Research Division Federal Reserve Bank of St. Louis Working Paper Series

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1 Research Dvson Federal Reserve Bank of S. Lous Workng Paper Seres Inflaon: Do Expecaons Trump he Gap? Jeremy M. Pger and Rober H. Rasche Workng Paper B hp://research.slousfed.org/wp/006/ pdf March 006 Revsed July 006 FEDERAL RESERVE BANK OF ST. LOUIS Research Dvson P.O. Box 44 S. Lous, MO 6366 The vews expressed are hose of he ndvdual auhors and do no necessarly reflec offcal posons of he Federal Reserve Bank of S. Lous, he Federal Reserve Sysem, or he Board of Governors. Federal Reserve Bank of S. Lous Workng Papers are prelmnary maerals crculaed o smulae dscusson and crcal commen. References n publcaons o Federal Reserve Bank of S. Lous Workng Papers (oher han an acknowledgmen ha he wrer has had access o unpublshed maeral) should be cleared wh he auhor or auhors.

2 Inflaon: Do Expecaons Trump he Gap? * Jeremy M. Pger Federal Reserve Bank of S. Lous Rober H. Rasche Federal Reserve Bank of S. Lous Frs Draf: March, 006 Ths Draf: July, 006 Absrac: We measure he relave conrbuon of he devaon of real acvy from s equlbrum (he gap), supply shock varables, and long-horzon nflaon forecass for explanng he U.S. nflaon rae n he pos-war perod. For alernave specfcaons for he nflaon drvng process and measures of nflaon and he gap we reach a smlar concluson: he conrbuon of changes n long-horzon nflaon forecass domnaes ha for he gap and supply shock varables. Pu anoher way, varaon n longhorzon nflaon forecass explans he bulk of he movemen n realzed nflaon. Furher, we fnd evdence ha long-horzon forecass have become subsanally less volale over he sample perod, suggesng ha permanen shocks o he nflaon rae have moderaed. Fnally, we use our preferred specfcaon for he nflaon drvng process o compue a hsory of model-based forecass of he nflaon rae. For boh shor and long horzons hese forecass are close o nflaon expecaons n surveys and marke daa. Keywords: Inflaon perssence, Inflaon forecas, Phllps Curve JEL Codes: C3, E3 * Pger: Research Deparmen, Federal Reserve Bank of S. Lous, P.O. Box 44, S. Lous, MO 6366 (pger@sls.frb.org); Rasche (correspondng auhor): Research Deparmen, Federal Reserve Bank of S. Lous, P.O. Box 44, S. Lous, MO 6366 (rasche@sls.frb.org). The vews expressed here are hose of he auhors and do no necessarly reflec offcal posons of he Federal Reserve Bank of S. Lous, he Federal Reserve Sysem, or he Board of Governors.

3 . Inroducon The Phllps Curve s one of he mos wdely recognzed conceps n modern macroeconomcs, and s wdely used as boh a heorecal consruc and emprcal ool. A he core of he Phllps Curve s a relaonshp beween nflaon and he real acvy gap, defned as he devaon of real economc acvy from s equlbrum level. The whn-sample sascal suppor for such a relaonshp n U.S. daa over he pos-war perod s well documened n a number of sudes, prmary among hem he work of Rober Gordon over he pas 0 years (Gordon, 98, 997, 998). In parcular, he gap s srongly sascally sgnfcan as an explanaory varable for nflaon, and hs sgnfcance s robus o a broad range of specfcaons of he Phllps Curve. More recenly, a number of papers have evaluaed he ou-of-sample forecasng performance of he Phllps curve. Here he evdence n favor of he gap as a drver for nflaon s more mxed, wh some papers documenng a subsanal ouof-sample relaonshp, (e.g. Sock and Wason, 999), whle ohers fnd ha nflaon forecass from a Phllps curve are no beer han hose from smple benchmark models such as a random walk or an auoregresson (e.g. Akeson and Ohanan, 00; Orphandes and Van Norden, 003). Clark and McCracken (003) provde a horough exploraon of he n-sample vs. ou-of-sample performance of he Phllps Curve. In hs paper we revs he mporance of he gap as an explanaory varable for U.S. nflaon over he pos-war perod. However, raher han measure mporance wh sascal sgnfcance, we nsead focus on he relave conrbuon of he gap and oher poenal nflaon drvers, such as changes n long-horzon nflaon forecass and supply shock varables, for explanng he realzed nflaon rae. The nal analyss uses a specfcaon for he nflaon drvng process smlar o ha espoused by Gordon (98, 997, 998). Subsequenly we

4 nvesgae a specfcaon ha replaces he dsrbued lag on he nflaon rae presen n he Gordon specfcaon wh a me-varyng nercep ha follows a random walk process. We show ha hs me-varyng nercep (TVI) model can be resaed n erms of he forward forecas of he nflaon rae and dsrbued lags on he gap and supply shock varables. The resuls from boh he Gordon and TVI specfcaons are clear: Changes n long-horzon nflaon forecass domnae he gap and supply shock varables n he deermnaon of acual nflaon. We hen urn o more dealed analyss of he TVI model-based nflaon forecass. To begn, we allow for a sequence of srucural breaks n he varance of shocks o he random walk nercep. The esmaes dsplay a hump-shaped paern, wh he varance rsng subsanally durng he lae 960s and he 970s from s value n he 950s and early 960s, fallng subsanally n he early 980s, and fallng agan n he early 990s o s lowes level observed over he pos-war perod. Ths suggess ha he sze of permanen shocks o he nflaon rae have vared subsanally over he sample perod. Nex, we use he TVI specfcaon o consruc hsores of boh shor (one-monh ahead) and long (0-year ahead) nflaon forecass and compare hese o survey-based nflaon forecass. The model-based forecass are que close o he survey measures of expeced nflaon, suggesng ha he TVI model provdes a good descrpon of he evoluon of expecaons. Gven hs success, we hen use he model-based measures of expeced nflaon o derve me seres esmaes of ex ane real neres raes a varous horzons for he pas 50 years. The remander of he paper proceeds as follows: Secon presens resuls for he Gordon-ype Phllps Curve specfcaon, whle Secon 3 descrbes he TVI model and presens Ths resul s remnscen of fndngs n he bond prcng leraure ha sugges changes n long-horzon nflaon expecaons are he domnan source of varaon n long-horzon bond yelds (e.g. Gürkaynak, Sack and Swanson, 003; Rudebusch and Wu, 004). Usng a model wh sochasc volaly, Sock and Wason (006) also fnd subsanal varably n he varance of shocks o he sochasc rend of nflaon.

5 resuls from hs specfcaon. Secon 4 compares he measures of nflaon forecass from he TVI model o survey-based measures of expeced nflaon and presens new esmaes of ex ane real neres raes over he pos-war perod usng he model-based nflaon forecass. Secon 5 concludes.. Resuls from he Gordon-Type Specfcaon. Model specfcaon and esmaon We begn wh he specfcaon ha s feaured n varous analyses conduced by Rober Gordon: π = a( L) π b( L) D c( L) X ε () Ths model relaes he rae of nflaon o a long (ypcally 4 quarer) dsrbued lag on nflaon, a dsrbued lag on eher he unemploymen rae or he devaon of he unemploymen rae from a me-varyng NAIRU (an ndex of excess demand, D,) dsrbued lags on varous supply shock varables ncludng changes n relave mpor prces, changes n he relave prce of food and energy, and/or devaons of producvy from rend, and dummy varables for he begnnng and ermnaon of he Nxon prce conrols n he early 970s (a vecor of supply shocks, X ). The dsrbued lag on nflaon, a( L) π, s generally nerpreed as reflecng he nfluence of several pas years of nflaon behavor on curren prce-seng, hrough some combnaon of expecaon formaon and overlappng wage and prce conracs. (Gordon, 998, p. 303) Our specfcaon dffers from ha n Gordon (998) n ha ) measures he gap usng he oupu gap, defned as he percenage devaon of real GDP from poenal GDP as measured by he CBO, ) uses four lags on all varables (n conras o he 4 lags on nflaon 3

6 used by Gordon), and 3) does no nclude he producvy devaons presen n he Gordon specfcaon. We use changes n mpor prces relave o he GDP prce ndex and changes n he core PCE prce ndex relave o he PCE prce ndex as does Gordon. All he esmaons follow Gordon and exclude a consan erm. 3 We consruc parallel analyses for he CPI, he PCE prce ndex and he GDP prce ndex, each of whch s measured n quarerly percenage changes a annual raes. Our esmaes over he same 96:Q 998:Q sample perod used n Gordon (998) are shown n Table. The dsrbued lag varables are specfed so ha he esmaed sum of he lag coeffcens appears n bold as he coeffcen on he frs varable (he frs varable n each lag dsrbuon s n levels, all subsequen varables are frs dfferences). In each of he hree regressons he sum of he esmaed coeffcens on lagged nflaon s no sgnfcanly dfferen from uny and ndeed never dffers from.0 by more han. The esmaed sum of he coeffcens on he oupu gap ranges from 0. o 0.6 and, conssen wh pror research, s hghly sgnfcan for all hree prce ndces. The esmaed sum of he coeffcens on changes n relave mpor prces ranges from 0.5 o 0.8 and s sgnfcan n wo of he hree equaons. The sgn of he sum of he esmaed coeffcens on changes n he relave prce of food and energy s no conssen across he hree equaons, and s no sgnfcan n any equaon, hough he mpac effec of hs varable s always large and sgnfcan.. Sably We nvesgae he robusness of hese resuls n Fgures -3, where we consruc forward and backward recursve regressons for each of he hree measures of nflaon. In he forward 3 Some nal regressons were consruced ha ncluded he consan erm. The esmaed consan was nsgnfcan and he esmaes of he parameers of neres were unaffeced by s omsson. 4

7 recursons he sample perod always begns n 96:Q. Inally he sample ends n 970:Q and hen s exended one quarer a a me hrough 005:Q. The graphs show he sum of he lag coeffcens on each of he four regressors. Once he sample ges suffcenly long, around 80 quarers, he long-run coeffcens on each of he varables seles down. However, for sample perods of less han 80 quarers he esmaed long-run coeffcens on he oupu gap, changes n relave mpor prces and changes n relave food and energy prces are very sensve o addonal observaons. For very shor sample perods (4 o 40 quarers) he sum of he lagged nflaon coeffcens n he CPI regresson s subsanally less han.0, bu as he sample lengh s ncreased he esmae becomes very sable a close o.0. For he PCE and GDP measures of nflaon he sum of he lagged nflaon coeffcens becomes close o.0 even for very shor samples. In some cases he sum of hese esmaed coeffcens even exceeds.0 mplyng, on he face of, an explosve process. In he backward recursve regressons he sample sze ncreases from he mos recen observaons. In all cases he end of he sample s fxed a 005:Q and he begnnng of he sample s nally 994:Q3 and hen shfed backward a quarer a a me unl 96:Q. In hese expermens he esmaed coeffcens on he change n relave mpor prces and he change n he relave prce of food and energy are hghly unsable across sample perods ha use only he daa from he lae 80s and 90s, regardless of he measure of nflaon chosen. Over hese same sample perods he esmaed coeffcen on he sum of he oupu gap erms s very small relave o he esmaed value n he longer sample perods. Fnally he sum of he esmaed lag coeffcens on nflaon s farly close o.0 regardless of he lengh of he sample perod n he backward recursve regressons. 5

8 .3 How much does he gap conrbue o explanng he nflaon process? In hs subsecon we nvesgae he relave conrbuon of he oupu gap for explanng nflaon dynamcs. We begn hs analyss wh Fgure 4. The panels n hs fgure llusrae he margnal adjused R defned as: s.0 s whgap nogap where s whgap s he squared sandard error of esmae from he regresson wh all he regressors ncludng he dsrbued lag on he oupu gap and s nogap s he squared sandard error of esmae from he regresson ha excludes he dsrbued lag on he oupu gap. For shor sample perods, probably no surprsngly gven he nsably of he coeffcen esmaes noed above, hs sasc s que varable for he forward recursve regressons for he hree measures of nflaon. For he PCE and GDP measures of nflaon for some samples he sasc s even negave, ndcang ha he oher regressors accoun for a hgher percenage of he varance of nflaon n he absence of he gap erms han does he full regresson specfcaon ncludng he gap erms. For he longer sample regressons usng he PCE or GDP measures of nflaon, he margnal conrbuon of he gap erms o accounng for he varance of nflaon s que low; on he order of 8 o 0 percen. For he CPI measure of nflaon he pcure s dfferen. The hghes margnal conrbuon of he gap erms occurs for he shorer sample perods (lae 60s and 70s) where a mes he sasc exceeds For he longer samples he sasc s generally around 0.4, subsanally larger han compued for he oher wo measures of nflaon bu sll ndcang relavely lle margnal explanaory power for he oupu gap erms. 6

9 The margnal adjused R from he reverse recursve regressons presen a conras o he sascs for he forward recursve regressons, bu do no aler he concluson ha he margnal explanaory power of he oupu gap erms s mnmal. The resuls for he CPI and GDP measures of nflaon are hghly varable as he sample sze changes. In conras, he resuls for he PCE measure of nflaon are negave for he samples ha nvolve only he mos recen years of daa. Anoher way o address hs queson s o compare he values of he erms a L) π, ( b ) ( L D, c L) X ( and ε for a regresson over he enre sample perod. These are shown n Fgure 5-7 for regressons consruced on he sample 96: 005:. The message from hese graphs s apparen and conssen wh he analyss above: he oupu gap (and supply shock varables) accouns for only a mnor poron of flucuaons n nflaon n hs specfcaon regardless of he measure of nflaon. In summary: for hs model, expecaons, as proxed by a dsrbued lag on nflaon whose coeffcens sum o.0, rump he gap! 3. Resuls from he Tme-Varyng Inercep Specfcaon Suppose ha he dsrbued lag on nflaon n he Gordon specfcaon represens a proxy for long-horzon expeced nflaon ha s specfed o appear wh a coeffcen of.0 so ha he long-run Phllps curve s vercal: π =.0π b( L) D c( L) X ε () e Alernavely hs equaon can be hough of as specfyng a me-varyng nercep (he expeced rae of nflaon) on a vecor of.0 s: 7

10 π =.0z b( L) D c( L) X ε (3) We assume ha z follows a random walk: 4 z = μ (4) z Equaon (4) mples ha, assumng saonary of D and X, he nfne-horzon forecas of nflaon s equal o z (see Beverdge and Nelson, 98). Thus, z has he nerpreaon of he long-horzon nflaon expecaon. 5 We esmae he model n (3) and (4) va maxmum lkelhood usng he Kalman fler. The esmaes of he model parameers are shown n Table for he sample perod 96:Q o 005:Q. Table also shows he sandard error of he esmae for he Gordon equaon esmaed over he same sample perod, whch demonsraes ha he me-varyng nercep specfcaon s compeve wh he Gordon specfcaon. We focus our analyss on an expanded verson of he me-varyng nercep specfcaon, he resuls of whch are presened n Table 3. Frs, we exend he sample perod back n me o nclude daa subsequen o he end of he Korean War. Snce he core PCE daa are no avalable before 959, we recompue he relave change n food and energy prces usng CPI daa. The core CPI s avalable sarng n 957. Pror o 957 we use he all ems CPI less food raher han he core CPI. The wo seres are hghly correlaed n he lae 950s, snce energy prces were no hghly volale unl he early 970s. Pror o 987 we compue he relave change n food and energy prces usng CPI daa on a 967=00 base, no seasonally adjused, and apply 4 Ths s smlar o Gordon s specfcaon of he me-varyng NAIRU n hs 997 and 998 papers. 5 Equaon (4) assumes ha he shocks o long-horzon nflaon expecaons are frequen and connuous. An alernave s ha shocks o long-horzon nflaon expecaons are nfrequen and dscree. For an example of such a specfcaon for modelng U.S. nflaon see Levn and Pger (00, 006). 8

11 he curren seasonal facors for hese years usng he base year daa. We do hs o avod he runcaon problems ha affec he compuaon of CPI nflaon raes n he early par of he sample perod when he base year s = 00 (see Kozck and Hoffman, 004). Second, we allow for srucural breaks n he varance of he nnovaons o he mevaryng nercep process o occur a several pons n he sample ha algn wh well known macroeconomc and moneary evens. The frs break s allowed o occur a he begnnng of he Grea Inflaon, whch we dae o he frs quarer of 967. The second break s mean o capure he begnnng of he large reducon n U.S. macroeconomc volaly ha has been observed over he pas wo decades. Based on he fndngs of Km and Nelson (999) and McConnell and Perez-Quros (000), we dae he begnnng of hs Grea Moderaon o he frs quarer of 984. We dae he hrd break a he frs quarer of 994 when he FOMC sared releasng nformaon on changes n he nended federal funds rae a he close of FOMC meengs. As Table 3 demonsraes, for all hree measures of nflaon he esmaed varance of he nnovaons o he me-varyng nercep ncreases sharply durng he Grea Inflaon, falls o percen of s value durng he frs decade of he Grea Moderaon, and hen declnes by roughly 50 percen of he value n he perod durng he mos recen decade (see Fgure 8 for a plo of he esmaed nnovaons). Ths paern for he volaly of shocks o he random-walk nercep suggess ha he sze of permanen shocks o he nflaon rae have vared subsanally over he sample perod, and ha such shocks are now que small from a hsorcal perspecve. The laes declne n volaly s conssen wh he noon ha longhorzon nflaon expecaons have become beer anchored durng he perod of ncreasng FOMC ransparency, alhough hs s no necessarly evdence of a causal relaonshp beween ncreased ransparency and lower volaly of long-erm nflaon expecaons. 9

12 The esmaes of he me-varyng nercep and he conrbuons of he gap and supply shocks from he esmaes n Table 3 are shown n Fgures 9- for he hree measures of nflaon. These graphs ndcae ha he me-varyng nercep erm domnaes he varaon n all hree measures of nflaon. The only cases where he dsrbued lags on he oupu gap and he supply shock erms accoun for a subsanal poron of he nflaon raes are n and o a lesser exen n Fnally, Fgure demonsraes ha he esmaed auocorrelaons of esmaed resduals of he PCE and GDP nflaon equaons are very small, hough here s some auocorrelaon n he resduals of he CPI nflaon equaon. In Table 4 anoher se of regressons wh a me-varyng nercep are repored, bu n hs case he CBO measure of he oupu gap has been replaced by he dfference beween he unemploymen rae and a me-varyng esmae of he NAIRU. We follow Gordon (997) and model he NAIRU as a random walk and consran he sandard devaon of he error erm n hs process o 0.. In addon a resrcon on he level of he NAIRU s requred n order o denfy hs process n he presence of he me-varyng nercep erm. We have resrced he NAIRU o equal he unemploymen rae n 995:, conssen wh Fgure 3 n Gordon (997). These resuls are subsanally he same as hose obaned wh he CBO oupu gap, suggesng ha our conclusons abou he conrbuon of he gap are no sensve o wheher s measured as an oupu or unemploymen gap. 4. TVI Model-Based Inflaon Forecass The TVI specfcaon n equaons (3-4) can be rewren n erms of he forward expecaon of he nflaon rae and dsrbued lags on he gap and supply shock varables, a 0

13 specfcaon ha has much n common wh he New Keynesan formulaon of he Phllps curve (Clarda, Gal and Gerler, 999). To begn, rewre equaon (3) as: N X D z ε α π = = 0 (5) where a s a vecor of coeffcens aken from he lag polynomals ) (L b and ) (L c and N s he lag order of hese lag polynomals. Incremenng he me ndex n equaon (5) by one quarer and akng condonal expecaons yelds: = = N X D X D E z E E 0 ] [ ] [ α α π, (6) Assume ha X D can be modeled as a saonary VAR process: 6 0 = = J v X D X D β. (7) Then: [ ] = = = N J X D X D z E 0 0 α β α π. (8) 6 Our forecasng model for ( ) ', S D s a resrced four lag VAR. Esmaes of an unresrced VAR, ( )( ) ', ) ( = v S D L I β ndcaed a lower rangular srucure for ) (L β when he hree varables are ordered ) relave food and energy prce changes, ) relave mpor prce changes and 3) he oupu gap. Ths srucure was mposed o generae our forecass.

14 Snce X D s assumed o be saonary, M M z E = π lm. Thus z represens he long horzon nflaon forecas from he model and, n he sense of Beverdge and Nelson (98), represens he long-run or permanen componen of nflaon. Lkewse, = = N J X D X D 0 0 α β α s hen he one-perod ahead ransory componen of expeced nflaon. 7 The nflaon forecas error from he TVI specfcaon s gven by: [ ] ] [ = = = J v X D X D E ε α μ ε β α μ π π. (9) Thus unpredced nflaon s he sum of hree erms: ) he nnovaon o long-horzon nflaon expecaons, ) he one-perod ahead forecas error for X D, and 3) he resdual of he Phllps curve. When 0 0 = α he one-perod ahead unexpeced nflaon s jus [ ] = E ε μ π π. Fnally, gven he expresson for [ ] E π, he Phllps Curve can be rewren as he sum of he forward predcon of he nflaon rae and dsrbued lags on he gap and supply shock varables: [ ] N N N N J X D X D X D E ε α α α β α π π = = = ] [. (0) 7 By consrucng mulsep dynamc forecass of ( ) ' X D he enre pah of he ransory componen of expeced nflaon can be esmaed.

15 In Fgures 3a 5a he acual nflaon raes are ploed agans he one-perod ahead projecons E [ π ] usng he esmaed coeffcens from Table 3. The mddle panels of each fgure (3b 5b) show he dfferences n he seres from he op panels he one-perod ahead nflaon forecas errors. 8 Fnally, he lower panels of each fgure (3c 5c) show he frs auocorrelaons of he compued one-perod ahead nflaon forecas errors. Noe ha for all hree nflaon measures he auocorrelaons are very small ndcang ha here s lle predcve conen n he hsory of he forecas errors for fuure forecas errors. In Fgure 6 we compare our esmaes of he one-perod ahead nflaon rae wh varous survey measures of expeced nflaon. There are wo surveys ha are avalable for CPI nflaon: he one-quarer ahead nflaon forecas from he Survey of Professonal Forecasers (avalable from 98:3 hrough 005:) and he one-quarer ahead nflaon forecas from he Blue Chp (avalable from 985: hrough 005:). The nflaon forecas measure from he TVI model s ploed n black n all hree panels of Fgure 6. The forecass from he Survey of Professonal Forecasers are ploed n blue (SPF -quarer) and he forecass from he Blue Chp are ploed n Green (BC-quarer). There s one survey avalable for GDP nflaon: he one-quarer ahead forecas from he Survey of Professonal Forecasers (avalable from 968:4 hrough 005:). Ths s ploed n blue (SPF -quarer) n he boom panel of Fgure 6. From he early 980s, he TVI esmaes rack he respecve survey measures que closely. In parcular for CPI nflaon he major spkes n he me-varyng nercep esmaes of nflaon are mrrored n he mng, and n many cases n he amplude by spkes n he SPF -quarer measure. The Blue Chp CPI nflaon forecass are less volale han he oher wo measures, bu agan he major 8 For purposes of hese graphs, we ncorporae he effecs of he Nxon prce conrol dummy varables, Nxon_On and Nxon_Off. Whle hese varables were consruced by Gordon expos, we beleve s reasonable o assume ha a he me ndvduals expeced some mpac on nflaon n he shor run of he mplemenaon and removal of he conrols. 3

16 spkes n hs seres mrror he mng of he major spkes n he seres derved from he mevaryng nercep model. Ths vsual mpresson s confrmed by heeroskedascy and auocorrelaon conssen E regressons of he nflaon forecas from he TVI model [ ] cp on he correspondng survey measure. For he sample perod 98:3 005: he regresson wh he Survey of Professonal Forecasers measure s: E cp = 6.08spf (0.45) (0.4) _ cp ε R =.68, see =.3, dw =.00 whle for he sample perod 985: 005: he regresson wh he Blue Chp measure s: E cp = bc _Q ε (0.37) (0.) R =.49, see = 0.94, dw =.6 In boh regressons he esmaed consan erm s no sgnfcanly dfferen from zero and he esmaed coeffcen of he survey measure s no sgnfcanly dfferen from one. The esmaed sandard errors of he resduals of hese regressons are farly large, bu he Durbn- Wason sascs do no ndcae any frs-order seral correlaon. For he GDP nflaon measure we have daa o compare wh a survey sarng n lae 968. There are subsanal dfferences n he wo measures n he lae 960s and hen agan n 973. The laer perod s srongly nfluenced by our decson o nclude he esmaed effec of he removal of he prce conrols n he TVI measure of expeced nflaon. Afer 973 he wo measures rack que well, hough he spkes n he me-varyng coeffcen measure are no as well algned wh he survey daa as s he case wh he CPI nflaon rae. A regresson of he TVI measure (E - gdp ) on he survey measure over sample perod 968:4 005: s: 4

17 E gdp = 7.09spf (0.) (7) _ gdp ε R =.78, see =.0, dw =. Agan he esmaed consan erm s no sgnfcanly dfferen from zero nor s he esmaed coeffcen on he survey measure of GDP nflaon sgnfcanly dfferen from one. The esmaed sandard error of he resduals s comparable o ha found for he CPI nflaon regressons, bu n hs case he Durbn-Wason sasc suggess ha subsanal frs-order seral correlaon remans n he esmaed resduals. The esmaed me seres of he me-varyng nercep (he permanen componen of nflaon) are shown n Fgure 7. The seres for all hree nflaon raes are que smlar, hough he one derved from he CPI s more volale han he oher wo up o he Grea Moderaon perod. The esmaes sugges ha long-erm expeced nflaon rose sharply n he lae 60s from less han percen n 964 o over 4 percen n 968. All hree seres level off n he lae 60s and declne a b n he early 70s before he frs energy shock. From 973 unl 98 all he seres rend up. From he rend s reversed and he seres level ou around 4 percen for he remander of he 80s. Afer 990 all he seres agan rend down hrough he md 90s, afer whch hey level ou around percen. The fnal lne (SPF_0) ploed on Fgure 7 s he 0-year ahead CPI nflaon forecas from he Survey of Professonal Forecasers. The general rend n he long-erm expeced CPI nflaon from he TVI model racks ha n he survey daa que well for he perod for whch he laer seres are avalable: 99:4 hrough 005:. A regresson of he model generaed daa on he survey daa shows: 5

18 Z cp = Spf (0.) (8) nf R =.86, see = 0.4, dw = 0.63 The consan n he regresson s sgnfcanly less han zero and he coeffcen on he survey daa s sgnfcanly greaer han one. These resuls are drven by he consan value of he survey daa over he pas fve years. Neverheless he relaonshp beween he wo seres s que close as judged by he large R and he low esmaed sandard error of he resduals. Goodfrend (993) hypoheszes four perods of nflaon scares durng he 980s. These perods are December 979 hrough February 980, June 980 hrough Ocober 98, May 983 hrough Augus 983 and March 987 hrough Ocober 987. He defnes a sgnfcan long-rae rse n he absence of an aggressve funds rae ghenng an nflaon scare snce reflecs rsng expeced long-run nflaon (p.8). Hence hs nflaon scares are nferred from he behavor of long-erm raes relave o shor-erm raes. Snce we have a measure of long-erm nflaon expecaons ha s derved ndependenly of any nformaon on he behavor of neres raes, he esmaes can be used as an ndependen check on Goodfrend s nflaon scare hypohess. The approxmae perods desgnaed as nflaon scares are shaded n Fgure 7. 9 Our measure of long-erm expeced CPI nflaon jumps up sharply n he frs hree desgnaed nflaon scares. There are no sharp ncreases n our measures of long-erm expeced PCE or expeced GDP nflaon for he frs wo desgnaed nflaon scares. For he hrd nflaon scare, he measure of expeced long-erm PCE nflaon jumps up, bu hs follows a shor-lved downward spke of almos he same magnude. The measure of expeced long-erm GDP nflaon connues on a downward rend durng he hrd nflaon scare. Fnally, none of 9 The shaded perods are only approxmae snce Goodfrend worked wh monhly daa and our models are esmaed on quarerly daa. 6

19 our measures of long-erm expeced nflaon exhb any major movemen durng he fourh perod desgnaed as an nflaon scare. Hence our measures of long-erm expeced nflaon, parcularly hose for GDP and PCE nflaon, do no provde srong evdence n favor of he nflaon scare hypohess. As an alernave check on wheher he esmaed me-varyng nercep s a reasonable proxy measure for long-erm expeced nflaon, we can subrac he esmaed z for each of he hree nflaon equaons from a long-erm rae of neres o ge an esmaed ex ane long-erm real rae. We use he 0 year Treasury bond rae for hs purpose. These esmaes are shown n Fgures 8a-c. The horzonal lne s drawn for reference a percen. In recen hsory here are wo comparson measures. Begnnng n 99 he Survey of Professonal Forecasers repored survey responses for a 0 year-ahead CPI nflaon rae. The dfference beween he 0 year nomnal rae and hese survey responses s ploed as he blue lne n Fgures 8a-c. Snce 997 he U.S. Treasury has ssued long-erm ndexed bonds. The yeld on hese bonds s shown as he green lne n Fgures 8a-c. 0 Regressons of he mpled long-erm real raes from he TVI model on he mpled longerm real rae from he Survey of Professonal Forecasers over he sample perod 99:4-005: are: (0.) (5) [ lrae _0] lrae Zcp = spf (8) (4) [ lrae _0] lrae Zpce = spf R R =.90, see = 0.7, dw = 0.45 =.9, see = 0.4, dw = The comparsons are only exac n Fgure a snce he Survey of Professonal Forecasers refers o he CPI and he TIPS are ndexed o he CPI. 7

20 (6) () [ lrae _0] lrae Zgdp = spf R =.98, see = 0.3, dw =.05 Srcly speakng only he frs of hese hree regressons s an exac comparson, snce he survey daa refer he CPI. In ha regresson he esmaed consan erm s no sgnfcanly dfferen from zero, and he esmaed coeffcen on he survey measure of he real long-erm rae s no sgnfcanly dfferen from one. Hence he wo measures appear on average o dffer by an nsgnfcan consan (wh he model-generaed esmae larger) and o move up and down ogeher durng he sample perod. The same concluson s approprae for he model based measure of he long-erm real rae based on PCE nflaon relave o he long-erm real rae derved from he survey daa, hough n hs case he average dfference s sgnfcanly dfferen from zero. The regresson wh he long-erm real rae derved from he model based esmae of long-erm GDP nflaon moves sgnfcanly more han one-for-one wh he real rae derved from he survey daa. A second comparson of real raes s provded by he Treasury ndexed bond daa, hough only for a shor me perod: 997: 005:. The real long-erm raes derved from our model of long-erm expeced nflaon for all hree measured nflaon raes do no move sgnfcanly dfferenly from one-for-one wh he TIPS rae over hs sample perod. lrae Zcp = ps (0.4) (8) lrae Zpce = ps (0.) (7) lrae Zgdp = ps (0.) (7) R R R =.69, see = 0.48, dw = 0.35 =.77, see = 0.43, dw = 0.34 =.73, see = 0.46, dw =

21 In all hree cases he esmaed sandard error of he resduals of he regressons are larger han he esmaed sandard error of he resduals from he correspondng regresson wh he survey based measures of he long-erm real rae. Ths may sugges a closer relaonshp beween our model-based esmaes and he survey based esmaes han beween he model-based esmaes and he TIPS raes, bu he dfferences may only reflec he relavely shor sample perod durng whch he TIPS raes are avalable. The model can be used o generae mulperod nflaon forecass for any horzon. As he horzon ges longer he forecas of he ransory componen of nflaon goes o zero and he forecas converges on he esmaed permanen componen of nflaon. The forecass for nflaon one o four quarers ahead can be combned o generae a one-year ahead nflaon forecas. Ths forecas s subraced from he one-year consan maury Treasury rae o produce a one-year ahead esmaed ex ane real rae. These model based one-year real raes are ploed n Fgure 9a-c along wh one-year real raes derved usng Mchgan, Survey of Professonal Forecasers and Blue Chp survey measures of fuure CPI and GDP nflaon raes. For he CPI measures, he model-based real raes rack he survey-based measures very closely snce he 980s when he survey daa sar. The model-based measure for GDP nflaon racks he measure derved from he Survey of Professonal Forecasers snce he md 970s. Fnally, we can use he model-based esmaes of one-perod ahead expeced nflaon and a hree monh neres rae o consruc an ex ane hree monh real rae. The nomnal rae ha we use for hese calculaons s he secondary marke rae on hree monh Treasury blls. In Fgure 0a-c we compare he erm srucure of real neres raes. In each panel of ha fgure he black lne s he one-quarer ahead real rae compued from our models, he blue lne s he modelbased one-year ahead real rae, and he green lne s he model-based long-erm (0 year) real 9

22 rae dscussed n he prevous secon. The resuls n he hree panels are que conssen. In each case he real erm srucure appears very fla hroughou he 960s. In he 970s he real erm srucure became posvely sloped. The really neresng perod s ha of he early 980s he perod of he New Operang Procedures. Durng hs perod he model based esmaes mply ha he real erm srucure shfed up rapdly, bu ha he erm srucure remaned essenally fla for he enre perod. There s no evdence ha he esmaed real erm srucure nvered durng hs perod, hough he nomnal erm srucure became sharply nvered a he me. Begnnng n he early 80s he real erm srucure s almos always posvely sloped and s he seepes n 990- and snce 000. In hose wo perods real rae spreads n he -0 year range became que large, bu hose n he 3-monh o -year range remaned relavely small. 5. Concluson We have presened evdence regardng he relave conrbuon of he real acvy gap and oher poenal nflaon drvers, such as changes n long-horzon nflaon expecaons and supply shock varables, for explanng he U.S. nflaon rae over he pos-war perod. Our resuls sugges ha realzed nflaon s domnaed by varaon n long-horzon expeced nflaon, whle he gap and supply shock varables play only a very lmed role. These resuls are robus o alerave specfcaons for he nflaon drvng process and measures of nflaon and he gap. Our preferred model specfcaon s one n whch nflaon s deermned by a random walk permanen componen (whch represens he long-horzon nflaon expecaon), a dsrbued lag on he real acvy gap, and a dsrbued lag on supply shock varables. Modelbased nflaon forecass algn closely wh forecass obaned from surveys a all horzons durng 0

23 he years for whch he survey daa s avalable. Ths suggess ha our model of he nflaon drvng process does a very good job of reproducng whaever process s drvng survey measures of fuure nflaon. Resuls from hs model also sugges ha he varance of he process ha generaes changes n long-erm expeced nflaon has changed over me. Ineresngly, hs varance has become very small over he las 0 years of he sample, suggesng ha long-erm expeced nflaon has become much beer anchored n he pas decade. Taken ogeher, he evdence presened here suggess ha he key o undersandng he nflaon process s o undersand wha drves changes n long-horzon nflaon expecaons. To hs end, furher research focused on aempng o relae hese changes o news could prove especally fruful.

24 References Akeson, A. and L.E. Ohanan, 00, Are Phllps Curves Useful for Forecasng Inflaon?, Federal Reserve Bank of Mnneapols Quarerly Revew 5, -. Beverdge, S. and C.R. Nelson, 98, A New Approach o Decomposon of Economc Tme Seres no Permanen and Transory Componens wh Parcular Aenon o Measuremen of he Busness Cycle, Journal of Moneary Economcs 7, 5-74 Clarda, R., J. Galí and M. Gerler, 999, The Scence of Moneary Polcy: A New Keynesan Perspecve, Journal of Economc Leraure 37, Clark, T. E. and M. W. McCracken, 003, The Predcve Conen of he Oupu Gap for Inflaon: Resolvng In-Sample and Ou-of-Sample Evdence, Federal Reserve Bank of Kansas Cy workng paper RWP Goodfrend, M., 993, Ineres Rae Polcy and he Inflaon Scare Problem: , Federal Reserve Bank of Rchmond Economc Quarerly 79, -4. Gordon, R. J., 98, Inflaon, Flexble Exchange Raes and he Naural Rae of Unemploymen, n Baly, M.N., ed., Workers, Jobs and Inflaon, Washngon, DC: Brookngs Insuon, pp Gordon, R. J., 997, The Tme-Varyng NAIRU and s Implcaons for Economc Polcy, Journal of Economc Perspecves, -3. Gordon, R. J., 998, Foundaons of he Goldlocks Economy: Supply Shocks and he Tme Varyng NAIRU, Brookngs Papers on Economc Acvy, Gürkaynak, R. S., B. Sack, and E. Swanson, 003, The Excess Sensvy of Long- Term Ineres Raes: Evdence and Implcaons for Macroeconomc Models, manuscrp, Federal Reserve Board. Km, C.-J., and C.R. Nelson, 999, Has he U.S. Economy Become More Sable? A Bayesan Approach Based on a Markov-swchng Model of he Busness Cycle, The Revew of Economcs and Sascs 8, Kozck, S. and B.Hoffman, 004, Roundng Error: A Dsorng Influence on Index Daa, Journal of Money, Cred, and Bankng 36, Levn, A. and J. Pger, 00, Is Inflaon Perssence Inrnsc In Indusral Economes?, Federal Reserve Bank of S. Lous Workng Paper # Levn, A. and J. Pger, 006, Bayesan Model Selecon for Mulple Srucural Break Models, manuscrp, Federal Reserve Bank of S. Lous.

25 McConnell, M. M. and G. P. Quros, 000, Oupu flucuaons n he Uned Saes: Wha has Changed Snce he Early 980s?, Amercan Economc Revew, 90, Orphandes, A. and S. van Norden, 003, The Relablly of Inflaon Forecass based on Oupu Gap Esmaes n Real Tme, Scenfc Seres 003s-0, CIRANO. Rudebusch, G. D. and T. Wu, 004, A Macro-Fnance Model of he Term-Srucure, Moneary Polcy, and he Economy, Federal Reserve Bank of San Francsco Workng Paper # Sock, J. H. and M.W. Wason, 999, Forecasng Inflaon, Journal of Moneary Economcs 44, Sock, J. H. and M.W. Wason, 006, Why has U.S. Inflaon Become Harder o Forecas?, NBER workng paper #34. 3

26 Table : Gordon-Type Regressons CPI PCE GDP π () () () Δπ (9) (9) (9) Δπ (9) (0.0) (9) Δπ (8) (9) (9) Gap (4) (3) (4) Δ Gap 7 7 (0.) (8) (0.0) ΔGap 0.3 (0.) (8) (0.0) ΔGap (0.) (8) (0.0) Gap Δ 3 (0.) (8) (0.0) Δ Rel Impor Prces (0.) (9) (0.) Δ Rel Impor Prces (0.) (8) (0.0) Δ Rel Impor Prces (9) (7) (9) Δ Rel Impor Prces (8) (6) (8) Δ Rel Impor Prces (6) (5) (6) Δ Rel Fd & Energy Prces (0.90) (0.7) (0.86) Δ Rel Fd & Energy Prces (0.85) (0.66) (0.8) Δ Rel Fd & Energy Prces (0.88) (0.68) (0.77) Δ Rel Fd & Energy Prces (0.8) (0.63) (0.66) Δ Rel Fd & Energy Prces (0.63) (0.47) (0.5) NIXON_ON (0.58) (0.46) (0.56) NIXON_OFF (0.63) (0.5) 0.60 R Mean Inflaon Rae Sd Error of he Inflaon Rae Sandard Error of he Esmae Durbn-Wason Sasc

27 Table : Tme-varyng Inercep Model wh CBO Gap CPI PCE GDP Sandard Devaon of Inercep (8) (5) (5) Gap (0.0) (6) (0) Gap 0 0 (0) (0) (7) Gap (0) (0) (0) Gap (0.) (8) (0) Gap (0.) (8) (9) Δ Rel Impor Prces (6) (4) (4) Δ Rel Impor Prces (6) (4) (5) Δ Rel Impor Prces (7) (5) (5) Δ Rel Impor Prces (6) (4) (5) Δ Rel Impor Prces (5) (4) (4) Δ Rel Fd & Energy Prces (0.33) (0.3) (0.5) Δ Rel Fd & Energy Prces (0.34) (0.3) (0.5) Δ Rel Fd & Energy Prces (0.36) (0.4) (0.9) Δ Rel Fd & Energy Prces (0.35) (0.3) (0.4) Δ Rel Fd & Energy Prces (0.7) (0.) (0.5) NIXON_ON (0.97) (0.65) (0.67) NIXON_OFF (0.79) (0.50) (0.59) Log Lkelhood Sandard Error of he Esmae Sandard Error of he Esmae (Gordon equaon) 5

28 Table 3: Tme-varyng Inercep Model wh CBO Gap and break n he Varance of he Inercep n 967, 984 and 994 CPI PCE GDP Sandard Devaon of Inercep (0.5) (0.) (0.5) Sandard Devaon of Inercep (0.9) (0.6) (0.) Sandard Devaon of Inercep (9) (6) (8) Sandard Devaon of Inercep (5) (6) (8) Gap (7) (7) (9) Gap (9) (9) (0.0) Gap (0.0) (9) (0.) Gap (0.0) (9) (0.) Gap (8) (7) (9) Δ Rel Impor Prces (4) (4) (5) Δ Rel Impor Prces (4) (4) (5) Δ Rel Impor Prces (4) (5) (5) Δ Rel Impor Prces (4) (4) (5) Δ Rel Impor Prces (4) (4) (5) Δ Rel Fd & Energy Prces (0.) (0.8) (0.) Δ Rel Fd & Energy Prces (0.) (0.3) (0.3) Δ Rel Fd & Energy Prces (0.) (0.3) (0.) Δ Rel Fd & Energy Prces (0.) (0.9) (0.33) Δ Rel Fd & Energy Prces (0.) (0.8) (0.) NIXON_ON (.75) (.08) (0.96) NIXON_OFF (.6) (0.73) 0.7 Log Lkelhood Sandard Error of he Esmae

29 Table 4: Tme-varyng Inercep Model wh Tme-varyng NAIRU and break n he Varance of he Inercep n 967, 984 and 994 CPI PCE GDP Sandard Devaon of Inercep (0.5) (0.0) (0.5) Sandard Devaon of Inercep (0.9) (0.5) (0.) Sandard Devaon of Inercep (7) (8) (8) Sandard Devaon of Inercep (6) (6) (7) NAIRU Gap (0.3) (0.9) (0.9) NAIRU Gap (0.5) (0.7) (0.5) NAIRU Gap (0.35) (0.8) (0.36) NAIRU Gap (0.34) (0.9) (0.37) NAIRU Gap (0.3) (0.9) (0.3) Δ Rel Impor Prces (4) (4) (5) Δ Rel Impor Prces (4) (4) (4) Δ Rel Impor Prces (4) (4) (5) Δ Rel Impor Prces (4) (4) (5) Δ Rel Impor Prces -4-3 (4) (4) (4) Δ Rel Fd & Energy Prces (0.) (0.8) (0.) Δ Rel Fd & Energy Prces (0.0) (0.8) (0.3) Δ Rel Fd & Energy Prces (0.) (0.) (0.) Δ Rel Fd & Energy Prces (0.9) (0.8) (0.) Δ Rel Fd & Energy Prces (0.0) (0.8) (0.) NIXON_ON (.69) (.09) (0.94) NIXON_OFF (.3) (0.73) (0.69) Log Lkelhood Sandard Error of he Esmae

30 Fgure CPI Inflaon Rae -- Gordon Equaon.5 Recursve Coeffcens of Lagged Inflaon 0.30 Recursve Coeffcens of Oupu Gap Forward Reverse Forward Reverse 0.8 Recursve Coeffcens of Relave Impor Prces 3 Recursve Coeffcens of Change n Food & Energy Prces Forward Reverse Forward Reverse 8

31 Fgure PCE Inflaon Rae -- Gordon Equaon.5 Recursve Coeffcens of Lagged Inflaon 0.30 Recursve Coeffcens of Oupu Gap Forward Reverse Forward Reverse 0.8 Recursve Coeffcens of Relave Impor Prces 3 Recursve Coeffcens of Change n Food & Energy Prces Forward Reverse Forward Reverse 9

32 Fgure 3 GDP Inflaon Rae -- Gordon Equaon.5 Recursve Coeffcens of Lagged Inflaon 0.30 Recursve Coeffcens of Oupu Gap Forward Reverse Forward Reverse 0.8 Recursve Coeffcens of Relave Impor Prces 3 Recursve Coeffcens of Change n Food & Energy Prces Forward Reverse Forward Reverse 30

33 Fgure 4 Margnal R Squares of Recursve Regressons 0.50 CPI Recursve Regressons Forward Reverse 0.50 PCE Recursve Regressons Forward Reverse 0.50 GDP Recursve Regressons Forward Reverse 3

34 Fgure 5 CPI Inflaon: Gordon Equaon: Sample Perod 96: - 005: Conrbuon of Lagged Inflaon Conrbuon of Supply Shocks INFCPI LAGINF INFCPI SUPPLY Conrbuon of Oupu Gap Resdual Conrbuon INFCPI LAGGAP INFCPI RESID 3

35 Fgure 6 PCE Inflaon: Gordon Equaon: Sample Perod 96: - 005: Conrbuon of Lagged Inflaon Conrbuon of Supply Shocks INFPCE LAGINF INFPCE SUPPLY Conrbuon of Oupu Gap Resdual Conrbuon INFPCE LAGGAP INFPCE RESID 33

36 Fgure 7 GDP Inflaon: Gordon Equaon: Sample Perod 964: - 005: Conrbuon of Lagged Inflaon Conrbuon of Supply Shocks INFGDP LAGINF INFGDP SUPPLY Conrbuon of Oupu Gap Resdual Conrbuon INFGDP LAGGAP INFGDP RESID 34

37 6 Fgure 8 Shocks o Permanen Inflaon CPI PCE GDP 35

38 Fgure 9 One-Perod Ahead CPI Inflaon Componens Tme-varyng consan Gap Componen IN F_C PI ZC() IN F_C PI GAPC() Energy Prce Componen Impor Prce Componen IN F_C PI EN C() IN F_C PI IMPC () 36

39 Fgure 0 One-Perod Ahead PCE Inflaon Componens.5 Tme-varyng consan.5 Gap Componen IN F_PC E ZC() IN F_PC E GAPC ().5 Energy Prce Componen.5 Impor Prce Componen IN F_PC E ENC() IN F_PC E IMPC () 37

40 Fgure One-Perod Ahead GDP Inflaon Componens.8 Tme-varyng consan.8 Gap Componen IN F_GDP ZC(3) IN F_GDP GAPC(3) Energy Prce Componen 4 Impor Prce Componen IN F_GDP ENC (3) IN F_GD P IMPC (3) 38

41 Fgure.00 a) Auocorrelaons of CPI Inflaon Esmaed Resduals b) Auocorrelaons of PCE Inflaon Esmaed Resduals c) Auocorrelaons of GDP Inflaon Esmaed Resduals

42 Fgure 3 a) CPI nflaon and predced nflaon - wh varance breaks b) CPI Predcon Errors - wh varance breaks c) Auocorrelaons of CPI Predcon Errors

43 Fgure 4 a) PCE nflaon and predced nflaon - wh varance breaks b) PCE Predcon Errors - wh varance breaks c) Auocorrelaons of PCE Predcon Errors

44 Fgure 5 4 a) GDP nflaon and predced nflaon - wh varance breaks b) GDP Predcon Errors - wh varance breaks c) Auocorrelaons of GDP Predcon Errors

45 Fgure 6 One-perod Predced CPI Inflaon - wh varance breaks Predced Inflaon SPF -Quarer BC -Quarer One-perod Predced PCE Inflaon - wh varance breaks Predced Inflaon 6 One-perod Predced GDP Inflaon - wh varance breaks Predced Inflaon SPF -Quarer BC -Quarer 43

46 Fgure 7 6 Expeced Long-erm Inflaon -- Z & SPF Z_cp Z_pce Z_gdp SPF_0 44

47 Fgure a) Long-erm Real Rae -- CPI Expeced Inflaon Ex-ane Real Long Rae Real Rae from SPF TIIS Two 8.4 b) Long-erm Real Rae -- PCE Expeced Inflaon Ex-ane Real Long Rae Real Rae from SPF TIIS Two 9.6 c) Long-erm Real Rae -- GDP Expeced Inflaon Ex-ane Real Long Rae Real Rae from SPF TIIS Two 45

48 Fgure 9 One-Year Exane Real Treasury Rae a) One-Year Real Raes CPI Expeced Inflaon Model-based One-year Real Rae MI Survey One-year Real Rae SPF Survey One-year Real Rae Blue Chp One-Year Real Rae b) One-Year Real Raes PCE Expeced Inflaon Model-based One-year Real Rae c) One-Year Real Raes GDP Expeced Inflaon Model-based One-year Real Rae SPF Survey One-year Real Rae Blue Chp One-Year Real Rae 46

49 Fgure 0 Real Treasury Rae Term Srucure a) Real Raes: CPI Expeced Inflaon Monh Real Rae One-year Real Rae Long-erm Real Rae b) Real Raes PCE Expeced Inflaon Monh Real Rae One-year Real Rae Long-erm Real Rae c) Real Raes GDP Expeced Inflaon Monh Real Rae One-year Real Rae Long-erm Real Rae 47