When can we forecas inflaion? Jonas D M Fisher, Chin Te Liu, and Ruilin Zhou Inroducion and summary The pracice of forecasing inflaion has generally been considered an imporan inpu in moneary policymaking Recenly, his view has come under aack In an aricle ha appeared in he Federal Reserve Bank of Minneapolis s Quarerly Review, Akeson and Ohanian (2001, hereafer A&O) argue ha he likelihood of accuraely predicing a change in inflaion using modern inflaion forecasing models is no beer han a coin flip They conclude ha hese forecasing models canno be considered a useful guide for moneary policy In his aricle, we reexamine he findings ha underlie his conclusion We show ha i may be possible o forecas inflaion over some horizons and in some periods A&O sudy he properies of sandard Phillipscurve-based inflaion forecasing models These models relae changes in inflaion o pas values of he unemploymen gap (he difference beween unemploymen and a measure of unemploymen believed o be associaed wih non-acceleraing inflaion, he so-called NAIRU [non-acceleraing inflaion rae of unemploymen]), pas changes in inflaion, and perhaps oher variables believed o be useful indicaors of inflaion 1 Recenly, Sock and Wason (1999, hereafer S&W) proposed a generalized version of he Phillips curve and argued ha heir generalizaion is superior o hese sandard models as a forecasing ool Focusing on he one-year-ahead forecas horizon, A&O argue ha unemploymen-based Phillips curve models and S&W generalized Phillips curve models can do no beer han a naive model, which says ha inflaion over he coming year is expeced o be he same as inflaion over he pas year This analysis focuses on he abiliy o forecas he magniude of inflaion in he Consumer Price Index (oal CPI), he CPI less food and energy componens (core CPI), and he personal consumpion expendiures deflaor (oal PCE) over he sample period 1985 o 2000 To gain some insigh ino hese findings, figure 1, panel A displays -monh changes in -monh core CPI from 1967 o 2000 The verical lines in his figure (in 1977, 1985, and 1993) divide he sample period ino four periods I is immediaely clear ha in he wo laer periods, ha is, he sample period considered by A&O, he volailiy of changes in inflaion was much lower han in he wo earlier periods This change in he behavior of inflaion seems o be coinciden wih he change in moneary policy regime ha is generally hough o have aken effec in he mid-1980s 2 The lower volailiy and he possibiliy of a changed moneary policy regime in he laer wo sample periods may favor he naive model sudied by A&O Figure 1, panel B shows ha PCE less food and energy componens (core PCE) behaves in a similar fashion These changes in he behavior of inflaion raise he quesion of wheher A&O s findings are due o special feaures of he daa in he sample period hey chose o focus on To address his possibiliy, we exend he A&O analysis by sudying hree disinc sample periods, 1977 84, 1985 92, and 1993 2000 In addiion, we add core PCE inflaion o he lis of inflaion measures and we consider a broader class of Sock Wason ype models A&O focus on he oneyear forecas horizon Given he lags inheren in he effecs of moneary policy acions, i is reasonable o consider wheher heir resuls exend o longer horizons Consequenly, we analyze boh he one-year and wo-year forecas horizons Our findings confirm he A&O resuls for he 1985 2000 period, bu no for 1977 84 The Phillips curve models perform poorly in boh he 1985 92 and 1993 2000 periods when forecasing core CPI Jonas D M Fisher is a senior economis, Chin Te Liu is an associae economis, and Ruilin Zhou is a senior economis a he Federal Reserve Bank of Chicago 30 1Q/2002, Economic Perspecives
FIGURE 1 -monh changes in -monh core inflaion A Core CPI 80 60 40 20 00-20 -40-60 -80 1967 '69 '71 '73 '75 '77 '79 '81 '83 '85 '87 '89 '91 '93 '95 '97 '99 '01 B Core PCE 80 60 40 20 00-20 -40-60 -80 1967 '69 '71 '73 '75 '77 '79 '81 '83 '85 '87 '89 '91 '93 '95 '97 '99 '01 Source: Haver Analyics, Inc, 2001, US economic saisics daabase, July However, when forecasing core PCE, hese models improve significanly relaive o he naive model in he 1993 2000 period While he Phillips curve models do poorly for he one-year-ahead forecas horizon, we do find evidence in favor of he Phillips curve models for he wo-year-ahead forecas horizon, a leas wih respec o core inflaion Taken ogeher, hese findings are consisen wih our suspicion ha periods of low inflaion volailiy and periods afer regime shifs favor he naive model The relaively poor performance of he Phillips curve models reflecs heir inabiliy o forecas he magniude of inflaion accuraely Ulimaely, he way we assess our forecasing models should reflec he usefulness of he forecass in policymaking In our view, policymakers undersand ha precise forecass of inflaion are fraugh wih error As a resul, hey pay considerable aenion o he direcion of change of fuure inflaion For his reason, we do no view measures of forecas performance used by A&O and Federal Reserve Bank of Chicago 31
many ohers ha emphasize magniude as he only crieria for evaluaing forecasing models Consequenly, we consider a complemenary approach o evaluaing forecasing models ha emphasizes he forecased direcion of change of fuure inflaion Under he assumpion ha forecas errors are symmerically disribued abou he forecas, he naive model provides no informaion abou fuure inflaion; i is no beer han a coin flip a predicing he fuure direcion of inflaion Under he same symmery assumpion, he Phillips curve models predic ha inflaion will change in he direcion indicaed by comparing he poin forecas wih he curren level of inflaion We analyze he abiliy of our Phillips curve models o forecas he direcion of inflaion and find ha hey do quie well Over he enire 1977 2000 period, he Phillips curve models are able o forecas he correc direcion of inflaion one year ahead beween 60 percen and 70 percen of he ime For he same period, he models forecas he correc direcion wo years ahead more han 70 percen of he ime These resuls sugges ha he Phillips curve models forecas he direcion of inflaion changes relaively well across measures of inflaion and across ime Bu when i comes o forecasing he magniude of inflaion changes, here may be imes, such as afer a change in moneary policy regime, when he naive model may do beer han he Phillips curve models The las quesion we address is wheher i is possible o improve on he forecass of he naive model in difficul imes by using he direcional informaion conained in he Phillips curve models We show ha i is possible o improve on he naive model, alhough he improvemen is modes One inerpreaion of our findings is ha i is possible o forecas inflaion accuraely during some periods, bu no ohers We argue ha he periods in which i is difficul o forecas inflaion are associaed wih changes in moneary policy regime, broadly inerpreed This implies ha if we are in a sable moneary regime and expec he regime o persis, hen i may make sense for policymakers o pay aenion o inflaion forecass In he nex secion, we ouline he differen forecasing models ha we consider in our analysis Nex, we discuss he sandard mehodology we implemen o evaluae he abiliy of hese models o forecas he magniude of fuure inflaion We hen discuss our resuls for forecasing magniude and presen our analysis of forecasing direcional changes in inflaion We describe our procedure for combining he naive model wih our direcional forecass and how well his procedure performs over our sample period Finally, we discuss some possible policy implicaions of our findings Saisical models of inflaion The sandard approach o forecasing inflaion is rooed in ideas associaed wih he Phillips curve, he saisical relaionship beween changes in inflaion and measures of overall economic aciviy The generalized version of he Phillips curve proposed by S&W involves variables ha summarize he informaion in a large number of inflaion indicaors S&W argue ha heir generalizaion is superior o convenional Phillips curves as a forecasing ool A&O argue ha neiher he convenional nor he generalized Phillips curve framework can do beer han a simple forecas (heir naive model) ha says inflaion over he coming year is expeced o be he same as inflaion over he pas year We reexamine his claim using a broader class of S&W-ype models han considered by A&O Now we describe in deail he models we sudy The naive model The benchmark for evaluaing our models is he naive model described by A&O The saring poin for he naive model is he maringale hypohesis, which saes ha he expeced value of inflaion over he nex monhs is equal o inflaion over he previous monhs Specifically, 1) E, Q Q where he -monh inflaion rae, Q is defined as he -monh change in he naural logarihm of he price indexes p, Q ln ln, p p and E denoes he expecaion condiional on dae informaion The naive model equaes he forecas of inflaion over he nex monhs, Q ˆ, wih is condiional expecaion Tha is, 2) Qˆ Q Noice ha if he maringale hypohesis holds, hen he expeced value of -monh inflaion in he second year following dae mus also equal inflaion over he monhs prior o dae, ha is E Q 24 Q Similar o he -monh forecas, he naive model equaes he forecas of inflaion over he nex 24 monhs, Q, wih is condiional expecaion: ˆ 24 32 1Q/2002, Economic Perspecives
3) Qˆ 24 Q Generalized Phillips curve models The simples alernaive o he naive model posulaes ha changes in -monh inflaion only depend on recen changes in one-monh inflaion Tha is, for J =, 24, 4) Q J Q BC( L) ( Q Q 1) FJ, where he one-monh inflaion rae, p, is defined by p = ln p ln p 1 In addiion, e is an error erm, and b(l) specifies he number of lags in he equaion 3 Below, we refer o his as model 1 The nex model we consider is based on he Chicago Fed Naional Aciviy Index (CFNAI) This index is a weighed average of 85 monhly indicaors of real economic aciviy The CFNAI provides a single, summary measure of a common facor in hese naional economic daa As such, hisorical movemens in he CFNAI closely rack periods of economic expansion and conracion The index is closely relaed o he Aciviy Index sudied in S&W 4 Our model based on his index posulaes ha changes in -monh inflaion, in addiion o recen changes in inflaion, also depend on curren and pas values of he CFNAI Tha is, for J =, 24, 5) Q J Q BC( L)( Q Q 1) H( L) a FJ, where a denoes he value of he CFNAI a dae, and b(l) and g(l) specify he number of lags in inflaion and he index, respecively, included in he equaion We refer o his as model 2 The remaining models we consider are based on he diffusion index mehodology described in S&W This mehodology uses a small number of unobserved indexes ha explain he movemens in a large number of macroeconomic ime series Our implemenaion of he S&W mehodology uses 154 daa series, including daa measuring producion, labor marke saus, he srengh of he household secor, invenories, sales, orders, financial marke, money supply, and price daa The procedure ha obains he indexes processes he informaion in he 154 series so ha each index is a weighed average of he series and each index is saisically independen of he ohers We consider six indexes, d 1, d 2,, d 6, which are ranked in descending order in erms of he amoun of informaion embedded in hem Our diffusion index models posulae ha changes in -monh inflaion depend on recen changes in inflaion, and curren and pas values of a number of diffusion indexes Tha is, for J =, 24, 6) QJ Q B C( L) ( Q Q 1) K Ri Ldi F J i1 ( ), where K = 1, 2,, 6, and b(l) and q i (L) specify he number of lags in inflaion and diffusion index i, respecively, included in he equaion As more indexes are included in he equaion, more informaion abou he 154 series is incorporaed in he forecas We refer o hese as models 3, 4,, 8 For all hese models, we equae he forecass of inflaion wih he condiional expecaion implied by he model Tha is, for J =, 24, Qˆ J EQJ We esimae all hese models by ordinary leas squares (OLS) In each case, we use he Bayes Informaion Crierion (BIC) o selec he number of lags of inflaion, he CFNAI, and he diffusion indexes Inuiively, BIC selecs he number of lags o improve he fi of he model wihou increasing by oo much he sampling error in he lag coefficiens We allowed for he possibiliy ha lags could vary from 0 o 11 In real ime, i is difficul o choose he appropriae model o use o form a forecas To address his issue, we consider a forecasing model in which he forecas of inflaion a any given dae is he median of he forecass of models 1 hrough 8 a ha dae 5 This procedure has he advanage ha i can be applied in real ime We call his he median model Sock and Wason (2001) use a similar model For convenience, we refer o he collecion of models comprising models 1 hrough 8 plus he median model as Phillips curve models Model evaluaion mehodology We evaluae he accuracy of he generalized Phillips curve models by comparing hem wih he naive model We do his hrough various simulaed ou-of-sample forecasing exercises These exercises involve consrucing inflaion forecass ha a model would have produced had i been used hisorically o generae forecass of inflaion Two drawbacks of our approach, which also affec A&O and S&W, are ha we do no use real-ime daa in our forecass and we assume all he daa are available up o he forecasing dae On a given dae, paricular daa series may no Federal Reserve Bank of Chicago 33
ye be published Also, many daa series are revised afer he iniial release dae In our forecasing exercises, we calculae he CFNAI and diffusion indexes assuming all he series underlying he indexes are available up o he forecas dae 6 In pracice, his is never he case and we mus fill in missing daa wih esimaes Since we do no use real-ime daa o consruc he CFNAI and diffusion indexes, we also absrac from problems associaed wih daa revisions We suspec ha hese drawbacks lead us o oversae he effeciveness of our CFNAI and diffusion index models Daa revision is also a problem for he lagged inflaion and naive PCE models, since his price index is subjec o revisions I does no affec he CPI versions of hese models, since he CPI is never revised To assess he accuracy of our various models, we firs consruc a measure of he average magniude of he forecasing error The measure we use is roo mean squared error (RMSE) The RMSE for any forecas is he square roo of he arihmeic average of he squared differences beween he acual inflaion rae and he prediced inflaion rae over he period for which simulaed forecass are consruced For J =, 24, 2 1/2 T 1 ˆ Q J Q ª J ¹ µ T 1 7) RMSE, where T denoes he number of forecass made over he period under consideraion We compare he forecas of a given Phillips curve model wih ha of he naive model by forming he raio of he RMSE for he Phillips curve model o he RMSE for he naive model We call his raio he relaive RMSE A raio less han 1 hus indicaes ha he Phillips curve model is more accurae han he naive model Subracing 1 from he raio and muliplying he resul by 100 gives he percenage difference in RMSE beween he wo models The RMSE migh be srongly affeced by one or wo large ouliers We reworked our analysis using a measure of forecasing error ha places equal weigh on all forecasing errors and found ha our findings are robus 7 The RMSE saisics are subjec o sampling variabiliy and, consequenly, are measured wih error In principle, we could use Mone Carlo mehods o assess he magniude of his error However, his would require specifying an underlying daageneraing process for all he variables in our analysis (more han 150 of hem) One should keep his sampling error in mind when inerpreing he resuls below The sample period of our analysis begins in 1967 We chose his dae because i is he beginning dae for he daa used o consruc he CFNAI and he diffusion indexes 8 We esimae he forecasing equaions using rolling regressions, a mehod ha keeps he number of observaions in he regression consan across forecass Since i excludes observaions from he disan pas, his approach can in principle accommodae he possibiliy of srucural change in he daa-generaing process We choose his sample lengh for he rolling regression procedure o be 15 years 9 Finally, we consider hree disinc periods over which o evaluae he forecass of he models: 1977 84, 1985 92, and 1993 2000 To compare our resuls wih hose in A&O, we also evaluae he overall performance of he models over he 1985 2000 period To complee he analysis, we sudy he performance of he models over he enire 1977 2000 period as well The 1977 84 period is one of high inflaion volailiy and general economic urbulence The 1985 92 period is generally associaed wih a new moneary policy regime This period also includes a mild recession The 1993 2000 period winessed uninerruped economic expansion, sable moneary policy, and declining inflaion Akeson and Ohanian revisied We esimaed he Phillips curve models for he five sample periods and compued he associaed RMSEs and he relaive RMSEs For models 1 8, we do no repor all he resuls, jus he resuls for he bes models We do his o demonsrae he poenial forecasing capaciy of hese models A&O repor he performance of he bes and wors models hey look a across differen lag lenghs S&W use BIC o selec lag lengh and repor he performance of all heir models All of hese approaches suffer from he deficiency ha in real ime one may no know which is he bes performing model Our median model overcomes his deficiency Table 1 displays he RMSE saisics of he bes and median -monh-ahead and 24-monhahead forecass for he five sample periods and four measures of inflaion The able also idenifies he bes performing models The numbers in bold in he able indicae cases in which he naive model ouperforms he Phillips curve models Finally, for each case we repor he RMSE for he naive model Regarding he -monh-ahead forecass in able 1, our findings are as follows Firs, over he 1985 2000 period, essenially all he relaive RMSEs are a leas as large as 1 Tha is, he naive model ouperforms all he Phillips curve models This finding confirms he resul repored in A&O ha Phillips curve models have no performed well over he las 15 years Second, while inflaion forecasing appears o have been quie difficul over he las 15 years, for core PCE i has become a lile easier in he mos recen forecasing 34 1Q/2002, Economic Perspecives
TABLE 1 Forecasing he magniude of inflaion: Phillips curve models vs naive model monhs ahead 24 monhs ahead Naive Bes Median Naive Bes Median model performing Rel rel model performing Rel rel Sample period RMSE model RMSE RMSE RMSE model RMSE RMSE Core CPI 1977:01 1984: 2360 2 0768 0885 3802 4 0930 0868 1985:01 1992: 0667 1 0985 1290 0780 1 0894 1615 1993:01 2000: 0341 2 1110 1181 0705 2 0765 0768 1985:01 2000: 0530 1 1016 1268 0744 1 0903 1304 1977:01 2000: 1430 2 0891 0927 2278 5 1000 0906 Core PCE 1977:01 1984: 1238 2 0954 1033 2100 5 0887 0765 1985:01 1992: 0481 1 1409 14 0617 1 1221 1197 1993:01 2000: 0514 4 0750 0749 0802 4 0532 0542 1985:01 2000: 0498 1 1188 1109 0716 6 0933 0847 1977:01 2000: 0822 2 1048 1052 1346 5 0902 0781 Toal CPI 1977:01 1984: 2674 2 0687 0765 4525 4 0744 0696 1985:01 1992: 1489 1 0982 0982 1695 1 0981 1245 1993:01 2000: 0716 1 1085 1193 1032 1 1035 1002 1985:01 2000: 1168 1 1002 1025 1403 1 0996 1184 1977:01 2000: 1815 2 0865 0845 2853 6 0954 0795 Toal PCE 1977:01 1984: 1705 2 0841 0953 2977 6 0751 0686 1985:01 1992: 1025 1 0978 10 1102 1 1029 1279 1993:01 2000: 0633 4 0953 0960 0924 6 0773 0772 1985:01 2000: 0852 1 1003 0998 1017 1 1020 1098 1977:01 2000: 1205 2 0974 0968 1909 6 0909 0781 Noes: Fifeen-year rolling regression RMSE is roo mean squared error Numbers in bold indicae cases in which he naive model ouperforms he Phillips curve models period In paricular, he forecas by he bes model and he median forecas have RMSEs 25 percen lower han he naive model over he 1993 2000 period Noe, however, ha his paern is no rue for core CPI Third, he Phillips curve models are generally beer han he naive model in he 1977 84 period This resul is uniform across inflaion measures, excep for he median forecas for core PCE In some cases he improvemen is quie dramaic For example, he bes CFNAI model is more han 30 percen beer han he naive model when forecasing oal CPI Even he median forecas is abou 24 percen beer han he naive model The resuls for he 24-monh-ahead forecass in able 1 sugges ha, over longer horizons han monhs, he Phillips curve models may more consisenly ouperform he naive model In paricular, he bes models a forecasing core inflaion ouperform he naive model in he 1985 2000 period However, he gains are no dramaic For core CPI, he gain is roughly 10 percen, and for core PCE i is abou 7 percen The median forecass for core CPI over his period fare worse, bu hey are beer for core PCE wih a gain of 15 percen over he naive model In he recen 1993 2000 period, he gains over he naive model are more subsanial The bes models improve relaive o he naive model by 24 percen for core CPI and 47 percen for core PCE We see similar gains for he median forecass Finally, here are across he board gains using Phillips curve models o forecas 24 monhs ahead for he 1977 84 period We can summarize hese findings as follows Firs, he naive model does poorly in he 1977 84 period and relaively well in he 1985 92 period, forecasing monhs ahead Second, he naive model does no do well forecasing PCE inflaion in he recen 1993 2000 period Finally, he naive model does beer forecasing monhs ahead han 24 monhs ahead We can aribue he firs finding o an apparen srucural change in he early 1980s and he consequen decline in inflaion volailiy in he pos-1984 period compared wih he previous period This decline in Federal Reserve Bank of Chicago 35
volailiy is eviden in he paern of RMSEs for he naive model in able 1 (also see figure 1) 10 Given ha he naive model predics no change in inflaion, i should do beer in a period of low inflaion volailiy han in a period of high volailiy I is unclear how he performance of he Phillips curve models is affeced by inflaion volailiy Neverheless, we suspec ha changes in inflaion volailiy are a conribuing facor o he poor performance of he naive model in he 1977 84 period and is significan improvemen in he mos recen 15 years Anoher facor ha probably plays an imporan par in explaining our firs finding is ha forecasing models do relaively well in a sable environmen If he srucure of he economy changes, hen regression equaions end o forecas wih more error We suspec he change in srucure in he early 1980s has a lo o do wih a change in moneary policy regime around ha ime We hink volailiy and srucural sabiliy change may explain he second finding as well In paricular, i appears ha here was a furher decline in core CPI volailiy in he 1993 2000 period, which is no mached by core PCE We hink one possible explanaion of he improved performance of he Phillips curve models a he 24-monh forecas horizon has o do wih he sluggish response of he economy o moneary policy acions I is generally undersood ha economic aciviy and inflaion respond wih a considerable lag o changes in moneary policy, and ha inflaion is more sluggish in is response han economic aciviy If his is rue hen here may be less informaion abou fuure inflaion in he -monh-ahead forecass han in he 24-monh-ahead forecass Noe ha as he forecas horizon is increased, forecasing performance in erms of RMSE generically worsens We can see his by comparing he RMSEs of -monh-ahead and 24-monh-ahead forecass of he naive model in able 1 Evidenly, he forecas errors for he Phillips curve models deeriorae a a slower rae han he forecas errors for he naive model Forecasing direcion In he previous secion we used he RMSE crierion o evaluae he models This measure emphasizes he abiliy of a forecasing model o predic he magniude of inflaion In his secion, we consider a complemenary approach o evaluaing forecasing models, which emphasizes he forecased direcion of change of fuure inflaion Wha do he models we have described have o say abou direcion of change of inflaion? Firs, consider he naive model Sricly speaking, according o equaions 2 and 3, his model always predics no change in inflaion In principle he maringale hypohesis, equaion 1, on which he naive model is based, could be used o make forecass abou direcion Given he condiional disribuion of inflaion monhs and 24 monhs ahead, we could assess he probabiliy of an increase or decrease in inflaion over hese horizons and use his o make predicions abou he direcion of change If his disribuion is symmeric around he condiional mean, hen he maringale hypohesis would sugges ha he likelihood of an increase in inflaion is always 50 percen If he disribuion is skewed, he odds of inflaion changing in a paricular direcion would be beer han a coin flip The maringale hypohesis does no provide any informaion abou he naure of he condiional disribuion Deriving predicions abou he direcion of inflaion changes from a Phillips curve model is more sraighforward The main difference from he naive model is ha he condiional expecaion of inflaion monhs and 24 monhs ahead is no consrained o equal curren inflaion Consequenly, we can infer he direcion of change by making minimal assumpions abou he disribuion of he error erms in equaions 4 6 Specifically, if hese disribuions are symmeric, hen he direcion of change is given by he sign of he difference beween he condiional forecas and he curren value of inflaion Now we analyze he abiliy of our models o forecas direcion We assume he forecas errors are symmerically disribued Therefore, he naive model predics inflaion increases wih probabiliy 50 percen We evaluae our Phillips curve models by assessing how well hey can forecas direcion relaive o his baseline Specifically, for a given Phillips curve model, le Dˆ J be he prediced direcion of change in inflaion J periods ahead We define Dˆ J as follows for J =, 24: ˆ 1ifE 8) D, «Q J Q J 1 oherwise where Dˆ J 1 indicaes a forecased increase in inflaion and Dˆ J 1 indicaes a decrease Acual changes in inflaion are defined analogously Le D Jbe he acual direcion of change in inflaion J periods ahead, for J =, 24, «Q J Q D J 1oherwise 1if We measure he direcional change performance of a model by measuring he percenage of he direcional 36 1Q/2002, Economic Perspecives
TABLE 2 Forecasing he direcion of inflaion changes monhs ahead 24 monhs ahead Bes Bes performing Median performing Median Sample period model PDPC PDPC model PDPC PDPC Core CPI 1977:01 1984: 3 750 719 3 917 823 1985:01 1992: 7 625 594 6 667 635 1993:01 2000: 4 781 802 1 854 781 1985:01 2000: 7 703 698 1 745 708 1977:01 2000: 7 691 705 3 750 747 Core PCE 1977:01 1984: 2 792 698 2 906 875 1985:01 1992: 1 615 427 6 615 521 1993:01 2000: 8 698 698 1 906 823 1985:01 2000: 1 641 563 6 708 672 1977:01 2000: 2 670 608 2 722 740 Toal CPI 1977:01 1984: 2 865 719 4 927 896 1985:01 1992: 8 604 583 6 760 729 1993:01 2000: 4 604 573 3 771 740 1985:01 2000: 5 594 578 5 734 734 1977:01 2000: 2 628 625 4 785 788 Toal PCE 1977:01 1984: 3 896 771 4 948 938 1985:01 1992: 1 563 521 4 688 625 1993:01 2000: 5 719 677 5 802 760 1985:01 2000: 7 620 599 5 740 693 1977:01 2000: 7 656 656 5 802 774 Noes: Fifeen-year rolling regression RMSE is roo mean squared error PDPC indicaes percenage of direcional predicions ha are correc Numbers in bold indicae failure wih respec o he naive model predicions ha are correc (PDPC) in a paricular sample period This percenage is defined as (for J =, 24), T 1 ˆ \ J J^, T 1 PDPC I D D where I akes he value 1 when is argumen is rue (ha is, D ˆ D ), and 0 oherwise J We used our esimaes J of he Phillips curve models compued for he RMSE comparisons in he previous secion o make predicions abou he direcion of change of inflaion according o equaion 8 We repor he findings for he bes Phillips curve models and for he median model Table 2 displays he - and 24-monh-ahead direcional predicions for he five sample periods and four measures of inflaion The able also idenifies he bes performing models Numbers in bold indicae failure wih respec o he naive model Our findings can be summarized as follows I is immediaely clear from he ables ha he Phillips curve models predic direcion in excess of 50 percen of he ime for boh -monh and 24-monh horizons in all bu one case Similar o heir performance in erms of RMSE, hese models are ypically bes a predicing direcional change during he 1977 84 period and wors in he 1985 92 period Ineresingly, he bes models a predicing direcional changes are no he same as he bes models in erms of RMSE For example, model 4 (he model ha includes d 1 and d 2 ) provides he bes -monh-ahead forecass of direcional changes of core CPI over he 1993 2000 period In erms of RMSE, model 2 provides he bes forecass over his sample period Moreover, i is possible for a model o do well on direcional changes while underperforming he naive model in erms of magniude In he example jus given, he bes direcional change model is correc more han 78 percen of he ime, bu he bes RMSE models in he corresponding period Federal Reserve Bank of Chicago 37
FIGURE 2 Median model direcional predicions of -monh changes in -monh core inflaion A Core CPI 705% correc 60 40 20 00-20 -40 Correc Incorrec -60 1977 '79 '81 '83 '85 '87 '89 '91 '93 '95 '97 '99 '01 B Core PCE 608% correc 60 40 20 00-20 -40 Correc Incorrec -60 1977 '79 '81 '83 '85 '87 '89 '91 '93 '95 '97 '99 '01 are worse han he naive model Finally, he 24-monhahead direcional change forecass perform beer han he -monh ahead forecass Figures 2 and 3 provide informaion on when our direcional change forecass are correc The bars indicae acual changes in core CPI and PCE inflaion and he green bars indicae he correc direcional predicions of he median model over he 1977 2000 period The main lesson from hese figures is ha much of he success of he direcional forecass derives from periods in which here is a consisen rend in one direcion or he oher he longer periods of consecuive increasing or decreasing inflaion are associaed wih beer direcional forecasing The relaively poor performance in he 1985 92 period may be parially due o he absence of a rend As wih our inerpreaion of he RMSE findings, we believe he change in moneary policy regime may also play a role Ineresingly, in he recen 1993 2000 period, despie he general downward rend in core CPI inflaion, he one-year direcional forecass are able o correcly anicipae he brief episodes of increasing inflaion 38 1Q/2002, Economic Perspecives
FIGURE 3 Median model direcional predicions of 24-monh changes in -monh core inflaion A Core CPI 747% correc 80 60 40 20 00-20 -40-60 Correc Incorrec -80 1977 '79 '81 '83 '85 '87 '89 '91 '93 '95 '97 '99 '01 B Core PCE 740% correc 80 60 40 20 00-20 -40-60 Correc Incorrec -80 1977 '79 '81 '83 '85 '87 '89 '91 '93 '95 '97 '99 '01 Can we improve on he naive model in difficul imes? Confirming he A&O findings, we show ha he naive model has done quie well over he las 15 years in forecasing he magniude of inflaion Over he same period, he Phillips curve models seem o provide informaion on he direcion of changes in inflaion A naural quesion is wheher we can combine hese models o ge a beer forecas for magniude Inuiively, we should be able o do his by shaving he naive model forecass up or down according o he direcional predicions In his secion, we explore his idea and show ha, indeed, i is possible o do somewha beer han he naive model We modify he naive model by adjusing is forecas in he direcion prediced by a given Phillips curve or median model Tha is, for J =, 24, Qˆ J Q DJ sv, where D ˆ J is defined in equaion 8 and v is he adjusmen facor The inuiion is ha, for small enough ˆ Federal Reserve Bank of Chicago 39
v, we should be able o improve on he naive model In addiion, we believe he magniude of v should be relaed o recen changes in inflaion Consequenly, we adjus he naive model by a percenage of he average inflaion change in he recen pas Tha is, we assume v evolves as follows: v Ms Qj Qj jn There is nohing in his approach ha pins down v, and one may define v in oher ways, provided ha i is no oo large This formulaion assumes symmery in magniude of increases and decreases in inflaion Choices of l and N reflec he forecaser s belief in he relevance of pas volailiy of inflaion for fuure volailiy For fixed N, inuiion suggess ha, for small enough l, here will be a leas a sligh improvemen over he naive model We choose l = 01 and N o correspond o he beginning of he regression sample We call his he combinaion model Table 3, consruced in he same way as able 1, shows how well he combinaion model performs relaive o he naive model These resuls confirm our belief ha we can improve on he naive model almos uniformly For example, over he 1985 2000 period, he improvemen of he bes performing combinaion model for core CPI is abou 7 percen and ha for core PCE is abou 3 percen for he - monh horizon For he 24-monh horizon, he gains are 9 percen and 6 percen, respecively Admiedly, hese are no large improvemens The resuls for he median-based combinaion forecass are less encouraging The bad performance in he 1985 92 period seems o be driven by he relaively poor performance of he direcional forecass for boh one-year and wo-year horizons The performance of he combinaion model may improve slighly by increasing l by a small amoun, bu no by much TABLE 3 Forecasing he magniude of inflaion: Combinaion models vs naive model monhs ahead 24 monhs ahead Naive Bes Median Naive Bes Median model performing Rel rel model performing Rel rel Sample period RMSE model RMSE RMSE RMSE model RMSE RMSE Core CPI 1977:01 1984: 2360 2 0959 0968 3802 3 0950 0963 1985:01 1992: 0667 7 0955 0981 0780 6 0965 0994 1993:01 2000: 0341 7 0855 0859 0705 1 0833 0854 1985:01 2000: 0530 7 0935 0957 0744 1 0910 0934 1977:01 2000: 1430 2 0965 0967 2278 3 0950 0961 Core PCE 1977:01 1984: 1238 5 0954 0962 2100 3 0945 0950 1985:01 1992: 0481 1 0992 1069 0617 6 0970 1016 1993:01 2000: 0514 1 0944 0942 0802 1 0910 0925 1985:01 2000: 0498 1 0967 1003 0716 6 0943 0960 1977:01 2000: 0822 7 0966 0972 1346 3 0948 0952 Toal CPI 1977:01 1984: 2674 3 0951 0959 4525 4 0949 0956 1985:01 1992: 1489 8 0983 0990 1695 6 0952 0969 1993:01 2000: 0716 5 0990 0997 1032 5 0915 0938 1985:01 2000: 1168 6 0987 0992 1403 6 0950 0961 1977:01 2000: 1815 2 0965 0968 2853 6 0952 0957 Toal PCE 1977:01 1984: 1705 3 0939 0958 2977 5 0941 0946 1985:01 1992: 1025 1 0988 1003 1102 5 0934 0961 1993:01 2000: 0633 5 0944 0962 0924 5 0911 0925 1985:01 2000: 0852 7 0982 0992 1017 5 0924 0946 1977:01 2000: 1205 2 0961 0970 1909 5 0938 0946 Noes: Fifeen-year rolling regression RMSE is roo mean squared error Numbers in bold indicae cases in which he naive model ouperforms he combinaion model 40 1Q/2002, Economic Perspecives
Conclusion We can summarize our main resuls as follows Firs, we show ha he A&O findings hold for a broader class of models han hey sudied, as well as for a longer forecasing horizon However, hey do no hold for he 1977 84 period We exend heir analysis o core PCE and show ha he naive model does beer over he sample period considered by A&O a he one-year horizon, bu no a he wo-year horizon In he 1993 2000 period, he Phillips curve models perform well a forecasing core PCE for boh horizons Second, we show ha Phillips curve models have predicive power for he direcion of change in inflaion This is paricularly rue in he 1977 84 and 1993 2000 periods However, in he 1985 92 period, he gain over he naive model is quie modes Third, in mos cases i is possible o combine he informaion in he direcional forecass wih he naive model o improve on he laer model s forecass A common hread in our resuls is he relaively poor performance of he Phillips curve models in he middle period, in erms of boh magniude and direcion We believe his is due o a reducion in inflaion volailiy and he change in moneary policy operaing characerisics ha ook effec in his ime Our findings sugges he following policy recommendaion If we expec he curren moneary regime o persis, hen we can have some degree of confidence in he Phillips curve models going forward On he oher hand, if we suspec ha a regime shif has recenly occurred, hen we should be skepical of he Phillips curve forecass In any case, here may be some direcional informaion in hese forecass, and we can use his o improve on naive forecass Our findings sugges ha more empirical and heoreical work is necessary o come o a complee answer o he quesion raised in he ile o his aricle An equivalen way of posing his quesion is o ask: Why does inflaion behave like a maringale over some periods while a oher imes i does no? We have suggesed some possible explanaions Empirically, we need o assess he robusness of our resuls o crosscounry analysis For example, here we have only one regime change and, hence, only one observaion for he regime-swich hypohesis Ulimaely, assessing he plausibiliy of various possible explanaions will require developing a fully specified heoreical model Such work may shed ligh on he connecion beween moneary policy and aggregae oucomes, as well as he naure of he price-seing mechanism NOTES 1 For a recen discussion of he inellecual hisory of he Phillips curve and NAIRU, see Gordon (1997) 2 See Bernanke and Mihov (1998), Bordo and Schwarz (1997), and Srongin (1995) for discussions of moneary regimes These papers argue ha during he Volker chairmanship of he Board of Governors from 1979 87 moneary policy shifed, in erms of operaing procedures and he Fed s increased willingness o comba inflaion Furhermore, Bernanke and Mihov (1998) esimae moneary policy rules and can rejec he hypohesis of parameer sabiliy for daes in he 1980s 3 Suppose here are K lags in he equaion, henÿb(l)x = b 0 x + b 1 x -1 + b K x -K, where he b parameers are scalars 4 For more deails on he CFNAI, see wwwchicagofedorg/ economicresearchanddaa/naional/indexcfm 5 Wih eigh models, he median is he average forecas of he fourh and fifh ranked forecass 6 One implicaion of his procedure is ha he hisorical pah of he indexes may change beween forecas daes 7 The alernaive measure we used was mean absolue value error T For J =, 24, his is expressed as (1/ T ) ˆ i1 QiJ QiJ 8 A&O use several sample periods for heir analysis When hey consider unemploymen-rae-based Phillips curves, heir sample begins in 1959 When hey consider CFNAI-based Phillips curves, heir sample begins in 1967 S&W begin heir analysis in 1959 9 We also considered esimaing he forecasing equaions using all he daa from 1967 up o he forecas dae The resuls obained indicaed eiher very similar forecas performance or, in a few cases, a sligh deerioraion relaive o he rolling regression procedure 10 S&W repor evidence supporing his hypohesis They find ha unemploymen-rae-based Phillips curve forecasing models exhibi parameer insabiliy during he 1980s Federal Reserve Bank of Chicago 41
REFERENCES Akeson, Andrew, and Lee E Ohanian, 2001, Are Phillips curves useful for forecasing inflaion?, Federal Reserve Bank of Minneapolis, Quarerly Review, Vol 25, No 1, Winer, pp 2 11 Bernanke, Ben, and Ilian Mihov, 1998, Measuring moneary policy, Quarerly Journal of Economics, Vol 113, No 3, Augus, pp 869 902 Bordo, Michael, and Anna Schwarz, 1997, Moneary policy regimes and economic performance: The hisorical record, Naional Bureau of Economic Research, working paper, No 6201 Sock, James H, and Mark W Wason, 2001, Forecasing oupu and inflaion: The role of asse prices, Princeon Universiy, manuscrip, February, 1999, Forecasing inflaion, Journal of Moneary Economics, Vol 44, pp 293 335 Srongin, Seven, 1995, The idenificaion of moneary policy disurbances: Explaining he liquidiy puzzle, Journal of Moneary Economics, Vol 35, pp 463 497 Gordon, Rober, 1997, The ime-varying NAIRU and is implicaions for economic policy, Journal of Economic Perspecives, Vol 11, No 1, Winer, pp 11 32 42 1Q/2002, Economic Perspecives