Understanding the role that resource utilization a gauge of the balance

Transcription

1 currnt FEDERAL RESERVE BANK OF NEW YORK issus IN ECONOMICS AND FINANCE Volum 7, Numbr How Dos Slack Influnc Inflation? Richard Pach, Robrt Rich, and Anna Cororaton Economists hav long studid th rlationship btwn rsourc utilization and inflation. Thory suggsts that whn firms us labor and capital vry intnsivly, production costs tnd to ris and firms hav mor scop to pass thos cost incrass along in th form of highr product prics. In contrast, whn that lvl of intnsity is rlativly low that is, whn th conomy is oprating with slack production costs tnd to ris mor slowly (or vn fall) and firms hav lss scop for raising prics. Empirical vidnc, howvr, has varid concrning th xact natur of th rlationship btwn rsourc utilization and inflation. In this study, th authors rxamin this rlationship by valuating th prsnc of thrshold ffcts. Thy find that th lvl of intnsity of rsourc utilization must b blow or abov crtain critical valus bfor it can hlp to forcast movmnts in inflation. Undrstanding th rol that rsourc utilization a gaug of th balanc btwn aggrgat dmand and supply in an conomy plays in th inflation procss is an important issu, particularly at a tim whn th unmploymnt rat rmains stubbornly high. Economic thory prdicts that inflation will incras whn an conomy is oprating abov its potntial whn firms ar likly to b using labor and capital vry intnsivly and will slow whn oprating blow its potntial. And, in fact, this rlationship is born out by mpirical analysis of post World War II U.S. data up to th mid-98s: Whn th unmploymnt rat was rlativly low, th rat of inflation incrasd. Convrsly, whn th unmploymnt rat was rlativly high, inflation slowd. Surprisingly, howvr, ovr th priod from th mid-98s through th mid-s, th rlationship btwn th unmploymnt rat and th lvl of inflation provd vry wak at bst, lading som commntators to conclud that masurs of rsourc utilization might no longr b usful prdictors of futur changs in th rat of inflation. Othr commntators, howvr, hav viwd this mixd mpirical vidnc as support for th hypothsis that th lvl of rsourc utilization must xcd or fall blow crtain thrsholds bfor it has a maningful impact on inflation. In othr words, th unmploymnt rat will hlp prdict futur inflation only whn it is abov or blow critical valus, as it occasionally was ovr th priod from th nd of World War II through th mid-98s. By contrast, th unmploymnt rat will hav littl powr to prdict inflation during priods whn movmnts of th unmploymnt rat ar rlativly mutd such as th priod btwn th mid-98s and th mid-s that conomists call th Grat Modration. In this dition of Currnt Issus, w valuat this hypothsis using a modl that rlats th rat of inflation to th unmploymnt gap th diffrnc btwn th actual unmploymnt rat and th non-acclrating inflation rat of unmploymnt,

2 CURRENT ISSUES IN ECONOMICS AND FINANCE Volum 7, Numbr or NAIRU. As its nam suggsts, th NAIRU is that lvl of th unmploymnt rat at which thr is no tndncy for inflation to incras or dcras. W us this modl to gaug th prsnc of thrsholds byond which th rlationship btwn inflation and th unmploymnt gap bcoms strongr in both conomic and statistical trms. W also xamin th modl s ability to forcast cor inflation an inflation masur that xcluds volatil food and nrgy prics ovr th priod from 8 through th nd of. Th rsults of our analysis indicat that th impact of th unmploymnt gap on inflation diffrs markdly within and outsid th stimatd thrsholds, with conomically and statistically significant ffcts associatd with dviations of th unmploymnt rat from th NAIRU largr than. prcntag points in absolut valu. In addition, w find that th modl-gnratd forcasts of inflation hav gnrally trackd th slowing of cor inflation ovr th 8- priod. W conclud that ths rsults, takn togthr, provid gnral support for th notion that th unmploymnt gap must b blow or abov crtain thrshold valus bfor it can hlp to prdict movmnts in inflation and thrby srv as a usful guid for montary policymakrs. Background Th invrs rlationship btwn inflation and unmploymnt is th dfining fatur of th Phillips curv, namd for th Nw Zaland born conomist A. W. Phillips. In a 958 study of U.K. conomic data from 8 to 957, Phillips documntd that nominal wags had grown fastr during priods whn th unmploymnt rat was low; whn unmploymnt was high, wags had grown mor slowly. Subsqunt intrprtrs of Phillips mpirical findings saw th rlationship btwn wag inflation and unmploymnt as a stabl on that would allow analysts to prdict how th inflation rat would chang in rspons to particular movmnts in th unmploymnt rat. Today, aftr fifty yars of additional rsarch, a modifid vrsion of th Phillips curv th xpctations-augmntd Phillips curv is a widly usd tool for xplaining and forcasting inflation. In this vrsion, th rat of inflation is dtrmind by a combination of inflation xpctations, som masur of th ovrall stat of rsourc utilization, and variabls that captur supply shocks such as larg, sharp changs in commodity prics. Commonly usd masurs of th stat of rsourc utilization ar th unmploymnt gap (dfind arlir) and th output gap actual GDP rlativ to th conomy s maximum sustainabl output, or potntial GDP. All ls qual, th xpctationsaugmntd Phillips curv posits that conditions of slack in th conomy that is, activity gap masurs indicating that output Potntial GDP is that lvl of ral output at which inflation would rmain stabl. Th potntial growth rat of ral GDP is that at which th unmploymnt rat would rmain unchangd. Chart Th Unmploymnt Gap and Cor PCE Inflation: Tim Sris of th Data Prcntag points Unmploymnt gap in quartr t Chang in cor PCE inflation from quartr t to quartr t+ 8 Sourcs: U.S. Burau of Economic Analysis; U.S. Burau of Labor Statistics; Congrssional Budgt Offic. Nots: Th unmploymnt gap is th diffrnc btwn th actual unmploymnt rat and th Congrssional Budgt Offic s stimat of th non-acclrating inflation rat of unmploymnt (NAIRU). Cor PCE inflation is th prsonal consumption xpnditurs dflator xcluding food and nrgy. and mploymnt ar blow thir potntial lvls will lad to a dclin in inflation and vic vrsa. Th rlationship btwn inflation and rsourc utilization ovr th last fifty yars is shown in Chart. Th chart prsnts a long tim sris of th four-quartr chang in th growth rat of th cor prsonal consumption xpnditurs (PCE) dflator, which xcluds nrgy and food. Also plottd is th unmploymnt gap, masurd as th diffrnc btwn th actual unmploymnt rat and th stimat of th NAIRU producd by th Congrssional Budgt Offic (CBO). Clarly visibl ar pisods in which th actual unmploymnt rat was abov th NAIRU and inflation subsquntly fll as wll as pisods in which th actual unmploymnt rat was blow th NAIRU and inflation subsquntly ros. Also vidnt, howvr, ar priods in which th linkag btwn th variabls appars to b rathr wak. Going forward, w will rfr to th xpctations-augmntd Phillips curv simply as th Phillips curv for as of xposition. Ltting π t dnot th (annualizd) growth rat in th cor PCE dflator indx from quartr t to quartr t, th sris is dfind as π t+ π t. Th plot of th sris in quartr t dpicts th valu of (π t+ π t ), with positiv (ngativ) valus rprsnting an incras (dcras) in th lvl of inflation ovr th nxt yar. Th PCE dflator, publishd by th U.S. Burau of Economic Analysis, is th pric indx for all goods and srvics consumd by th houshold sctor, rgardlss of who pays for thos goods and srvics. It diffrs in scop from th mor familiar consumr pric indx (CPI), which is a pric indx of goods and srvics that housholds pay for out of pockt. Lik th cor CPI, th cor PCE dflator xcluds food and nrgy. Howvr, in th cas of th PCE dflator, only food purchasd for off-prmiss consumption is xcludd, whil food consumd away from hom (at a rstaurant) is includd in th cor masur

3 Chart Th Unmploymnt Gap and Cor PCE Inflation: Scattr-Plot of th Data Four-quartr chang in cor PCE inflation (prcntag points) 8 Inflation pr-98 Inflation post-98 - Post-98 linar trnd (slop = -.) - Pr-98 linar trnd (slop = -.9) Unmploymnt gap in quartr t (prcntag points) Sourcs: U.S. Burau of Economic Analysis; U.S. Burau of Labor Statistics; Congrssional Budgt Offic. Nots: Th unmploymnt gap is th diffrnc btwn th actual unmploymnt rat and th Congrssional Budgt Offic s stimat of th non-acclrating inflation rat of unmploymnt (NAIRU). Cor PCE inflation is th prsonal consumption xpnditurs dflator xcluding food and nrgy. Anothr way of viwing th rlationship btwn rsourc utilization and inflation is prsntd in Chart, whr th data in Chart now appar in th form of a scattr-plot. Each dot rprsnts an obsrvation of th four-quartr chang in cor PCE dflator inflation and th corrsponding valu of th unmploymnt gap. Th dots ar color codd to sparat pr-98 (blu) and post-98 (orang) obsrvations. Not that th stimatd slop of th pr-98 obsrvations is rlativly stp, whras th slop of th post-98 obsrvations is quit shallow. Spcifically, th stimatd slop ovr th post-98 priod is lss than half th valu obsrvd ovr th pr-98 priod. Th implication is that th rlationship btwn th unmploymnt gap and inflation waknd in th post-98 priod. Th tnuous rlationship btwn rsourc utilization and inflation ovr th post-98 priod could b intrprtd as vidnc of a long-trm structural chang in th conomy that has mad th Phillips curv rlationship much lss usful as a tool for forcasting inflation. Considr, howvr, that th priod from th mid-98s through th mid-s was unusually stabl from a macroconomic prspctiv. Output gaps and unmploymnt gaps wr rlativly small, and masurd inflation xpctations wr rlativly low and stabl. Consquntly, whil th data indicat a waknd rlationship btwn slack and inflation, this vidnc could b an artifact of th Grat Modration. Anothr look at Chart offrs som prliminary support for this claim: th pr-98 priod xhibits mor xtrm valus of th unmploymnt gap than dos th post-98 priod. Earlir Viws on th Prdictiv Powr of th Phillips Curv How usful is th Phillips curv in forcasting inflation ovr a on-to-two-yar horizon? In a vry influntial articl on this topic, Atkson and Ohanian () conduct a hors rac btwn thr altrnativ spcifications of a Phillips curv modl and a so-calld naïv modl that assums that inflation ovr th nxt yar will simply qual what it was ovr th prcding yar. Th authors conclud that for on-yar-ahad forcasts of inflation ovr th priod, all thr sts of NAIRU Phillips curv basd inflation forcasts hav bn no mor accurat than th forcast from our naïv modl.... W conclud that NAIRU Phillips curvs ar not usful for forcasting inflation (p. ). Othr rsarchrs hav challngd th findings of Atkson and Ohanian. Stock and Watson (9) compar th accuracy of svral diffrnt typs of inflation-forcasting modls, including univariat modls thos that rly xclusivly on on or mor past valus of inflation to prdict inflation (th naïv modl dscribd abov is a particular xampl of a univariat modl). As th authors rport, on of our ky findings is that th prformanc of Phillips curv forcasts is pisodic: thr ar tims, such as th lat 99s, whn Phillips curv forcasts improvd upon univariat forcasts, but thr ar othr tims (such as th mid-99s) whn a forcastr would hav bn bttr off using a univariat forcast (p. ). Morovr, thy find that th tims whn a Phillips curv modl outprforms a univariat forcast ar thos in which th output gap or unmploymnt gap is rlativly larg. Liu and Rudbusch () dvlop a statistical modl in which changs in inflation in a givn priod dpnd on prvious changs in inflation and th prvious unmploymnt gap. Thy also considr a univariat modl that includs only th prvious changs in inflation. Thy stimat th two inflation modls ovr a sampl priod from first-quartr 98 to fourth-quartr 7, and thn gnrat out-of-sampl forcasts for th priod from firstquartr 8 through third-quartr 9. Judging th accuracy of th two modls by a masur known as root man squard rror (RMSE) th squar root of th avrag squard diffrnc btwn th prdictd and th actual valus of inflation th authors find that th modl with th unmploymnt gap has an RMSE that is only about 5 prcnt that of th univariat modl. Thy conclud that th high lvl of th unmploymnt gap during 8-9 contributd to th substantial dclin in th inflation rat as prdictd by th Phillips curv. Whil th studis summarizd hr appar contradictory, it is possibl to rconcil th rsults by arguing that th Phillips curv displays thrshold ffcts. That is, th natur of th rlationship btwn inflation and an activity variabl such as th unmploymnt gap may chang according to whthr th gap lis abov or blow a particular valu, or thrshold. This viw is consistnt with Stock and Watson s finding that masurs of conomic activity do not hlp improv th accuracy of inflation forcasts in rlativly

4 CURRENT ISSUES IN ECONOMICS AND FINANCE Volum 7, Numbr Chart Th Thrshold Phillips Curv Inflation Extrior rgion Intrior rgion Extrior rgion γ L γ U (Lowr thrshold) (Uppr thrshold) Unmploymnt gap Nots: Th chart shows th rspons of inflation to xtrm movmnts in th unmploymnt gap (th xtrior rgions) and to mor modrat movmnts in th gap (th intrior rgion). Th unmploymnt gap is th diffrnc btwn th actual unmploymnt rat and th Congrssional Budgt Offic s stimat of th non-acclrating inflation rat of unmploymnt (NAIRU). tranquil priods, but do hlp to prdict inflation in priods whn th unmploymnt rat dviats markdly from NAIRU. Th viw can also accommodat th smingly contrary rsults obtaind by Atkson and Ohanian, on th on hand, and Liu and Rudbusch, on th othr. Th authors forcast xrciss tak plac during vry diffrnt tims a priod of rlativ tranquility in th cas of th first study and a larg conomic downturn in th cas of th scond. Th ida of a thrshold rlationship btwn activity masurs and inflation was prviously formalizd by Barns and Olivi (), who proposd a picwis linar Phillips curv spcification. In this typ of rlationship, dpictd in Chart, inflation displays littl rspons to movmnts in th unmploymnt gap that occur btwn a lowr thrshold (γ L ) and uppr thrshold (γ U ), but shows a mor pronouncd rspons to movmnts in th unmploymnt gap outsid of this intrval. Whil Barns and Olivi found vidnc to support thir thrshold Phillips curv spcification, thir analysis ndd in. Now, with th unmploymnt rat still quit high narly two full yars into th rcovry, w bliv it would b usful to rxamin th issu of a thrshold rlationship btwn inflation and conomic slack with th addition of mor currnt data. Pric Inflation Phillips Curv Modl Our spcification of th Phillips curv modl draws upon Gordon s (99) triangl modl of inflation with minor modifications. In th triangl modl, thr ar thr dtrminants of inflation: an inrtial componnt, an activity gap masur, and a supply shock variabl. Inrtia rfrs to th tndncy of inflation to dviat only gradually from its own past valus owing to th slow adjustmnt of inflation xpctations, proxid hr by a wightd avrag of past inflation and a masur of long-run (tn-yar) inflation xpctations. Our activity gap variabl dfind as th diffrnc btwn th unmploymnt rat and th CBO stimat of th NAIRU is mant to account for conditions of tightnss or slack in th conomy. 5 Th third dtrminant of inflation in th modl is th supply shock variabl. W us rlativ import pric inflation, or th growth rat of import prics rlativ to th domstic inflation rat, as our supply shock variabl. Whil on might argu that th xchang valu of th dollar should b usd instad, th fact that th linkag btwn th xchang rat and import prics varis substantially ovr tim maks this masur lss usful. Our analysis involvs svral stps. First, w stimat a Phillips curv modl in which th rat of inflation is dtrmind by a combination of past inflation, inflation xpctations, th unmploymnt gap, and rlativ import prics. In this standard modl, th impact of th unmploymnt gap on inflation dos not chang. W thn stimat a scond modl in which w allow for th prsnc of thrshold ffcts, maning that thr ar valus of th unmploymnt gap byond which th ffct on inflation diffrs from what it is whn th gap is within thos thrsholds. Th dtails of this xrcis ar providd in th accompanying box. Bcaus quations () and () in th box hav vry diffrnt prdictions for th rol of activity gaps in th inflation procss, it would sm that tsting dirctly for th prsnc of thrshold ffcts in th data would b a natural approach to valuat th compting modls. Unfortunatly, tsting for thrshold ffcts is complx and th stimation of thrsholds also involvs uncrtainty. 7 Bcaus of ths difficultis, w rly on a lss formal approach to assss th prsnc of thrshold ffcts. Spcifically, w xamin if thr is a markd diffrnc in th stimatd slops of th Phillips curv with and without thrshold ffcts and, in th thrshold cas, compar stimats for th intrior and xtrior rgions of th curv. In addition, w xamin whthr th forcast profil of inflation from th thrshold Phillips curv modl is consistnt with th rcnt path of inflation, givn th obsrvd paths of long-run inflation xpctations, th unmploymnt gap, and import prics. Whil ths xrciss should not b viwd as a prfct substitut for mor formal tsting procdurs, thy ar instructiv and allow us to gain insights into th xtnt to which activity gaps ar usful componnts of mpirical modls of inflation. Th inclusion of laggd, or past, inflation rats can b viwd ithr as capturing a backward-looking componnt of inflation xpctations or as an additional sourc of inrtia stmming from wag and pric contracts in th conomy. 5 S U.S. Congrssional Budgt Offic () for a discussion of how this stimat of NAIRU is drivd. Oil prics ar includd as a componnt in th import pric sris. 7 S Hansn (99, ) for a mor dtaild discussion.

5 Th Thrshold Phillips Curv Modl To undrstand th thrshold Phillips curv modl, considr first th spcification of th standard Phillips curv modl usd in our analysis: () πt = απ i t i+ λπt + βu t + χzt + εt, whr π t is (annualizd) quartrly cor PCE inflation, π t,...,π t ar thr laggd valus of inflation, π t is th laggd valu of long-run PCE ~ inflation xpctations, u t is th laggd valu of th unmploymnt gap, z t is th laggd valu of th supply shock variabl, and ε t is an rror trm. Th masur of long-run PCE inflation xpctations is a hybrid of two diffrnt data sris. For th priod bfor fourth-quartr 99, th masur of inflation xpctations is takn from th Fdral Rsrv Board s FRB/US modl. From fourth-quartr 99 onward, th sris is calculatd as th tn-yar-ahad consumr pric indx (CPI) inflation xpctations sris from th Survy of Profssional Forcastrs lss 55 basis points to account for th historical diffrnc btwn th two inflation sris. Th unmploymnt gap is masurd as th diffrnc btwn th unmploymnt rat and th Congrssional Budgt Offic s ~ stimat of th tim-varying NAIRU (u=u u NAIRU ). Rlativ import pric inflation is masurd as th quartrly (annualizd) growth rat of import prics lss quartrly (annualizd) cor PCE inflation (π IMPORT π). Th thrshold Phillips curv modl provids a countrpart to th standard spcification in quation () and is givn by: i= () π = απ + λπ + β u + χz + ε, if γ u γ t i t i t Ι t t t i= t i t i t E t t t i= L t U π = απ + λπ + β u + χz + ε, othrwis, whr th modification in quation () allows th trad-off btwn inflation and unmploymnt to dpnd on th lvl of th unmploymnt gap. In particular, w assum that th slop of th Phillips curv can chang according to whthr th unmploymnt gap lis btwn or outsid th thrshold valus. If th unmploymnt gap is btwn th lowr thrshold (γ L ) and th uppr thrshold (γ U ), thn th cofficint β Ι masurs th slop of th Phillips curv in this intrior rgion. By contrast, if th unmploymnt gap lis blow th lowr thrshold or abov th uppr thrshold, thn th cofficint β Ε masurs th slop of th Phillips curv in ithr xtrior rgion. It is assumd that th othr variabls in th modl do not produc thrshold ffcts on th inflation procss, although w allow rlativ import pric inflation to hav diffrntial ffcts bfor and aftr 98. a Estimation of th thrshold Phillips curv modl is basd on a grid sarch mthod. Spcifically, a rang of possibl valus is spcifid for th lowr thrshold and for th uppr thrshold, with a rstriction on th rang rquird to nsur that th numbr of obsrvations in th intrior and xtrior rgions is sufficint for modl stimation. W allow th symmtric valus of th lowr (uppr) thrshold to rang from -.8 (.8) to -. (.), with th thrshold valus changing in incrmnts of. within ths rangs. b W also rstrict th slop of th Phillips curv to b th sam blow th lowr thrshold and abov th uppr thrshold. Th stimation procdur thn slcts as th thrsholds thos combinations that rsult in th lowst sum of squard rsiduals. Th stimation rsults for th standard and thrshold Phillips curv modls ar prsntd blow. Phillips Curv Modl Estimats Paramtr Standard Phillips Curv Modl α. *** (.7) α.9 ** (.7) α.57 ** (.8) λ β. *** (.) -. *** (.5) β I β E χ pr-8.55 *** (.7) χ post-8. (.) Thrshold Phillips Curv Modl. *** (.7).87 ** (.7). ** (.7).7 *** (.) -.77 (.8) -.7 *** (.5).57 *** (.7).8 (.) R.9.9 Not: Standard rrors ar rportd in parnthss. *** Significant at th prcnt lvl. ** Significant at th 5 prcnt lvl. a S Taylor () and Hookr () for furthr discussion. Ths studis documnt a dclin sinc th mid-98s in th impact of import prics and oil prics on th U.S. inflation procss, and ascrib this dvlopmnt to th conduct of montary policy and th stablishmnt of a crdibl low-inflation nvironmnt. b Onc valus ar spcifid for γ L and γ U, th thrshold modl in quation () can b stimatd using th mthod of ordinary last squars. 5

6 CURRENT ISSUES IN ECONOMICS AND FINANCE Volum 7, Numbr Chart Th Unmploymnt Gap and Estimatd Symmtric Thrsholds Chart 5 Phillips Curv Modl Forcasts On-Quartr-Ahad Cor PCE Inflation Prcntag points 5 Prcnt.5. Thrshold modl forcast.5 Uppr thrshold: Cor PCE actual inflation Lowr thrshold: Sourcs: U.S. Burau of Labor Statistics; Congrssional Budgt Offic; authors calculations. Not: Th unmploymnt gap is th diffrnc btwn th actual unmploymnt rat and th Congrssional Budgt Offic s stimat of th non-acclrating inflation rat of unmploymnt (NAIRU). Estimation Rsults Th masur of inflation whos movmnts w sk to xplain is th annualizd quartrly prcntag chang in th cor PCE dflator. Th modls for cor PCE dflator inflation ar stimatd ovr th priod from first-quartr 9 through fourth-quartr 7 to mitigat th influnc of th Grat Rcssion. Th stimation rsults ar prsntd in th tabl on pag 5. 8 Th rgrssion rsults for th standard Phillips curv yild a statistically significant slop stimat of -.. For th thrshold Phillips curv modl, two ky rsults mrg. First, th stimatd (absolut) valu of th thrshold unmploymnt gap is.5 prcntag points. This figur is vry clos to th.5 prcntag point figur idntifid by Stock and Watson (9) as th thrshold byond which Phillips curv modls provid forcast improvmnts ovr univariat modls for inflation. 9 As shown in Chart, which prsnts a long tim sris of th unmploymnt gap, thr hav bn rlativly fw pisods whn it has xcdd ths stimatd thrsholds. Four pisods, including th most rcnt, corrspond to particularly svr rcssions. Anothr, ovr th scond half of th 9s and into th arly 97s, corrsponds to an xtndd priod of intns rsourc utilization. Th scond ky finding is that th slops associatd with th thrsholds diffr markdly in both conomic 8 To nsur that thr is no long-run trad-off btwn inflation and unmploymnt, w undrtak stimation of both modls imposing th constraint that th cofficints on laggd inflation and th masur of inflation xpctations sum to unity. This rstriction was not rjctd for ithr modl. 9 Barns and Olivi () allow for asymmtric thrsholds and rport stimats of -. prcnt and. prcnt, rspctivly, for th lowr and uppr thrsholds of thir cor PCE dflator Phillips curv modl. Whn w allow for asymmtric thrsholds, w obtain similar stimats of -. prcnt and. prcnt. W lctd to stimat th modl with symmtric thrsholds so that w could compar our findings with thos of Stock and Watson (9), who incorporat mor rcnt data. Sourcs: U.S. Burau of Economic Analysis; authors calculations. Not: Cor PCE inflation is th prsonal consumption xpnditurs dflator xcluding food and nrgy. and statistical significanc. Th stimatd slop in th xtrior rgion is -.7 and is statistically significant, but th stimatd slop dclins to -.7 and is not statistically significant whn th unmploymnt gap lis in th intrior rgion. Th initial rsults ar consistnt with th ida that th link from activity gaps to inflation is pisodic that is, th rlationship is rlvant only whn conditions in th conomy ar ithr xtrmly slack or xtrmly tight. To xamin th thrshold Phillips curv modl s usfulnss as a forcasting tool, w conduct a dynamic simulation to judg how wll th modl s forcasts track th rcnt path of inflation. For th simulation, w rtain th modl s stimatd paramtrs through th fourth quartr of 7 to gnrat a on-quartr-ahad prdictd valu for first-quartr 8 cor PCE inflation. W thn rpat th xrcis for ach subsqunt priod using th actual paths of long-run inflation xpctations, th unmploymnt gap, and import prics as th xplanatory variabls. No actual valus of inflation ovr th rcnt rcssion ar usd in th simulation. Rathr, th simulation uss th post-7 inflation forcasts from th modl to forcast th subsqunt valus of inflation. In this mannr, w gnrat a squnc of cor PCE inflation forcasts for th priod from first-quartr 8 to fourth-quartr. Importantly, th on-quartr-ahad inflation forcasts producd by our dynamic simulation gnrally track th slowing obsrvd in actual cor PCE inflation sinc th first quartr of 8 (Chart 5). To b sur, thr hav bn som larg dviations btwn th ralizd and forcastd valus on a quartr-to quartr basis. For xampl, forcastd inflation appars to hav laggd As a robustnss chck, w xprimntd with diffrnt choics for th thrsholds but found that th slop stimats of th Phillips curv and th inflation forcast profils did not matrially chang.

7 th dclration of actual inflation through th middl of scondquartr 9, prhaps bcaus of th rol of inrtia in th modl. In addition, actual cor inflation ros and thn stabilizd in 9 whil its forcastd valu continud to dclin. Mor rcntly, howvr, actual cor inflation has movd significantly lowr as prdictd by th modl forcasts with th modl also pointing to som risk of dflation. It is important to not that th obsrvd downward trnd in actual and forcastd inflation occurs in spit of th fact that inflation xpctations hav rmaind quit stady: spcifically, th inflation xpctations sris usd in our modl ssntially hld stady at prcnt ovr th out-of-sampl forcast xrcis. Conclusion Thr has bn considrabl dbat rcntly about th rol of slack in th inflation procss. Our study contributs to th dbat by prsnting vidnc that th rlationship btwn labor markt slack and inflation is nonlinar in particular, slack must xcd a thrshold bfor xrting a statistically and conomically significant ffct on inflation. Importantly, our thrshold modl tracks th considrabl slowing of cor inflation that has occurrd sinc th nd of 7 and can thrfor srv as a usful guid in th montary policy procss. Nvrthlss, w rcogniz that som caution should b xrcisd in th intrprtation of our rsults. For xampl, thr is littl thortical work to xplain th picwis linar Phillips curv. In addition, thr is a gnral absnc of pisods in which low inflation and larg unmploymnt gaps coincidd in th sampl priod. Finally, th singl-quation thrshold Phillips curv modl assums that inflation xpctations ar not influncd by othr variabls in th modl. It is likly, howvr, that inflation xpctations ar influncd by th amount of slack in th conomy, which in turn could affct th stimats of th thrsholds. Whil byond th scop of this articl, an intrsting xtnsion of our work would b th stimation of a multi-quation modl that would trat inflation xpctations as bing influncd by variabls such as th unmploymnt gap. W ar gratful to Giovanni Olivi of th Fdral Rsrv Bank of Boston for his assistanc and hlpful commnts. Rfrncs Atkson, Andrw, and L E. Ohanian.. Ar Phillips Curvs Usful for Forcasting Inflation? Fdral Rsrv Bank of Minnapolis Quartrly Rviw 5, no. : -. Barns, Michll, and Giovanni Olivi.. Insid and Outsid Bounds: Thrshold Estimats of th Phillips Curv. Fdral Rsrv Bank of Boston Nw England Economic Rviw, -8. Gordon, Robrt. 99. U.S. Inflation, Labor s Shar, and th Natural Rat of Unmploymnt. In Hinz Konig, d., Economics of Wag Dtrmination. Brlin: Springr-Vrlag. Hansn, Bruc. 99. Infrnc Whn a Nuisanc Paramtr Is Not Idntifid undr th Null Hypothsis. Economtrica, no. : -... Sampl Splitting and Thrshold Estimation. Economtrica 8, no. : Hookr, Mark A.. Ar Oil Shocks Inflationary? Asymmtric and Nonlinar Spcifications vrsus Changs in Rgim. Journal of Mony, Crdit, and Banking, no. : 5-. Liu, Zhng, and Glnn Rudbusch.. Inflation: Mind th Gap. Fdral Rsrv Bank of San Francisco Economic Lttr, no. -. Phillips, A. W Th Rlationship btwn Unmploymnt and th Rat of Chang of Mony Wags in th Unitd Kingdom, Economica 5, no. : Stock, Jams, and Mark Watson. 9. Phillips Curv Inflation Forcasts. In Undrstanding Inflation and th Implications for Montary Policy: A Phillips Curv Rtrospctiv. Procdings of th Fdral Rsrv Bank of Boston s 8 conomic confrnc. Cambridg, Mass.: MIT Prss. Taylor, John B.. Low Inflation, Pass-thru, and th Pricing Powr of Firms. Europan Economic Rviw, no. 7: U.S. Congrssional Budgt Offic.. Th Effct of Changs in Labor Markts on th Natural Rat of Unmploymnt. April. ABOUT THE AUTHORS Richard Pach is a snior vic prsidnt, Robrt Rich an assistant vic prsidnt, and Anna Cororaton an assistant conomist in th Macroconomic and Montary Studis Function of th Fdral Rsrv Bank of Nw York. Currnt Issus in Economics and Financ is publishd by th Rsarch and Statistics Group of th Fdral Rsrv Bank of Nw York. Linda Goldbrg and Erica L. Groshn ar th ditors. Editorial Staff: Valri LaPort, Mik D Mott, Michll Bailr, Karn Cartr Production: Carol Prlmuttr, David Rosnbrg, Jan Urry Subscriptions to Currnt Issus ar fr. Snd an -mail to Rsarch.Publications@ny.frb.org or writ to th Publications Function, Fdral Rsrv Bank of Nw York, Librty Strt, Nw York, N.Y. 5-. Back issus of Currnt Issus ar availabl at Th viws xprssd in this articl ar thos of th authors and do not ncssarily rflct th position of th Fdral Rsrv Bank of Nw York or th Fdral Rsrv Systm. 7