deriving SRNs for differen values of his raio provides 9 See Greenslade, Pierse and Saleheen (2003) for a more horough discussion of his issue. 10 When we resric his raio o 0 resuls do no converge, so we op for a small non-zero number in he analysis. 11 Noe ha when he signal-o-noise raio is freely esimaed, he poin esimae is numerically larger han he resricion used hroughou his paper (0.16) bu lies wihin he confidence inerval. The resuling NAIRU esimaes show implausibly large variaion (perhaps because he model insufficienly capures supply side or expecaions shocks, paricularly in he 1970s), so we mainain he lower figure. Turner e al. (2001) also calculae shor-run NAIRU esimaes based on ime-varying esimaion echniques, hough heir LRN esimaes are even less volaile han hose repored in his paper and so are less plausible for he UK. 9

12 an idea of he sensiiviy of our resuls. Finally, he hird LRN measure also imposes a noiseo-signal raio of 0.16, bu differs from he second LRN measure because i excludes emporary supply shocks from he Phillips curve model. In oher words, his hird measure is esimaed by resricing o zero, so ha any informaion from he z vecor is subsumed in he ime-variaion of u *. Because he longer-run NAIRU esimaes from his hird measure are subjec o emporary supply shocks, hey are close concepually o esimaes of he shorer-run NAIRU alhough, as we shall see below, hese wo ses of esimaes are no idenical since he laer also include ineria in he inflaion adjusmen process. Maximum likelihood esimaes of sysem (2)-(3) for hese various specificaions are repored in Table 1 below. Table 1: Price Inflaion Phillips Curve Models esimaed using he Kalman filer, 1973Q1 2001Q4 Dependen variable RPIX RPIX RPIX (rpix) (1) (2) (3) Signal-o-noise resricion u-u* [-2.67] [-3.08] Real Impor Price Inflaion [3.09] Real Impor Price Inflaion [2.14] Real Oil Price Inflaion [1.13] [-4.59] [-4.96] 0.32 [3.43] 0.25 [2.43] 0.19 [1.89] [-4.61] [-5.21] D79/ [-5.81] [-6.72] [-6.54] LL LL is he log-likelihood, -saisics are in parenheses. To derive resuls in Table 1 we employ a general o specific esimaion mehodology. We sar wih a se of regressors including he curren value of he unemploymen gap, lagged annual RPIX inflaion erms and lagged real impor price inflaion and real oil price inflaion erms (which measure supply shocks) and es down o obain a more parsimonious represenaion. The firs row of he able shows ha changes in inflaion are negaively correlaed wih he unemploymen gap, suggesing ha when unemploymen is below he NAIRU inflaion will 10

13 rise and vice versa, subjec o addiional effecs from he ineria and supply componens in he model. 12 Real impor prices are srongly significan in model 1 (where he variance is resriced o be 0.002); by conras, in his model real oil prices are no significan a sandard levels of esing. When we increase he value of he noise-o-signal raio o 0.16 (model 2), real oil prices are however significan a he 90% level of esing. The final column of Table 1 shows wha happens when we exclude supply shock variables from he model (model 3). The zero resricion on he coefficiens of he supply shock erms is srongly rejeced by he daa and so model 3 has a much lower likelihood han models 1 and Sep 2: Deriving he SRN Once we have esimaes of he LRN we can easily recover measures of he SRN. In line wih Braun (1984), Layard and Bean (1989), Esrella (1997) and Esrella and Mishkin (1999), using he analyical se up and he noaion of equaion (2) we define his as: 0 1 ( L) ( L) u u * 1 * us u ( L) z (4) which reduces o (5) below when, as in our case, changes in inflaion depend significanly only on he curren unemploymen gap, (u u *) and no in lags of his gap : us * u 1 0 L 0 ( L) 1 u * 1 0 L z 0 u u * ( L) z (5) I is sraighforward o show ha he change in inflaion on he lef-hand-side of equaion (2) can always be re-expressed as a funcion of he difference beween unemploymen and he SRN, us *, as follows: * 0 ( u us (6) ) 12 Preliminary work (based on an HP filered NAIRU) suggesed ha he equaion diagnosics were improved by he inclusion of a dummy (= 1 in 1979 Q3, 1 in 1980 Q3, 0 a all oher imes). A VAT change occurred a his 11

14 Equaion (6) illusraes ha he SRN us * defined as in (4) and (5) is he unemploymen level ha would give no inflaion change in quarer. Modelling changes in inflaion as in (6) insead of as in (2) may be advanageous because he SRN condiions on all shor-run deerminans of inflaion, and so i provides a more inuiive benchmark agains which o compare unemploymen over he horizon relevan for policy. In addiion, conrary o previous work assuming a consan longer-run NAIRU, he SRN here depends also on movemens in he longer-run NAIRU. Thereby he SRN sill capures shifs in srucural unemploymen, u *, inasmuch as hey maer for changes in inflaion in he immediae fuure. Finally, since he shor-run unemploymen gap embraces all he predicive power of he sysem (2)-(3), we expec i o be a good predicor of inflaion over he policy horizon. 2.2 RPIX-based SRNs compared In his subsecion we presen esimaes of sysem (2)-(3) derived according o he differen parameerisaions oulined above, and also show esimaes of he associaed SRNs and shorrun/long-run unemploymen gaps. We examine each parameerisaion in urn. In Secion 3 we hen analyse how good hese various unemploymen gaps are a explaining RPIX inflaion in he UK SRN based on quasi-consan LRN Our firs measure of he shor-run NAIRU assumes a quasi-consan LRN (LRN1, hereafer). As explained before, his implies ha in his case he LRN is derived esimaing sysem (2)- (3) by consraining he noise-o-signal raio 2 / 2 o be equal o 0.002, so ha he LRN is pracically consan (when his raio is zero, 2, he LRN is exacly consan). This is a resricive assumpion, and one no in line wih empirical evidence on equilibrium unemploymen in he UK. Indeed many conribuions in he lieraure agree ha he longerrun NAIRU has fallen in he UK over he las weny years, following he barrage of srucural reforms in he UK labour marke noably he decline in he role of he rade unions and heir progress owards a more co-operaive naure, especially in he privae secor, he promoion of flexible working arrangemens and he reducion in generosiy of he benefi sysem. 13 ime, and his resul suggess ha he shock was so large ha normally disribued errors could only be achieved by including a dummy variable for his period. 13 The sligh decline in unemploymen benefis, changes in he srucure of he produc marke or he launch of he Naional Minimum Wage do no appear o have played a significan role. See Nickell (2001) for a deailed 12

15 However, looking a an almos consan LRN is sill ineresing here because i faciliaes comparison wih similar work by Esrella and Mishkin (1999), Ball and Moffi (2001) and Meyer (2000) on SRN for he US based on a similar assumpion. Seing he raio so low allows us o sudy he behaviour of a much less variable longer-run NAIRU in he same framework in which we analyse ime-varying LRNs. Esimaes of he sysem (2)-(3) when 2 / 2 = are shown in column (1) of Table 1. As poined ou before, all along we sared wih a fairly general specificaion of equaion (2) wih lags of boh inflaion changes, long-erm unemploymen gaps and z-vecor dynamics and subsequenly converged o a final, more parsimonious represenaion by discarding insignifican erms (ypically, hose wih a -saisic smaller han uniy). The parsimonious specificaion of for his model includes among is regressors he curren value of he longerm unemploymen gap, and wo predeermined supply-side shocks namely he firs and fourh lag of real impor price inflaion and he fourh lag of real oil price inflaion. As expeced, he esimaion resuls shown in column (1) above suggess ha changes in inflaion depend negaively on he long-erm unemploymen gap, so ha when u is below u *, inflaion acceleraes and vice versa. Changes in inflaion also appear o be posiively correlaed wih rises in real impor price inflaion and rises in he real growh of oil prices, in line wih economic inuiion. Given values of esimaed coefficiens of sysem (2)-(3) in column (1), he associaed profile for u * and he daa on z, equaion (4) defines a series for his firs SRN (SRN1 hereafer). Char 2 shows our esimaes of LRN1 and SRN1 vis-à-vis Labour Force Survey unemploymen since 1973 Q1. Char 3 shows he associaed shor-erm unemploymen gap (u us *). Char 2 indicaes ha LFS unemploymen has been falling since 1993, and i is now a a level ha is considerably lower han he previous rough in 1990 Q2. 14 The longer-run NAIRU (LRN1) is basically consan around a full-sample average of 7.1%. discussion of he main facors underlying he fall in he longer-run NAIRU in he UK. Subsecion examines in more deail he hypohesis of a fall in he longer-run NAIRU since he early 1990s. 14 Noe ha since recenly, he duraion paern of reducions in unemploymen has changed. Whereas in 1999 he reducions were accouned for mainly by lower shor-erm unemploymen, in 2000 he declines have been dominaed by falls in long-erm unemploymen. These composiional shifs should exer smaller pressure on earnings, given he remaining supply shocks and changes in inflaion expecaions, because he shor-erm 13

16 A few oher imporan poins emerge by looking a Char 2. Firs our measure of SRN is very volaile in he 1970s. SRN1 is even negaive a imes, which is probably a consequence of he quasi-consancy resricion on he LRN, as his implies a higher level of equilibrium unemploymen in he 1970s han he plausible acual level a he ime. Since he mid-1980s SRN1 seems o have oscillaed around a lower mean han he LRN. For he same level of acual unemploymen his means ha he shor-erm unemploymen gap (GAP1) in Char 3 has in fac been posiive for mos of he pas weny years hough i was close o zero during 2000 and negaive hereafer. Char 2: LFS Unemploymen and NAIRU Esimaes (Model 1) LFS unemploymen LRN1 SRN Char 3: Unemploymen Gaps (Model 1) GAP1 (Longer-run) GAP1 (Shor-run) Since his measure of SRN1 is based on he assumpion ha LRN is almos consan, and his is conradiced by empirical sudies on he UK equilibrium unemploymen, in he nex subsecion we examine wha happens o he SRN when we allow he LRN o vary more freely SRNs based on ime-varying LRNs In his subsecion we focus on wo alernaive measures of SRNs based, in urn, on wo disinc measures of he longer-run NAIRU. unemployed end o search more inensively for jobs han he long-erm unemployed, reducing he need for firms o raise wages o fill vacancies. We do no analyse he implicaions of his when deriving and discussing our measures of shor-run NAIRU. 14

17 The firs, LRN2 is obained by re-esimaing he price equaion-lrn sysem of he previous subsecion [column (1) of Table 1], bu his ime seing he noise-o-signal raio equal o a value of As said before, his value of he raio seems consisen wih empirical priors in he UK. The SRN (SRN2) is hen derived in he usual way. The hird LRN (LRN3) measure also assumes 2 / 2 = 0.16 bu is esimaed by resricing o zero in he sysem (2)-(3), so ha any informaion from he z vecor is subsumed in he ime-variaion of u *. On one hand, since i excludes emporary supply shocks from he Phillips curve, he hird longer-run NAIRU ha we obain is somewha analogous o a shor-run NAIRU. In fac, his hird measure coincides wih he level of unemploymen ha is compaible wih sable prices given emporary supply side shocks. On he oher hand, his hird longer-run measure differs from a shor-run NAIRU in ha is variaions do no accoun for changes in lagged inflaion. So, as in he previous wo cases, here as well we can derive a shor-run measure of he NAIRU based on our esimae of he longer-run NAIRU. Maximum likelihood esimaes of he sysem (2)- (3) when 2 / 2 = 0.16 under hese wo specificaions are again shown in Table 1, columns (2) and (3) respecively. Chars 4 and 5 plo respecively SRN2 and LRN2 vis-à-vis LFS unemploymen (Char 4), and he shor-erm unemploymen gap, GAP2, (Char 5). Char 4 indicaes ha allowing for more realisic volailiy in he longer-run NAIRU gives a profile for his which racks acual unemploymen more closely; he wo series are, in fac, srongly posiively correlaed, wih a conemporaneous correlaion coefficien equal o The char shows ha he Kalmanfiler-esimaed longer-run NAIRU possibly peaked in he mid-1980s and fell back hereafer. This profile is broadly in line wih numerous oher empirical sudies of ime-varying NAIRUs for he UK (see Coulon and Cromb (1994)). Asley and Yaes (1999), for insance, derive a measure of he long-run naural rae by using a srucural VAR and find a zenih for he LRN around 1986, wih he LRN well below acual unemploymen from 1992 o 1997, and hen gradually declining hereafer. 15 The SRN esimaes are volaile in he mid-1970s, despie allowing for more plausible variabiliy of he LRN esimaes. There were sharp movemens in oil prices and impor prices during his ime. Since we are using changes in annual inflaion raes, he large swings in hese variables are likely o accoun for such volailiy in our esimaes. 15

18 Char 4: LFS Unemploymen and NAIRU Esimaes (Model 2) LFS unemploymen LRN2 SRN Char 5: Unemploymen Gaps (Model 2) GAP2 (Longer-run) GAP2 (Shor-run) If we absrac from he oscillaory 1970s period, under his new, considerably ime-varying measure of he LRN, he shor-run NAIRU (SRN2) now moves more in synchrony wih boh acual unemploymen and equilibrium unemploymen. 16 I follows ha overall he shor-erm unemploymen gap flucuaions are more mued han wha suggesed in Char 3, alhough he shor-erm unemploymen gap appears o have hi high poins boh in 1986 Q2 (+2%) and 1991 Q2 (+3%) and roughed in 1990 Q2 ( %) and 2001 Q1 ( %), suggesing alernae deflaionary and inflaionary pressures. For example, in he period, he shor-run NAIRU was noiceably below acual unemploymen, in conras wih is longer-run counerpar. This difference can be aribued o favourable supply shocks, as boh real impor prices and real oil prices declined a his ime. The period from 1997 o early 2000 is also ineresing o consider. During his period i appears ha he longer-run NAIRU esimaes have declined, hough a a less rapid pace han have he shor-run NAIRU esimaes, providing differen signals from he resuling unemploymen gaps. Focussing on he shor-run NAIRU, he fall in real impor prices ha occurred in he period from 1997 o early 2000 may have allowed unemploymen o fall below he NAIRU wihou being accompanied by higher inflaionary pressure. So, once we consider he simulaneous impac of favourable supply shocks, he shor-run NAIRU indicaes ha here was in fac a lo of running room for unemploymen o decline before giving rise o inflaionary pressures. More recenly in 2000 and early in 2001, as hese shocks unravelled (paricularly hose o oil prices), he level of unemploymen compaible wih sable inflaion in he shor-run given our esimaes seems higher han acual unemploymen. This generaes a 16

19 negaive shor-erm unemploymen gap (see Char 5), ha in urn indicaes upward pressure on inflaion, hough a he end of our sample, our unemploymen gap is close o zero. Char 6 below plos saic conribuions o annual RPIX inflaion. Two main messages can be drawn from his char. Firs, he lagged inflaion erm appears o have played a major role in predicing inflaion. This is equivalen o saying ha inflaion expecaions (of he backwardlooking kind) appear o have played a major role in inflaion deerminaion in he UK over he pas fifeen years. Their conribuion o inflaion seems o have diminished more recenly. This may be a consequence of he fac ha expecaions have sabilised around he announced inflaion arge, by virue of he shif o a regime of explici inflaion argeing in Second, from he end of 1996 o lae 1999, here seems o have been wo opposie effecs on inflaion. On one side, he unemploymen gap (LRN2) has been exering upward pressure on inflaion wih he LRN above acual unemploymen. There would of course have been more upward pressure from his source if he LRN had no fallen during his period. On he oher side, low impor and oil prices have depressed impored inflaion and pu downward pressure on RPIX inflaion. Pu differenly, he downward pressure on inflaion from impor and oil prices has allowed lower levels of unemploymen han longer-run NAIRU-implied o remain compaible wih sable inflaion as implied by a SRN lower han he LRN, namely by he difference beween he green and he blue lines in Char 4. The surge in oil prices ha hen ook place pu upward pressure on RPIX inflaion owards he end of 2000 which corresponds o he SRN being above he LRN esimaes. 16 Indeed, since he SRN is a direc funcion of he LRN, i will end o follow his if changes in he laer are dominan relaive o supply side shocks or changes in inflaion expecaions. 17

20 Char 6: Conribuions o annual RPIX inflaion (based on model 2) Percenage poins 10 sum u-u* lagged inflaion impor prices and oil residuals Finally, Chars 7 and 8 below graph wo furher measures of shor and longer-run NAIRUs over he same sample. This ime he LRN (LRN3) is esimaed by resricing o zero he coefficiens on supply side variables (i.e. he coefficiens in equaion (2)). So his LRN subsumes variaion in no jus he acual longer-run level of unemploymen bu also he explanaory power of hese omied variables. In his sense i can be inerpreed as a measure of a shorer-run NAIRU. However, i sill includes ineria in he dynamic inflaion adjusmen process. Thus we neverheless need o derive a shor-run measure of he NAIRU ha is consisen wih hose in Chars 2-5, by sripping ou such influences. By looking a Chars 7 and 8, i emerges ha boh ses of NAIRU esimaes ha we obain when he supply variables are excluded from he model (shor- and long-run) have been mirroring almos exacly he profile of acual unemploymen since early This implies ha under his definiion of shor-run NAIRU, he level of unemploymen ha we have observed has been compaible wih sable inflaion since 1995 Q1 given he combinaion of real impor price and real oil price shocks ha maerialised over his period. This is no rue of he 1970s, or of he 1980s, albei his measure of SRN suggess smaller variaions (a a maximum 3pp) in he shor-erm unemploymen gap (GAP3, Char 8) over he 1980s han hose suggesed by he previous SRN measure (see Char 5). 18

21 Char 7: LFS Unemploymen and NAIRU Esimaes (Model 3) Char 8: Unemploymen Gaps (Model 3) LFS unemploymen LRN3 2 SRN GAP3 (Longer-run) -2 GAP3 (Shor-run) CPI-based SRNs compared As a cross-check on our previous resuls, here we derive SRNs by re-esimaing sysem (2)- (3) using he change in he annual rae of Consumer Price Index (CPI) inflaion insead of he RPIX measure as he dependen variable. To do so, we use he same resricion for he noiseo-signal raio used in models 2 and 3 (i.e. 0.16). The general profile of hese NAIRU esimaes is similar o hose obained for he RPIX based specificaion (Model 2). Char 9: LFS Unemploymen and CPI based NAIRU Esimaes (Model 4) Char 10: Unemploymen Gaps (Model 4) LFS unemploymen LRN4 SRN GAP4 (Longer-run) GAP4 (Shor-run)

22 3. Indicaor properies of he shor-erm unemploymen gaps Wha is he benefi of looking a a SRN gap for predicing inflaion? One answer o his quesion can be obained by looking a equaion (6), which we rewrie below, for convenience. * 0 ( u us (6) ) Equaion (6) says ha changes in inflaion depend on he shor-run unemploymen gap a ime. In oher words, given our definiion of he shor-run NAIRU in equaion (5), deviaions of he acual rae of unemploymen from his rae should have he same informaion conen as all he regressors of inflaion (aken ogeher) in equaion (1). Table 2 below lends some formal suppor o his view by presening dynamic correlaions compued over he period 1973 Q1 and 2001 Q4 beween changes in he four-quarer change in RPIX (D4RPIX ) and he various ime-varying LRN-based SRN gaps GAP2 and GAP3 eiher in levels or in 5-quarer backward-looking moving averages (MA5SRNs ). In addiion, he able liss similar correlaions beween D4RPIX and a measure of he SRN gap obained by esimaing sysem (2)-(3) by using CPI insead of RPIX inflaion. We label his gap by GAP2CPI -k. Correlaions beween changes in RPIX inflaion (DD4RPIX ) and he gaps are also shown in he able. Finally, as a memo iem, Table 2 also presens correlaions beween (i) changes in RPIX inflaion and acual unemploymen raes; (ii) changes in RPIX inflaion and he deviaion of LFS unemploymen from a longer-run NAIRU (LRN2); and, finally, correlaions beween (iii) inflaion (or changes in inflaion) and a commonly-used measure of he oupu gap, namely he deviaion of he log of real oupu, y, from is Hodrick-Presco rend (smoohing parameer = 1,600), y*. 17 Inuiively, changes in inflaion should be negaively correlaed wih he SRN gap variables (a posiive SRN gap implying eiher unemploymen above is long-run rae and/or favourable supply side shocks or expecaions of lower inflaion, and hence, falling inflaion, and vice versa). By conrary, changes in inflaion should in principle be posiively correlaed wih he 17 We measure poenial oupu via real oupu HP rend for simpliciy. Ideally, we should have re-esimaed equaion (2) subsiuing he unemploymen gap wih he oupu gap, and hus esimaed poenial oupu as a 20

23 oupu gap, as a posiive gap, i.e. demand ousripping supply, ypically exers upward pressure on inflaion. Table 2: Dynamic correlaions beween RPIX inflaion and he SRN gaps k Lags Corr(D4RPIX, GAP2 -k ) a,b a,b Corr(D4RPIX,GAP3 -k ) a,b a,b Corr(D4RPIX, GAP2CPI -k a,b a,b Corr(D4RPIX, MA5GAP2 -k Corr(D4RPIX,MA5GAP3 -k ) Corr(D4RPIX, MA5GAP2CPI -k ) Corr(DD4RPIX, GAP2 -k ) a,b a,b Corr(DD4RPIX,GAP3 -k ) a,b a,b Corr(DD4RPIX, GAP2CPI -k ) a,b a,b Memo iem Corr (DD4RPIX,u -k ) a,b a,b Corr (DD4RPIX,u -k LRN2 -k * ) a,b Corr (D4RPIX,y -k y -k * ) Corr (DD4RPIX,y -k y -k * ) (a) Significanly differen from zero using convenional -es. (b) Significanly differen from zero using Newey-Wes -es. Two imporan messages emerge from Table 2. Firs, he correlaions beween he level of annual inflaion and he SRN gaps have he righ (negaive) sign a all lags. This is no rue of he oupu gap, which exhibis he wrong (negaive) sign wih inflaion a lags 0, 1 and 2. Second, correlaions beween changes in inflaion as implied from a model assuming a verical Phillips curve in he long run and our gap measures (GAP2 and GAP3) are higher, a 0.75 and 0.77, for our shor-run gap measures han any oher predicor of inflaion aken in isolaion. Noably, hey are sronger han he conemporaneous cross-correlaion beween changes in inflaion and he oupu gap he one of ineres here given our definiion of he shor-run gap in equaion (6). Imporanly, correlaions beween inflaion (or changes in) and our measures of SRNs gaps are significan (especially a shorer lags as we would expec by he definiion of SRNs) whereas dynamic correlaions beween inflaion (or changes in) and laen variable. This way he comparison in cross correlaions beween our shor-run unemploymen gap measures and an oupu gap measure would have been on he same level playing field. 21

24 he oupu gap are no, a any lag. 18 Dynamic correlaion coefficiens beween he level of inflaion and he moving averages of he SRN gaps are also negaive and very srong, especially a longer lags, alhough no significan. Regressions of changes in RPIX inflaion on four lags of iself, he ime- oupu gap and he ime- GAP2 as well as four lags of each of he laer esimaed over he period 1973 Q Q4, confirm his evidence by showing ha he ime- SRN gap and is fourh lag ener he equaion significanly, wih boh he shor- and he long-run regression coefficiens large and properly signed (suggesing ha a high level of he SRN is associaed wih falling inflaion and vice versa). In conras, he oupu gap is no significan in he long run equaion and has he wrong (negaive) sign. 19 This implies ha he oupu gap (defined as here) does no conain any incremenal informaion relaive o our measures of he SRN gap when used in an equaion o predic inflaion. Taken ogeher, hese resuls seem o sugges ha focusing on variaions in inflaion due o changes in he deviaion of acual unemploymen from hese shor-run NAIRU measures, i.e. he combinaion of shifs in LRN, supply shocks and changes o inflaion expecaions, helps predic inflaion. They also sugges ha SRN gaps may help forecasing inflaion in a superior way han frequenly advocaed measures of goods marke capaciy uilizaion like he oupu gap. 4. Applicaions In his secion we sugges examples of applicaions for our measures of he shor-run NAIRU. More specifically, we show how we can derive unemploymen levels compaible wih sable inflaion in he shor run under alernaive supply shock scenarios (Subsecion 4.1). This exercise can help formulae forecass by examining wha would happen o he shor-run NAIRU (and hence inflaion) if some exising shocks unwind, say. I can also help inerpre he source of inflaionary pressures looking backwards. As a second applicaion we hen show how he shor-run NAIRU can be used as a feedback variable in Taylor rules, insead of usual feedbacks, noably inflaion deviaions from arge and he oupu gap (Subsecion 4.2). 18 Noe however ha he correlaions above do no condiion on lags of inflaion. This may have implicaions for he differences ha we observe in Table Neiss and Nelson (2002) also find his. However, hey argue ha when he oupu gap is based on a heoreical model, hen New Keynesian Phillips curve esimaes deliver posiive coefficiens on he oupu gap. 22

25 4.1 Alernaive supply shock scenario Real impor prices fell significanly afer around mid-1996 (as a resul of he appreciaion of serling). For illusraive purposes, we can experimen wih wha would have happened had hese relaive prices no behaved he way hey have done hisorically a counerfacual experimen. For insance we can sudy he implicaions for he SRN if he impor price deflaor in nominal erms had remained fla a is 1996 Q3 value (ha is, real impor prices inflaion falls a around 2% per year). For simpliciy we assume ha RPIX inflaion is unchanged, hough in pracice changes in impor prices will of course influence RPIX inflaion. 20 The longer-run NAIRU esimaes for he acual impor price ouurns and alernaive scenario are shown in Char 11 below. If impor prices had been held fla (ie if impor prices had fallen by around 2% in real erms raher han he observed falls ha were ofen in he 5-10% range), hen given he ouurns o RPIX inflaion, his would be consisen wih a lower longer-run NAIRU in he second half of he 1990s. And he associaed alernaive shor-run NAIRU esimaes would have been higher han he esimaes based on he observed oucomes for impor prices during much of his period. This is because he shorerm supply shocks in he alernaive scenario are less favourable han he observed decreases in real impor prices ha acually occurred, resuling in he shor-run esimaes falling less dramaically. Oher ineresing scenarios ha can be examined wihin his analyical framework include he possible impac of he forhcoming changes in Naional Insurance Conribuions (NICs). However, since he main impac of changes in NICs may be on wage inflaion, i may be more appropriae o analyse hese effecs using SRNs derived from Kalman filer esimaes of a sysem specified in erms of average earnings, raher han in erms of RPIX inflaion. 20 A possible alernaive scenario is o consider real impor prices being fla hroughou his period. For breviy, hese resuls are no shown. 23

26 Char 11: LFS Unemploymen and Longer-run NAIRU Esimaes (Model 2) Char 12: LFS Unemploymen and Shor-run NAIRU Esimaes (Model 2) LFS unemploymen LRN2 LRN2 PM fla 4 2 LFS unemploymen SRN2 SRN2 PM fla Taylor rules based on shor-run NAIRU gaps One furher possible use of our measures of he shor-run NAIRU is as a proxy for one or more of he feedback variables in a rule for moneary policy, like ha suggesed in Taylor (1993). There are various reasons for why i may be ineresing o look a simple rules à la Taylor. Firs, Taylor-ype rules seem o have racked reasonably accuraely he hisorical pah of ineres raes in he Unied Saes during periods of good policy performance, bu o have depared from acual policy during bad periods as in he 1960s when recession followed policy overighening or in he 1970s when inflaion accompanied excessive ease in policy (see Taylor 1993, 1999). To a lesser exen, his propery of he rule seems o apply o oher counries oo, including he UK (see Baini and Tucker (1999)). Second, Taylor rules feed back on a limied se of variables, and so are simple by definiion, and herefore easy o use and updae. 21 Third, Taylor rule mechanically generaes ineres rae pahs using acual daa. So i provides one poenial crosscheck on policy. Pu somewha differenly, simple rules migh help guard agains big misakes, even if hey are guily of allowing small ones. The main feaures of he Taylor rule are ha, as any feedback rule, i seeks o correc hrough moneary policy any deviaion beween he growh of nominal magniudes and heir 21 However, because he Taylor rule responds o he oupu gap and requires a measure of he real equilibrium ineres rae, i can be difficul o compue in pracice. 24

27 argeed values. In his sense, he rule is consisen ex ane, in he medium erm, wih he UK s 2.5% inflaion arge. Ye imporanly, because i also responds o he oupu gap, he rule also guards agains excessive flucuaions in real oupu in he course of hiing his medium-erm inflaion goal. In shor, he Taylor rule offers a pah for he shor-erm nominal ineres rae (R ). Concepually, however, i is easier o hink of he rule as seing a pah for he shor-erm expos real ineres rae (R 1, where 1 refers o las period s inflaion rae) relaive o is equilibrium or neural value (r*). These deviaions of real raes from heir neural value in urn depend on wo feedback erms: he deviaion of acual oupu (y) from is rend value (y*); and he deviaion of inflaion from is arge value ( *). Boh he oupu and inflaion gap erms are lagged, on grounds of daa availabiliy. 22 The feedback erms are given weighs of 1 and 2 respecively. The Taylor rule formula is hence: R = (y y*) 1+ 2 ( *) 1+ r* (7) The concepual basis of he Taylor rule is minimalis bu enirely sandard. Taylor inerpres he rule as an invered money demand relaionship, wih ineres raes adjused o mainain equilibrium in real and nominal magniudes over he medium erm (Taylor (1999)). In consrucing his rule for he UK we have o proxy all of he erms in (1). We concenrae on a quarerly version of he Taylor rule because our SRN GAP measures are quarerly in frequency. The proxies ha we use are: (i) For inflaion ( ), he annual rae of RPIX inflaion; (ii) For he inflaion arge ( *), 2.5%; (iii) For he equilibrium real ineres rae, a Hodrick-Presco filer (wih smoohing parameer se equal o 10,000) of he en-year real ineres rae, derived from he index-linked yield curve; (iv) For he oupu gap, we experimen wih hree differen conceps. Firs, an oupu gap variable ha we define in erms of he deviaion of curren oupu from a measure of poenial oupu derived from a Cobb-Douglas producion funcion (quarerly Taylor rule). Second, our preferred longer-run NAIRU gap (LRN GAP2), ha is he difference beween 22 Taylor s (1993) original specificaion used curren values of inflaion and he oupu gap, bu here are quesions hen abou he operaionaliy of such a specificaion if i is o be used in real ime. 25