No. -4 Inflaion Expecaions and he Evoluion of U.S. Inflaion Jeffrey C. Fuhrer Absrac: Much recen commenary has cenered on he imporance of well-anchored inflaion expecaions as he foundaion of a well-behaved inflaion rae. Bu he difficuly in relying on his principle is ha inflaion expecaions are no direcly observable. Thus i is hard o know wheher expecaions play such an anchoring role in he evoluion of inflaion. In he curren circumsances his quesion is of much more han academic ineres, as widely used measures sugges he coincidence of a large unemploymen gap and mued producion coss wih fairly sable long-run inflaion expecaions. While a high unemploymen rae and mued producion coss would end o depress inflaion, well-anchored inflaion expecaions may serve as a counerweigh o downward pressure. Which effec will prevail? This brief examines he role of expecaions and anchoring by employing expecaions proxies derived from surveys of professional forecasers. The brief concludes ha here is some evidence ha sable long-run expecaions have an indirec anchoring effec on inflaion, bu ha he effec of resource slack o dae remains considerable. JEL Codes: E3, E5 Jeffrey C. Fuhrer is an execuive vice presiden and senior policy advisor a he Federal Reserve Bank of Boson. His e-mail address is jeff.fuhrer@bos.frb.org. This brief, which may be revised, is available on he web sie of he Federal Reserve Bank of Boson a hp://www.bosonfed.org/economic/ppb/index.hm. The views expressed in his brief are he auhors and do no necessarily reflec he official posiion of he Federal Reserve Bank of Boson or he Federal Reserve Sysem. This version: November 3,
A widely cied nosrum of curren moneary policy heory and pracice holds ha wellanchored inflaion expecaions preven curren inflaion from dropping oo far or oo fas in he presence of subdued producion coss and a subsanial margin of underuilized resources. The mos widely embraced definiion of well-anchored holds ha inflaion expecaions adhere fairly closely o he explici or inferred long-erm inflaion goal of he counry s cenral bank. This adherence reflecs confidence on he par of he public ha he cenral bank will guide inflaion from wherever i is oday o is long-run goal, and reurn i wihin a reasonable period of ime. If price-seers a individual firms believe ha his will occur, hey may no allow recen inflaion ha deviaes from he cenral bank s long-erm goal o unduly influence he nominal rae of increase ha hey build ino heir own prices, oher hings equal. A very simple represenaion of his sory regarding well-anchored expecaions suggess ha inflaion depends only on long-run inflaion expecaions (a proxy for he cenral bank s inflaion goal) and on curren excess capaciy, expressed mahemaically as π = Eπ + au U LR * ( ), where π sands for inflaion in period, E means he expecaion of, LR π sands for long-run inflaion, and U U *, a measure of excess capaciy in he economy, represens he deviaion of unemploymen from is naural rae, or he amoun of unemploymen ha would be presen in he economy when all individuals who wan o work have a job. The op panel of figure displays a measure of core inflaion along wih a measure of long-run inflaion expecaions he average inflaion rae expeced over he nex six o en years derived from he Survey of Professional Forecasers (SPF). As he panel indicaes, he long-run expecaion capures he overall rend of inflaion, bu clearly does no follow is shor-erm flucuaions in recen years. Bu one could also inerpre figure as suggesing ha inflaion ends o reurn oward he long-run rend proxied by he long-run inflaion expecaions. If so, hen one could view his as evidence ha inflaion is anchored o he long-run expecaions. Noe also ha he relaionship posied above suggess ha unemploymen evenually reurns o a rae consisen wih full * employmen ( U ), and ha inflaion will always reurn o he long-run expecaion of inflaion. The measure employed here is derived from he SPF variable, and is aken from he Federal Reserve Board s FRB/US economeric model of he economy. The variable mnemonic is PTR.
7 6 5 4 3 Figure A long-run expecaions model of inflaion Core inflaion Long-run expecaions 98 985 99 995 5 5 7 6 5 4 3 π LR * = Eπ.35 ( U U ) (.4) Core inflaion Model fied value 98 985 99 995 5 5 Year Sources: Bureau of Labor Saisics (core inflaion), Board of Governors of he Federal Reserve Sysem, FRB/US model (long-run expecaions), auhor s calculaions The boom panel of figure displays he resuls from esimaing his relaionship. The equaion s fi, especially over he pas 5 years, is quie good. As displayed in he op panel, i is clear from he sabiliy of he long-run expecaion over he pas decade) ha he preponderance of he model s igh fi in recen years comes from he correspondence beween curren inflaion and unemploymen flucuaions. In fac, an esimae of his same model over he pas years reveals an The resricion ha he long-run expecaions ener wih a coefficien of one is rejeced a he percen level. The esimaed coefficien wihou his consrain is.88.
esimaed coefficien on he long-run expecaion ha is saisically indisinguishable from zero, suggesing ha all of he model s fi derives from he resource uilizaion measure. 3 This Brief invesigaes he role of expecaions in he evoluion of U.S. inflaion. Firs i will review he underlying heory ha moivaes a role for expecaions, boh shor-run and long-run, and hen provide some empirical evidence ha aemps o sor ou he roles ha expecaions and resource slack play in deermining inflaion, boh in earlier periods and more recenly. Moivaing Theory Behind his qualiaive descripion of he well-anchored inflaion expecaions sory is a hos of empirical economic research and debae, mos of which ceners on versions of he eponymous Phillips curve ha suggess a shor-run radeoff beween higher inflaion and lower unemploymen. 4 The crux of modern versions of his heory lies in he following observaions and implicaions:. Prices for many goods and services are adjused somewha infrequenly;. This implies ha when seing prices, firms will ry o ake accoun of he condiions prevailing over he ime hey expec he price o be in effec; 3. Thus expecaions of fuure condiions relevan for price-seing should maer; 4. The relevan condiions include he sae of excess capaciy and a relaed concep, he marginal cos of producing addiional goods; 5. A convenien way of represening hese ideas is as follows: 6. Inflaion oday = Nex period s expeced inflaion + he effec of excess capaciy and/or coss or in mahemaical form π = π + + E bx, where x sands for excess capaciy and/or coss of producion. This equaion implies ha oday s inflaion depends on he expeced values for x in he curren and all fuure periods (hink of wha he expecaion of nex period s inflaion mus depend on nex period s excess capaciy and he () LR * 3 The esimaed equaion is π =.49 Eπ.33 ( U U ) (.38) (.5). 4 For an accessible summary of much of his debae, see Fuhrer, Kodrzycki, Lile and Olivei, The Phillips Curve in Hisorical Conex, in Undersanding Inflaion and he Implicaions for Moneary Policy: A Phillips Curve Rerospecive, ed. Fuhrer, Kodrzycki, Lile and Olivei, pp. 3 68, Cambridge, MA: The MIT Press, 9. This chaper is available online: hp://mipress.mi.edu/books/chapers/6363chap.pdf. 3
following period s inflaion. This recursion can go on indefiniely). This equaion and variaions of i are used widely by economiss who hink abou, model, and forecas inflaion. An imporan and more recen modificaion recognizes ha over longer ime spans, inflaion has risen and fallen quie significanly in ways ha may be difficul for his simple model o capure. Tha is, in addiion o being influenced by near-erm expecaions and he effec of resource slack, inflaion has a more slowly moving rend componen. The long-run inflaion expecaion displayed by he red line in he op panel of figure may be considered an esimae of rend inflaion. The mos common inerpreaion of he slowly moving inflaion rend is ha i represens gradual changes in he cenral bank s explici long-run goal (implici in he U.S.) for inflaion. The model hen suggess ha price-seers expec inflaion evenually o rever o he long-run rend he Fed s inflaion goal and hus hey always hink of inflaion in erms of is deviaion from ha rend. Accouning for his rend in inflaion gives rise o he following model: Inflaion oday relaive o rend = Nex period s expeced inflaion relaive o rend + he effec of excess capaciy and/or coss In mahemaical form, his may be expressed as π π = E( π π ) + bx, + + where π is he rend rae of inflaion (perhaps he cenral bank s inflaion goal) in period. Thus inflaion should depend on boh shor-run and long-run inflaion expecaions, alhough he heory suggess ha each one has somewha differen anchoring role. A key difficuly wih his equaion is ha neiher he expecaion of nex period s inflaion nor he rend inflaion rae is direcly observable. Economiss have used several approaches o proxy for hese unobserved linchpins in he Phillips curve:. Proxy for expeced inflaion wih an average of he recen observaions for inflaion;. Assume ha raional expecaions correspond well o he acual expecaions used by price-seing firms; 5 or 3. Employ surveys of people and firms who forecas inflaion. () 5 Recall ha he concep of raional expecaions implies he efficien use of all available informaion in forecasing inflaion. In sricer forms, raional expecaions becomes model-consisen expecaions, so ha in addiion o efficienly using informaion, price-seers a firms are assumed o use he same model o forecas inflaion as he economis wries down. 4
Opion () was widely-used by many economiss (see especially Gordon 977) prior o he more widespread use of he raional expecaions (RE) hypohesis of John Muh (96), popularized in macroeconomics by Sargen and Wallace (975) and many ohers. Over he pas 5 years, he RE assumpion has dominaed inflaion models. In par because of he exreme informaion assumpions required by he RE hypohesis (see Friedman 979), and in par because he RE versions of Phillips curves me wih only parial empirical success (see Rudd and Whelan (6); Robers (997)), recen work has begun o consider wheher survey expecaions migh consiue a reasonable middle ground beween he loose proxies afforded by lagged inflaion and he more heoreically rigorous assumpions of he RE hypohesis (see Adam and Padula (); Robers (997); and Nunes (); Fuhrer(forhcoming)). Empirical Evidence on Expecaions and Inflaion Using Survey Measures Figure, on he following page, displays core CPI inflaion along wih a shor (one-year) and a longer-erm measure (he FRB/US model variable wih mnemonic PTR displayed above and defined in foonoe ) of inflaion expecaions. The figure suggess ha here may well be a role for boh expecaions measures in explaining inflaion. The long-run expecaion capures he long-run or rend movemens in inflaion, while he shorer-run expecaion appears o capure higherfrequency movemens in inflaion. Figure also suggess ha here has been an imporan change in he behavior of U.S. inflaion over he pas 3 years. In he firs half of his period, inflaion exhibied a fairly pronounced downward rend, and he long-run expecaion raced ou ha slower movemen. In he second half, inflaion appears o have flucuaed around a relaively fla rend of abou percen, perhaps reflecing a widely held percepion ha he Fed s unofficial inflaion goal is abou percen. 5
Figure Shor- and long-run inflaion expecaions 7 6 Core inflaion SPF 4-qr. PTR 5 4 3-98 985 99 995 5 5 Year Sources: Bureau of Labor Saisics (core inflaion), Survey of Professional Forecasers (four-quarer inflaion expecaions), Board of Governors of he Federal Reserve Sysem, FRB/US model (long-run expecaions). Of key ineres a presen is he movemen of inflaion below he percen rend in he wake of he Grea Recession. If he long-run expecaions serve as an anchor for inflaion, hen his may pu some upward pressure on inflaion ha parly offses he downward pressure implied by he large amoun of excess capaciy in he economy a presen. If no, hen one would expec his slack o exer downward pressure on inflaion, hus implying a coninued decline in inflaion going forward. In assessing he role of he anchoring of longer-run expecaions, an imporan difficuly lies in he behavior of expecaions over he pas dozen years. As figures and illusrae, long-run expecaions have remained remarkably sable over his recen period hese expecaions have almos lierally fla-lined. As a consequence, a model ha suggess ha curren inflaion equals he long-run inflaion expecaion adjused for he influence of he unemploymen gap behaves essenially he same as a model ha suggess inflaion equals a consan rae is average over he pas dozen years adjused for he unemploymen gap. Table and figure 3 display he fi of hese wo alernaives. One would be hard-pressed o declare one or he oher he winner in his cones. 6
Table Esimaes of simple inflaion equaions LR * π = aπ bu ( U ) * π = c du ( U ) Core CPI inflaion, :Q-:Q Variable Coefficien Significance Coefficien Significance Long-run expecaion (a). srong - - Inercep (c) - -. srong Unemploymen gap (b,d) -.8 srong -.6 srong Figure 3 Comparison of PTR and Inercep model of inflaion, -:Q 3.5 3.5.5.5 Core inflaion Fied, PTR Fied, inercep -.5 4 6 8 Year Sources: Bureau of Labor Saisics (core inflaion), Board of Governors of he Federal Reserve Sysem, FRB/US model (long-run expecaions), auhor s calculaions These inconclusive resuls make i difficul o inerpre he role ha long-run expecaions have had in influencing shor-erm inflaion in recen years. Are he expecaions irrelevan fla a percen and unrelaed o recen flucuaions in inflaion? Or are he long-run expecaions he anchor ha pulls inflaion back, implying ha inflaion mus average abou percen over his period? 7
A Phillips Curve Perspecive on he Role of Expecaions Recall from he discussion above ha received heory suggess a role for boh shor- and long-run inflaion expecaions in deermining inflaion. Using he Phillips curve, which imposes a bi more economic srucure on inflaion and relaed daa, may help us o sor ou he relaive roles played by long- and shor-run expecaions. In paricular, if we cas he Phillips curve in is deviaion from rend form as in equaion () above, how much predicive power do we gain relaive o a Phillips curve ha excludes he long-run rend over he pas 3 years? How much do we gain in explaining inflaion during recen years? These quesions are addressed in figure 4, shown on he following page. Wheher we consider he full sample since 983 (during which inflaion exhibied a pronounced downward rend), or he mos recen dozen years (during which inflaion exhibied no rend), he answer is nohing a all. The fied values for he wo models lie nearly on op of one anoher, and his suggess ha adding he rend inflaion proxy o he model has lile effec. The relaive goodnessof-fi (R-squared) measures for he wo models are displayed in able below. There is lierally no evidence suggesing ha one needs o include he long-run expecaion once shor-run expecaions are accouned for. 8
6 Figure 4 How imporan is he rend inflaion? Full sample 983-:Q 4 Core CPI Fi wih rend Fi wihou rend - 98 985 99 995 5 5 Year 4 -:Q 3-4 6 8 Year Sources: Bureau of Labor Saisics (core CPI inflaion), auhor s calculaions Table goodness of fi measures for inflaion models including and excluding rend inflaion Sample Wih rend Wihou 983-:Q.97.97 :Q-:Q.94.94 9
In hese esimaes, noe he role ha resource slack plays. Table 3 displays esimaes of he unemploymen coefficien for seleced subsamples, while figure 5 shows he esimaes from rolling -year quarerly regressions from 99 o he presen. In mos all cases, he coefficien on resource slack is sizable and significanly esimaed. I may be ha using survey expecaions as he inflaion expecaions proxy helps us o beer idenify he role of resource slack, paricularly in recen years. Table 3 Unemploymen gap coefficiens in Phillips curves Coefficien Significance Deviaions, 83- -.8 High Deviaions, - -.8 High No rend, 83- -. High No rend, - -. High. -. Figure 5 The role of resource uilizaion in inflaion, 99-presen Unemploymen gap coefficien Wih rend inflaion Wihou -. -.3 -.4 5 5 5 3 35 4 45 5 p-value.8.6.4. 5 5 5 3 35 4 45 5 Saring year of esimaion Sources: Auhor s calculaions
Do Long-Run Expecaions Play Any Role in Deermining Inflaion? So far, one migh conclude from his brief ha we can happily ignore long-run or rend inflaion measures in explaining U.S. inflaion behavior over he pas 3 years. No so fas. The resuls of he preceding secion sugges ha a combinaion of shor-run expecaions and a measure of resource uilizaion do quie well a explaining inflaion flucuaions. However, his does no enirely preclude a role for long-run expecaions. In fac, i appears ha long-run expecaions may serve as an anchor for shor-run expecaions. To illusrae his, we examine a simple depicion of he relaionship beween shor- and longrun inflaion expecaions. In paricular, we examine an error-correcion model of inflaion expecaions, which answers he quesion: when shor- and long-run expecaions diverge, which pah is more likely o rever o he oher measure? Figure 6 displays he resuls from simple error-correcion regressions ha ake he form SR SR LR SR LR S( ) i i j i i= j= LR SR LR SR LR L( ) i i j i i= j= Eπ = ec Eπ Eπ + a Eπ + b Eπ Eπ = ec Eπ Eπ + a Eπ + b Eπ. The coefficien of ineres is ec, which deermines wheher he expecaion measure (shor- or longrun) moves consisenly o close he gap beween he shor-run and long-run expecaions. If he long-run expecaion serves as an anchor for he shor-run expecaion, hen he coefficien should be negaive because his implies ha when he shor-run expecaion is above (below) he long-run, he shor-run expecaion will fall (rise). The figure displays he resuls of rolling regressions ha employ a 5-quarer sample wih he firs sar dae in 983:Q. The solid line is he esimaed error-correcion coefficien, and he shaded area depics he wo-sandard-error deviaion band around he esimae. The resuls in figure 6 show a fairly srong endency for he shor-run expecaion o move oward he long-run expecaion when he wo diverge, bu he opposie movemen does no occur. In fac, over he pas 3 years he error-correcion coefficien for he long-run expecaion is almos never significan a he 5 percen level. This simple es suggess ha by and large, he long-run inflaion expecaion serves as an anchor for he shor-run inflaion expecaion. ec S
. Figure 6 Error-correcion of shor- and long-run expecaions -sandard error band in gray shading EC of shor o gap -. -.4 -.6 -.8 98 984 986 988 99 99 994 996 998 Year.4 EC of long o gap. -. -.4 98 984 986 988 99 99 994 996 998 Year Sources: Auhor s calculaions Bu i is clear from figure ha while shor-run expecaions end o rever oward long-run expecaions, oher facors influence how he shor-run expecaions are formed. The logic of he Phillips curve, which posis a relaionship beween inflaion and resource uilizaion, migh sugges ha shor-run expecaions of inflaion would depend on shor-run expecaions of resource uilizaion. We can use he SPF forecass of unemploymen o proxy for hese expecaions. Thus a simple model for shor-run expecaions ha employs survey daa and is consisen wih he heory behind he Phillips curve would be SPF SPF SPF * Eπ = Eπ LR be( U+ U+ ). An esimae of his equaion yields he coefficiens displayed in able 4, and he fied values for he regression are shown in figure 7. The coefficien on he unemploymen forecas gap is sizable and significan, and he fi for he pas years appears quie reasonable. The consrain ha he long-
run expecaion eners wih a coefficien of one is no rejeced in he laer sample covering he period, bu i is rejeced for he full sample. 6 Table 4 Esimaes of simple model for shor-run inflaion expecaions Esimae (significance) Coefficien 983- - SPF Eπ LR (imposed) b -.9 (<%) (imposed) -.6 (<%) Figure 7 Simple model for shor-run expecaions Anchored by long-run expecaions.8.6 SPF 4-qr. expecaion Fied.4..8.6.4 4 6 8 Year Sources: Survey of Professional Forecasers (4-quarer expecaion), Auhor s calculaions Overall, his simple survey-based model explains he flucuaions in inflaion and shor-run economic flucuaions quie well, and helps o sor ou he role ha expecaions play in deermining inflaion in he Unied Saes. 6 The unconsrained esimae for he coefficien on he long-run expecaion over he full sample is.74. 3
Conclusions The diagram below provides a schemaic illusraion of he linkages among he curren inflaion rae, shor- and long-run expecaions, and moneary policy ha are consisen wih he resuls in his Brief. The cenral bank s implici or explici goal for inflaion deermines long-run inflaion expecaions. These in urn ac as an anchor for shor-run expecaions. The combinaion of shor-run expecaions and resource uilizaion deermine he curren rae of inflaion. Cenral bank s inflaion goal deermines Long-run inflaion expecaions, which anchor Exhibi A Simple Model of Expecaions and Inflaion Shor-run inflaion expecaions E a Resource uilizaion Which ogeher deermine E a sands for Expecaion of Curren Inflaion Rae Wha does his model imply for he curren rajecory of inflaion? Will he anchoring of shor-run expecaions help o anchor inflaion expecaions, even in he presence of a large unemploymen gap? A full answer o his quesion lies ouside he scope of his brief, bu i surely depends on he following:. Do long-run inflaion expecaions remain anchored a abou percen? This may depend on he Federal Reserve s perceived commimen o such an inflaion goal bu i may depend on oher facors as well, such as he exen of resource slack and he rae of increase of producion coss. 4
. Will he unemploymen gap remain elevaed for an exended period? If so, his will exer coninued downward pressure on inflaion, parly or compleely offseing he upward pull of long-run expecaions. The final exercise conducs a simulaion in which We impose ha long-run expecaions remain anchored a percen; The unemploymen gap gradually declines from is curren level (where he curren gap is compued using he CBO esimae of he naural rae of unemploymen), and We use he esimaed relaionship among he curren inflaion rae, he shor-run inflaion expecaion, and he unemploymen gap; and he relaionship among he shor-run inflaion expecaion, he long-run expecaion, and he expeced (survey) unemploymen gap. The simulaion yields he resuls depiced in figure 7, which appears on he following page. The simulaed values begin in :Q3 and he model views recen elevaed inflaion raes as ransiory. The simulaion suggess an inflaion rae ha rises quie gradually from below. o a bi below.5 percen in lae 4. Long-run inflaion expecaions anchor shor-run expecaions, which keep he curren inflaion rae from declining much below. percen, bu he U.S. economy experiences a susained period of quie low inflaion. 5
Figure 7 Implicaions of simple survey-expecaions inflaion model for near-erm inflaion Inflaion.5 Inflaion Shor-run expecaion.5.5 :Q4 :Q :Q4 :Q :Q4 3:Q 3:Q4 4:Q 4:Q4 4 Unemploymen gap 3.5 3.5 :Q4 :Q :Q4 :Q :Q4 3:Q 3:Q4 4:Q 4:Q4 Dae Sources: Auhor s calculaions 6
References Adam, Klaus, and Mario Padula.. Inflaion Dynamics and Subjecive Expecaions in he Unied Saes. Economic Inquiry 49(): 3 5. Friedman, Benjamin M. 979. Opimal Expecaions and he Exreme Informaion Assumpions of Raional Expecaions Macromodels. Journal of Moneary Economics 5(): 3 4. Fuhrer, Jeffry. (Forhcoming). The Role of Expecaions in Inflaion Dynamics. Inernaional Journal of Cenral Banking. Gordon, Rober. J. 977. The Theory of Domesic Inflaion. American Economic Review 67(): 8 34. Muh, John. 96. Raional Expecaions and he Theory of Price Movemens. Economerica9(3): 35 335 Nunes, Ricardo.. Inflaion Dynamics: The Role of Expecaions. Journal of Money, Credi and Banking4(6): 6 7. Robers, John M. 997. Is Inflaion Sicky? Journal of Moneary Economics 39(): 73 96. Rudd, Jeremy, and Karl Whelan. 7. Modeling Inflaion Dynamics: A Criical Review of Recen Research. Journal of Money, Credi and Banking, 39():55 7. Sargen, Thomas. J., and Neil Wallace. 975. Raional Expecaions, he Opimal Moneary Insrumen, and he Opimal Money Supply Rule. Journal of Poliical Economy 83(): 4 54. 7