FEDERAL RESERVE BANK OF SAN FRANCISCO WORKING PAPER SERIES Survey Measures of Expeced Inflaion and he Inflaion Process Bhara Trehan Federal Reserve Bank of San Francisco February 2010 Working Paper 2009-10 hp://www.frbsf.org/publicaions/economics/papers/2009/wp09-10bk.pdf The views in his paper are solely he responsibiliy of he auhors and should no be inerpreed as reflecing he views of he Federal Reserve Bank of San Francisco or he Board of Governors of he Federal Reserve Sysem.
Survey Measures of Expeced Inflaion and he Inflaion Process Revised: February 2010 Bhara Trehan* Federal Reserve Bank of San Francisco Absrac This paper uses daa from surveys of expeced inflaion o learn how expecaions processes have changed following recen changes in he behavior of inflaion. Households do no appear o have recognized he change in he process, and are placing subsanially more weigh han appears warraned on recen inflaion daa when forming expecaions abou inflaion over he nex year. A firs glance, professional forecasers do appear o have changed how hey predic inflaion. Bu a closer look a he daa reveals ha professionals are relying on core raher han headline inflaion, and are placing oo much weigh on recen core inflaion daa. These errors show up in a noiceable (absolue and relaive) deerioraion in he forecas accuracy of boh households and professionals. * I would like o hank Oscar Jorda and an anonymous referee for helpful commens. Wayne Huang and Punee Chehal provided high qualiy research assisance. Any opinions expressed in his paper are hose of he auhor and no hose of he Federal Reserve Bank of San Francisco or he Federal Reserve Sysem.
In he firs half of 2008, some U.S. surveys showed noiceable increases in expeced inflaion, leading o concerns abou a possible increase in he inflaion rae and abou he credibiliy of he Federal Reserve. Such concerns can be jusified on he basis of a number of recen sudies. For insance, Ang, Bekaer and Wei (2007) show ha survey measures of expeced inflaion provide beer forecass of inflaion han any oher alernaive ha hey consider, including abou a dozen varians each of Phillips curve and erm srucure models, as well as simple regime swiching models. Mehra and Herringon (2008) use a VAR specified by Leduc, Sill and Sark (2007) o examine measures of survey expecaions following he change in he moneary policy regime ha ook place around he end of he 1970s. They find ha he expecaions process changed in a way ha is consisen wih he change in he inflaion process ha ook place a abou he same ime, suggesing ha survey paricipans are able o deec changes in he inflaion process relaively quickly. 1 And Bernanke, Laubach, Mishkin and Posen (2001) discuss how he behavior of survey forecass relaive o he moneary auhoriy s inflaion arge provides informaion abou credibiliy. 2 Though he raionaliy of survey forecass has been debaed (see Croushore, 1998, for a discussion and a defense), hey are generally well regarded, especially he forecass made by he professionals. For insance, Carrol (2003) argues ha forecass from he Sociey of Professional Forecasers pass all he imporan ess for raionaliy and goes on o model households forecass as adjusing gradually o he forecass of professionals. Ang, e. al., (ABW) are posiive abou boh household and professional forecass: Tha he median Livingson and SPF forecass do well is perhaps no surprising However, even paricipans in he Michigan surveys who are consumers, no professionals, produce accurae ou-of-sample forecass, which are only slighly worse han hose of he professionals. They go on o speculae ha he superior performance of he professionals may resul from heir abiliy o recognize srucural change more quickly han mechanical model forecass can. This paper argues ha neiher households nor professional forecasers are quie as sophisicaed as hese argumens make hem ou o be. The evidence suggess ha here have 1 There is a debae abou he naure of he change in he inflaion process ha ook place a his ime. This issue is aken up below. 2 This in no way exhauss he lis of uses o which inflaion survey daa have been pu. For insance, Mankiw, Reis and Wolfers (2003) and Orphanides and Williams (2005) use hese daa o inform aspecs of model specificaion. For an exensive discussion of how various kinds of survey daa are used for modeling expecaions and esing hypoheses abou expecaions formaion see Pesaran and Weale (2006). 1
been some changes in he inflaion process in recen years, bu neiher households nor professionals have responded appropriaely so far. More specifically, he evidence suggess ha he inflaion process has become noiceably less persisen since he beginning of he decade. As wih he change in he inflaion process around he end of he 1970s, his change could be modeled as a change in he auoregressive coefficiens of he inflaion process or as a change in he variance of he shocks o he process. In eiher case, as argued below, he change in he inflaion process should show up as a change in he relaionship beween survey expecaions daa and realized inflaion. Bu he survey daa sugges ha here has been lile, if any, change a all in he way ha households reac o inflaion daa. In paricular, i appears ha households are placing oo large a weigh on recen inflaion daa when forming expecaions. Consisen wih his finding, household forecass of inflaion are now abou he wors of all he alernaives considered below. This conrass sharply wih Ang, e al (2007), who find ha--over an earlier sample--household forecass are among he bes. Professional forecasers, on he oher hand, do appear o have changed how hey reac o recen inflaion daa, bu his change is no fully consisen wih he observed change in he inflaion process. Specifically, professionals seem o be paying less aenion o headline inflaion daa bu are sill relying heavily on core inflaion daa. This is consisen wih he posiion advocaed by Blinder and Reis (2005) ha i is beer o predic headline inflaion using lagged core --- raher han headline --- inflaion. I urns ou, however, ha SPF forecass of headline inflaion have deerioraed in recen years as well, and are now worse han forecass based on lagged headline inflaion alone. Surprisingly, SPF forecass of headline inflaion are raher good forecass of core inflaion, which suggess ha he professionals may now be implicily forecasing he core CPI, insead of he headline CPI (which is wha hey are asked o forecas). Such a swich would be consisen wih he argumen pu forward by Blinder and Reis (henceforh BR) ha hen-chairman Greenspan s advocacy of he core inflaion concep has shifed U.S. public discourse abou inflaion from headline o core inflaion. If professional forecasers have indeed begun o pay more aenion o core CPI because of Chairman Greenspan s advocacy, hen his swich provides unusual evidence on he Federal Reserve s (Fed s) credibiliy. 3 This finding can also be seen as augmening he findings of 3 The SPF forecass provide more convenional evidence of Fed credibiliy as well: The 10-year ahead inflaion forecas has been quie sable for more han 10 years now. 2
Orphanides and Williams, whose analysis suggess ha he professional forecasers are backward looking (as heir forecass can be approximaed wih a Kalman filered version of pas inflaion daa). Our resuls sugges ha he professionals are sensiive o oher aspecs of he environmen as well, hough his may no always lead o improved forecas accuracy. 1. The daa The Survey of Consumers was iniiaed in 1946 and is currenly conduced monhly by he Universiy of Michigan s Survey Research Cener. Each monh, a randomly seleced sample of approximaely 500 American households are asked (in elephone inerviews) abou expeced changes o key macroeconomic variables such as inflaion, ineres raes, and unemploymen. The sample is designed o be roaing, in ha for any one survey, approximaely 60% of respondens are new and he remaining 40% of respondens are inerviewed for a second ime. Since 1977, respondens have been asked he following quesion abou inflaion: By abou wha percen do you expec prices o go (up/down) on he average, during he nex 12 monhs? Coninuous monhly daa on he answers o his quesion are available since January 1978. Quarerly daa are available prior o ha, bu no for every quarer; hese daa are no used here. The Survey of Professional Forecasers was firs conduced in he fourh quarer of 1968 by he American Saisical Associaion and he Naional Bureau of Economic Research. I has been conduced by he Philadelphia Fed since he second quarer of 1990. Sample size has varied noiceably over ime; as of his wriing, heir websie idenifies more han 50 respondens and here are some anonymous respondens as well. Beginning in 1981Q3, paricipans were asked o forecas quarerly and annual CPI. Since he Survey of Professional Forecasers (SPF) is only conduced once a quarer, he analysis of he daa from he consumer survey is carried ou a a quarerly frequency as well. For he consumer survey, I use daa from he hird monh of each quarer. The implicaions of his choice for various forecas comparisons are discussed below. Figure 1 plos daa on expeced inflaion over he nex year from boh he Michigan and he SPF surveys. In recen years, he SPF forecass have been percepibly below he expecaions from he Michigan survey. Also noiceable is he increased volailiy of he Michigan expecaions daa owards he end of he sample. 3
2. The household survey of expeced inflaion Do survey respondens use he informaion in recen inflaion daa in ways ha are consisen wih he inflaion process? To answer his quesion, wo projecions are compared: he projecion of expeced inflaion on recen inflaion daa and he projecion of acual inflaion over he same horizon on recen inflaion daa. Changes over ime in he laer provide informaion abou how he inflaion process has changed. The nex sep is o deermine wheher he projecions involving inflaion expecaions show similar changes. 4 The saring poin is a regression of CPI inflaion over he nex year on he inflaion rae for he curren quarer and 7 lags. The esimaed equaion is 8, 4 0 i i, i 1 1 i 1 (1) where, 4 measures inflaion from o +4, i.e., over he nex year, which is he same horizon as in he Michigan survey. Quarerly daa are used here o allow for easy comparison wih he resuls for he SPF forecass below. Very similar resuls were obained when he lag lengh was varied by four, when monhly daa were used insead of quarerly, and when a four quarer average of inflaion was used as he explanaory variable. The firs column of Figure 2 shows ha i has become harder o predic fuure inflaion over ime. Each poin on he middle line ploed in he upper lef hand panel of Figure 2 is he value of (ha is, he sum of he coefficiens on inflaion) when he regression described above is esimaed over a 15-year window ha ends in he quarer agains which he poin is ploed. Also shown are wo-sandard-error bands, based on HAC sandard errors. The lower lef hand panel shows how he fi of his equaion changes over ime. Taken ogeher, he wo panels in he firs column reveal ha conemporaneous and lagged inflaion daa conain less and less informaion abou fuure inflaion as ime goes on. For sample periods whose endpoin lies wihin he las wo or hree years, he poin esimae (ha is, 4 ) is noiceably below zero, and even he upper bound of he confidence inerval is no oo far above zero. Furhermore, he he adjused-r 2 is negaive or close o zero since he beginning of 2005. Though uneven, he 4 Under he mainained assumpion ha inflaion is an auoregressive process, Pesando (1975) argues ha if expecaions are raional, he corresponding coefficiens in he wo regressions should be equal. Mullineaux (1980) projecs expeced inflaion on lagged inflaion and money growh and examines how he coefficiens evolve over ime.
decline appears o have aken place in wo seps; firs, over he firs half of he 1990s and he second over he las five years or so of he sample. The firs decline appears relaed o he early 1980s dropping ou of he sample; for insance, if a 10-year rolling window is used in place of a 15-year window, he firs drop in he sum of he coefficiens is complee by he early 1990s, insead of he addiional 5 years or so ha i akes in he plo shown in Figure 2. These resuls sugges a decline in he persisence of inflaion, hough he lef hand side variable is no wha radiionally would be used in a regression mean o examine changes in persisence. 5 The second column of Figure 2 shows wha happens when he exercise above is repeaed using he following equaion: M E 8, 4 0 i i, i 1 2 i 1 (2) M where E, 4 denoes he 1-year-ahead expeced inflaion from he Michigan survey. 6 The op panel on he righ hand side shows ha while he sum of lagged coefficiens did decline in he mid-1990s (jus as is he case in he panel on he lef hand side), here is no evidence of any decline since he lae 1990s. Insead, over he las few years he sum of lagged coefficiens acually increased, so ha one would be hard pressed o say ha he sum of he coefficiens a he end of he sample is any differen from wha i was in he beginning of he sample. Thus, i appears ha---when forming expecaions abou inflaion over he nex year---households have coninued o place a large weigh upon recen inflaion daa ill he very end of he sample. The adjused-r 2 does show a decline owards he end of he sample, bu is sill subsanial and quie a bi higher han wha is obained in he case of realized inflaion. More formal ess on he sabiliy of he wo equaions provide consisen resuls. Table 1 shows how he coefficiens in equaions (1) and (2) change over he wo halves of he 1978Q1-2009Q3 sample. Specifically, a dummy variable ha is 0 unil he end of 1993 and 1 aferwards is included boh by iself and afer being ineraced wih he inflaion erms. In he firs column (where realized inflaion is he dependen variable), he sum of he coefficiens on he inflaion 5 Regressing 1-quarer-ahead inflaion on curren and lagged quarerly inflaion (which would be he radiional specificaion) leads o resuls ha are very close o hose shown in Char 2. 6 In view of he disincion beween core and headline inflaion ha comes up when he SPF forecass are examined below, i is worh noing ha no evidence was found o sugges ha household inflaion expecaions are more (or less) sensiive o oil or food prices han o oher kinds of inflaion. More specifically, erms represening increases in he price of oil, he price of food or he level of non-core inflaion (as defined below) were almos always insignifican a he 10 percen level when included in equaion (2). 5
erms ineraced wih he dummy (ha is, he DP i erms) is significanly negaive, implying a significan decline in he inflaion coefficiens over he second half of he sample. Furher, he null hypohesis ha hese erms can be dropped from he equaion can be rejeced a he 1 percen level. Noably, he hypohesis ha he sum of he coefficiens on all he inflaion erms is zero in he second half of he sample canno be rejeced a he 5 percen level, hough i can be rejeced a he 10 percen level. The resuls for he expeced inflaion equaion are quie differen. Alhough he sum of he coefficiens on inflaion during he firs half of he sample is close o ha for he firs equaion, he resuls for he second half are very differen. Mos imporanly, one canno rejec he hypohesis ha here has been no change in he sum of hese coefficiens over he second half of he sample a convenional significance levels. And one can clearly rejec he hypohesis ha he sum of coefficiens on all he inflaion erms is zero in he second sample (ha is, one can easily rejec he hypohesis ha ΣP i + ΣDP i = 0). An alernaive procedure o es he sabiliy of he equaions is o use he Bai-Perron ess, where boh he daes of he breaks and he number of breaks are assumed o be unknown. 7 For he realized inflaion regression, he WDMax es saisic is 130.2, compared o a 1 percen criical value of 24.8. Thus, he null of no break is decisively rejeced. The sequenial es finds four breaks a he five percen level: in 1981Q1, 1986Q1, 2004Q2 and 1990Q2 (in ha order). In conras, for he expeced inflaion regression, he value of he WDMax saisic is 15.8, compared o a 10 percen criical value of 18.1. And he sequenial es finds no breaks a he 10 percen level. Thus, he resuls from he Bai-Perron ess reinforce he findings in Table 1. A sraighforward inerpreaion of he decline in he sum of he coefficiens on lagged inflaion shown in he firs column of Figure 2 is ha inflaion is becoming less persisen over ime, wih a noiceable change in persisence having aken place in he early par of his decade. Given his resul, he second column of chars suggess ha in forming expecaions abou inflaion over he nex year, households are placing subsanially more weigh han hey should on recen quarerly inflaion daa. 8 7 These ess are discussed in Bai and Perron (1998). 8 Longer erm consumer inflaion expecaions also appear o be excessively sensiive o recen inflaion daa. When expeced inflaion over he 5-o-10 year horizon is regressed on he curren and 7 lags of quarerly inflaion (for a 15-year rolling window whose righ end poin moves from 2004 o 2009), he sum of he coefficiens is posiive and always significanly differen from zero. By conras, in he regression for acual inflaion over he same horizon, he sum of coefficiens on quarerly inflaion is always negaive and significanly differen from zero for he las 10 years or so. Because of daa availabiliy, he wo ses of regressions do no span exacly he same period. Over he roughly 10-year overlapping sample period, he regression wih realized inflaion as he dependen variable has an 6
The recen decline in inflaion persisence could well be par of a rend of declining persisence ha has been in place since he 1980s. Among ohers, Taylor (2000), Cogley and Sargen (2005) and Levin and Piger (2004) have argued ha he persisence of inflaion has declined. Along he same lines, Blanchard and Gali (2007) and Mishkin (2007) argue ha here has been a change in he way inflaion responds o shocks. And, as noed above, boh Leduc, Sill and Sark (2007) and Mehra and Herringon (2008) conclude ha (roughly) since he 1980s, U.S. inflaion has been a saionary process. Many of hese auhors have suggesed ha he change in he inflaion process represens a change in he conduc of policy. Bu here has been considerable debae abou his. As poined ou by Sims (1999), wha appears o be ime variaion in he esimaed coefficiens could really be he resul of changes in he shocks hiing he sysem; his argumen has been elaboraed in Sims and Zha (2006). Using he Cogley-Sargen echnology, Clark and Nakaa conclude ha a reducion in he size of he shocks hiing he economy is largely responsible for he reducion in he volailiy of inflaion and inflaion expecaions in recen years. In a similar vein, Pivea and Reis (2007) argue ha inflaion persisence has no changed much over he poswar period because here has been lile change in he size of he larges roo in he inflaion process since he 1960s. Sock and Wason (2007) provide a reconciliaion of hese findings in a model where inflaion has boh a permanen and a emporary componen. In his model, a reducion in he variance of he innovaion o he permanen componen implies ha a given change in inflaion is more likely o be reversed han before, even hough here has been no change in he larges roo of he process. The Sock and Wason (SW) model provides a characerizaion of he inflaion process which is very differen from he univariae auoregressions presened above. (According o SW, The ime-varying rend-cycle model is equivalen o a ime-varying firs-order inegraed moving average (IMA(1,1)) model for inflaion, in which he magniude of he MA coefficien varies inversely wih he raio of he permanen o he ransiory disurbance variance, p. 4) I is herefore ineresing o see how heir specificaion inerpres recen changes in he inflaion process. SW posulae a model in which inflaion has wo componens: a sochasic permanen componen and a serially uncorrelaed emporary componen. The variance of he disurbance adjused-r 2 of 0.13 wih he sum of inflaion coefficiens equal o -0.14 while he regression for he Michigan survey daa has an adjused-r 2 of 0.92 and he sum of inflaion coefficiens is 0.48. 7
erms is allowed o change over ime. Specifically, heir (unobserved componens-sochasic volailiy) model is given by:, ln ln 2, 2, 1, ln ln 2, 1 2, 1,,,,,, where, ) is i.i.d. N(0,I 2 ) and, ) (,, (,, independenly disribued, and is a scalar parameer. is i.i.d. N(0, I 2 ). and are The esimaes of, and, (he sandard deviaions of he shocks o he emporary and permanen componens) are ploed in Figure 3, ogeher wih an esimae of, he permanen componen of inflaion. As poined ou by SW, he sandard deviaion of he permanen componen of inflaion (shown in he middle panel) rose significanly from he 1960s o he early 1980s, before declining sharply over he remainder of ha decade. I has moved very lile since he mid-1990s. The sandard deviaion of he emporary componen has moved in almos he opposie way; i did no move around very much prior o 2000, especially when compared o he permanen componen. However, i has risen sharply since he beginning of his decade. By he end of he sample, i is more han six imes as large as he conemporaneous sandard deviaion of he permanen componen, and nearly wice as large as he maximum aained by he laer in he early 1980s. As discussed by SW, he decline in he persisence of inflaion afer 1980 can be explained by he drop in he variance of he permanen componen; as his variance declined over he second half of he 1980s and he early 1990s, movemens in CPI inflaion came o be dominaed by he emporary componen. Inflaion became harder o forecas, even as he variance of inflaion was falling. The relaive imporance of he permanen componen has fallen even furher in his decade hus making inflaion even harder o forecas bu ha s happened because he variance of he emporary componen has increased sharply. 9 9 The finding ha he increase in variabiliy is concenraed a he high frequencies does no hinge upon he funcional form ha is imposed upon he inflaion process, bu is eviden in he raw inflaion daa iself. For insance, if a 10-year rolling window is used o calculae he variance of monhly inflaion, here is a noiceable drop in he variance of inflaion beginning (wih samples ha end) in he mid-1990s (which is he same ime ha he 8
Assume, now, ha he only change ha has aken place in he inflaion process recenly is an increase in he variance of he emporary componen. Inuiively, his means ha he curren level of inflaion has become a more noisy indicaor of fuure inflaion han before. The lieraure on inference suggess ha when a signal becomes more noisy one should pay less aenion o i. To see how his inuiion applies o he case a hand, suppose (firs) ha he inflaion process is given by he Sock-Wason specificaion. For simpliciy, also assume ha households know he inflaion process and he curren period emporary shock. Expeced inflaion nex period is hen given by: E 1 Regressing his forecas of nex period s inflaion rae on oday s inflaion rae (an exercise similar o regression (2) above) leads o he following esimaed coefficien: 1 where is he sample size. For he fixed sample size used in he rolling regressions above, his coefficien will decline as he variance of he emporary componen (η) increases. Alernaively, if one assumes ha he long lived componen of inflaion is auoregressive of order one wih a roo 1/α ha is close o, bu no equal o, one, regressing he inflaion rae expeced o prevail nex period on oday s inflaion rae leads o he coefficien var( ) (1 ) var( ) 1 var( ) var( ) which, again, will be smaller in a regime where he variance of he emporary shock is higher. Thus, even if he change in he inflaion process is beer modeled as an increase in he variance regression coefficiens change in he chars above), followed by an increase ha begins in he early 2000s. This increase is much more obvious when one looks a he difference of inflaion (which ends o emphasize higher frequency movemens), and by he end of he sample he variance is slighly above he highs of he 1980s. When he same exercise is repeaed a he annual frequency, here is only a very small increase in he variance of eiher inflaion or he difference of inflaion a he very end of he sample. The resuls a he quarerly frequency lie in beween. 9
of he emporary componen, he sum of coefficiens ploed in he op panel on he righ hand side of Figure 2 should decline over ime. 3. The forecass from he SPF survey This secion examines he forecass from he survey of professional forecasers. The lef hand column of chars in Figure 4 repeas for he SPF forecass--he exercise seen in Figure 2 above, ha is, i shows wha happens when he year-ahead SPF inflaion forecass are regressed on curren and lagged inflaion. The resuls urn ou o be similar o hose for acual inflaion (see he lef hand column in Figure 2). Thus, he forecasers in he SPF panel appear o be placing less weigh on recen inflaion daa, and one could conclude ha he professionals have recognized he change ha has aken place in he inflaion process, much as hypohesized by ABW. However, a closer look a he daa reveals ha here is anoher dimension along which he forecasers behavior looks quie differen. The chars on he righ hand side of Figure 4 show wha happens when he SPF forecass are projeced on core CPI inflaion daa. If anyhing, he SPF forecass have become more sensiive o core CPI daa in recen years, hough---given he size of he wo-sandard-error band--- one canno rejec he argumen ha here has been no change in heir response o hese daa over he enire sample. Table 2 provides more direc evidence on hese issues. The firs column presens he esimaes from a full sample regression of he SPF forecass on quarerly CPI inflaion, in which he consan and he coefficiens on he inflaion erms are allowed o change approximaely midway hrough he sample (specifically, a he end of 1993, o allow comparison wih he resuls in Table 1). The sum of he coefficiens on he inflaion erms ineraced wih he dummy variable is negaive and significanly differen from zero. As indicaed a he boom of he able, hese variables canno be excluded from he equaion a he one percen level. And one canno rejec he hypohesis ha during he second half of he sample, changes in CPI inflaion have no permanen effec on he SPF forecass. The resuls in he second column, where he SPF forecas is regressed on core CPI inflaion, are quie differen from hose in he firs. The coefficiens on he inflaion erms ha have been ineraced wih he dummy are insignificanly differen from zero and one can easily rejec he hypohesis ha he sum of all he coefficiens on he core inflaion erms is zero in he second half of he 10
sample. Noe ha he fi of his equaion is marginally beer han he firs, in which he forecass are projeced on headline inflaion measures. One way o reconcile hese resuls is o argue ha he SPF forecasers used o pay aenion o boh he core and non-core componens of inflaion unil recenly and now pay aenion only o he former. An alernaive argumen is ha he SPF forecasers always paid aenion o he core CPI and no he headline, bu his has only become obvious following he recen decline in he correlaion beween core and headline CPI inflaion. I discuss each of hese possibiliies in urn. Before doing so, i is worh noing he resuls of an experimen mean o disinguish beween he wo. Specifically, he exercise in Figure 4 was repeaed, excep ha he core and non-core 10 componens of CPI inflaion were enered separaely. I urns ou ha while he noncore inflaion erms did no accoun for much of he variaion in he SPF forecas, hey could no be excluded from he SPF regression for samples ha end before 2002; afer ha, he evidence is mixed, wih he noncore componens significan for some samples and no ohers. Why migh he professional forecasers have reduced he aenion hey pay o he noncore componen? One possible reason is ha he increased noise idenified earlier in he CPI is concenraed in his componen, which would sugges ha one should reduce he weigh one aaches o he noncore componen bu coninue o pay aenion o he core inflaion rae. In order o see if he daa are consisen wih his hypohesis, Figure 5 shows he resuls obained when he SW specificaion is imposed upon he core CPI inflaion process. The decline in he variance of he permanen componen is similar o ha seen in he case of he headline CPI. Imporanly, while he variance of he emporary componen has been going up recenly, he increase is nowhere near as marked as i was for headline CPI inflaion. 11 Thus, an argumen can be made ha because of recen changes in he inflaion process, i is appropriae o pay less aenion o he non-core componen of CPI inflaion. 12 Bu ha does no jusify he SPF forecasers pracice of coninuing o place a large weigh on core inflaion daa when predicing headline inflaion. The firs column in Figure 6 demonsraes his poin. I 10 Non-core inflaion is defined as he rae of headline inflaion relaive o core, following Sock and Wason (2008). 11 In conras o he headline CPI (see foonoe 9), he raw daa for core CPI do no provide clear evidence of changes in volailiy. 12 Even in his case, he pracice of placing a zero weigh on food and energy price daa is hard o jusify. Firs, i ignores he dynamics of he known emporary componen, which is unlikely o be whie noise. More problemaic is he assumpion of independence beween he core and non-core componens. Specifically, he non-core componen will affec he core componen (given he range of hisorical responses of moneary policy o such shocks); e.g., oil shocks are likely o affec oher prices in he economy and so should be aken ino accoun. 11
shows wha happens when headline CPI inflaion over he nex year is regressed upon core CPI inflaion, similar o he rolling regressions seen earlier. As can be seen, he relaionship beween headline and core inflaion has deerioraed quie noiceably in recen years. For samples ending in he las four o five years, core CPI inflaion daa provide no informaion abou fuure headline inflaion, which is almos exacly he same resul shown in Figure 2--where he righ hand side variable was headline CPI inflaion. This resul could no be more differen from ha in Figure 4, where he SPF forecass of headline inflaion appear o have become more sensiive o core inflaion daa in recen years. These resuls make one wonder wheher i is only he relaionship beween headline and core inflaion ha has changed or if here has been a change in he behavior of core inflaion as well. The panels on he righ hand side of Figure 6 address his issue by regressing 1-year-ahead core CPI inflaion on quarerly core CPI inflaion. While he deerioraion in he predicive power of he equaion is no as grea as when headline CPI inflaion is regressed on iself (see Figure 2), he paern is similar. The relaionship begins o deeriorae by he mid-2000s; by he end of he sample period, he sum of he coefficiens on inflaion canno be disinguished from zero and he adjused-r 2 is below 0.1. The daa sugges ha hese regressions could look worse as ime goes by; when a 10-year rolling window is used (insead of he 15-year window used for he graphs), he sum of he coefficiens on core inflaion falls below zero in 2006 and coninues o fall hrough he end of he sample. As menioned above, he oher possibiliy is ha he SPF forecasers have always relied on core inflaion o forecas headline inflaion, bu his has only become obvious following he recen change in he relaionship beween he wo. The SPF forecasers would no be unique in following such a procedure, if his is indeed wha hey were doing. For insance, Blinder and Reis (BR, 2005) argue ha even if one is ineresed in headline inflaion, i is beer o generae forecass of his variable by using daa on core inflaion. Based on a series of resuls for forecasing inflaion a he 6, 12, 24 and 36 monh forecasing horizons, hey sae ha: Every specificaion in he able poins o he same conclusion: ha recen core inflaion is a beer predicor of fuure headline inflaion han is recen headline inflaion. Indeed, once you ake core inflaion ino accoun, adding headline inflaion has a bes no effec on forecasing performance, and a mos horizons makes forecass even worse. 12
So, one could argue ha he forecasers decision o focus on core inflaion was a reflecion of prevailing opinion. 13 Bu, even if his was he righ way o proceed in he pas, should he forecasers have coninued o do so in ligh of he evidence above? Table 3 provides a comparison of differen ways of forecasing CPI inflaion since he beginning of 2003, which is jus afer he ABW (2007) sample ends and close o he ime ha he inflaion process appears o have changed. The Michigan and SPF forecass are compared o forecass from several alernaive specificaions: A random walk, Sock and Wason s unobserved-componen sochasic-volailiy model, and hree regression based specificaions. Two of he regressions involve only inflaion daa (eiher headline or core) while he hird is a Phillips curve specificaion, which adds he unemploymen rae and noncore inflaion. Each forecas from hese equaions is obained by regressing inflaion on a consan and he explanaory variable(s) over a 15 year sample ha ends in he period prior o he forecas. The esimaed equaion is hen used o forecas nex period s inflaion. The specificaion used here is he same as ha used by BR (2005). Timing issues become imporan when he regression based forecass are compared o he survey forecass. Boh ABW and BR include he laes inflaion daa on he righ hand side when esimaing equaions o predic fuure inflaion. 14 As inflaion daa are released wih a lag, his means ha he forecass obained from he regressions will be based on more informaion han he survey respondens had when hey made heir forecass. Noe ha he difference is less han one quarer, as survey respondens have access o monhly daa bu are being asked o forecas quarerly inflaion once a quarer (SPF) or annual inflaion every monh (Michigan). More specifically, for he Michigan survey, his paper uses daa from he final reading in he hird monh of he quarer, which is released a he end of ha monh. Since CPI daa end o be released around he middle of he monh, he quarerly Michigan forecas used here is likely o be based on he monhly inflaion rae for he firs wo monhs of he quarer. This is quie good, since he las monh of daa has a low weigh in calculaing he quarerly average inflaion rae. Things are differen for he SPF survey, as i is conduced once a quarer and is released in he middle of he middle monh of he quarer. Thus, depending upon survey and daa release daes, SPF survey respondens may or may no have informaion abou CPI inflaion in he firs monh 13 However, such an opinion was no universally held. For an alernaive, see Smih (2005). 14 BR do no compare he equaion based forecass wih he survey forecass. 13
of he quarer. In order o avoid sacking he deck agains he survey respondens, his paper excludes quarer informaion from he righ hand side of he esimaed equaions. In he second specificaion in Table 3A, for insance, inflaion from quarer o quarer +4 is prediced using inflaion daa hrough quarer -1. Thus, he iming convenion here differs from boh ABW and BR. The resuls urn ou o be very differen from hese sudies as well, hough no because of he iming convenion. Using lagged CPI inflaion o predic headline inflaion leads o he smalles roo mean squared error in Table 3. According o he Diebold-Mariano-Wes (or DMW) es, 15 hese forecass are beer han he SPF forecass a he 1 percen level. Forecass from he Phillips curve specificaion are beer han he SPF forecass a he 10 percen level. Forecass based on lagged core inflaion are he hird mos accurae (ou of seven), hough he associaed RMSE is close o ha for he SPF forecass. This similariy is no surprising given he resuls above suggesing ha he SPF forecass can be well described as a linear combinaion of lagged core CPI inflaion daa. The Michigan survey forecass, he forecass from he unobserved componens sochasic volailiy model and he random walk specificaion bring up he rear, wih RMSEs ha are jus above 2 percen. For comparison, he lower panel of Table 3 presens resuls from a sample of he same size which ends a he end of 2002. Here we replicae he resuls found by ABW and BR. In paricular, as poined ou by ABW, he SPF survey does bes of all, and he Michigan survey has almos exacly he same RMSE. The forecass from he SPF survey are beer han hose based on lagged core inflaion a he 1 percen level and are beer han hose from he Phillips curve specificaion a he 5 percen level (DMW es again). And consisen wih BR, forecass of headline CPI inflaion based on core CPI inflaion are beer han hose based on headline CPI daa. The RMSEs in he pos 2002 sample are noiceably larger han he earlier sample for every specificaion in Table 3. This reflecs he increase in high frequency noise in CPI inflaion over his period. Even so, he deerioraion in he SPF forecas is surprising. Since 2003, professional forecasers are doing worse han a forecas based on headline inflaion alone; here, i is worh poining ou ha he laer specificaion has almos no abiliy o explain inflaion wihin sample (in erms of he adjused-r 2 ). This evidence makes one wonder wheher he SPF 15 See Wes (2006). 14
forecasers apparen decision o pay lile or no aenion o he non-core inflaion daa in recen years and o coninue o place a large weigh on he core inflaion daa was moivaed by a desire o predic headline inflaion more accuraely or in pursui of some oher objecive. BR (2005) provide an ineresing raionale for wha migh be going on: Anoher Greenspan innovaion, which is rarely menioned bu is likely o prove durable, is he way he has focused boh he Fed and he financial markes on core, raher han headline, inflaion. This aspec of Federal Reserve moneary policy conrass sharply wih he concenraion on headline inflaion a he ECB and o he saed inflaion arges of mos oher cenral banks, which are rarely core raes. Perhaps here is more han one realizes o he Blinder and Reis argumen ha Chairman Greenspan urned public aenion owards he core inflaion daa. Could i be ha he SPF forecasers have followed he Fed and swiched heir aenion o forecasing core CPI, even hough hey are being asked o forecas headline CPI? Table 4 presens some evidence ha is consisen wih his hypohesis. I shows wha happens (over he period since he beginning of 2003) when he SPF forecas of headline CPI inflaion is reaed as a forecas of core CPI inflaion. For comparison, forecass from he oher specificaions in Table 3 are also included, wih he excepion of he one ha uses headline CPI on he righ hand side. As can be seen, he SPF forecas of headline inflaion urns ou o be a prey good predicor of core inflaion. I is beer han he random walk specificaion a he 1 percen level. And he RMSE of he SPF forecas is slighly beer han ha obained when core CPI inflaion is used o predic fuure core inflaion, hough he difference is nowhere near saisically significan. The Phillips curve specificaion urns ou o be he bes, hough i ouperforms he SPF forecas only a he 10 percen level. The Michigan survey is he wors by a wide margin. This is no a big surprise, as he respondens are being asked o predic headline and no core--inflaion; he surprise is ha he SPF survey does so well. 15
Secion 4: Conclusions The evidence suggess ha he inflaion process has changed in recen years. The auoregressive represenaion of CPI inflaion shows a noiceable decline in he sum of he coefficiens on lagged inflaion over ime and by he end of he sample lagged inflaion daa have no predicive power for fuure inflaion a all. If, insead, Sock and Wason s unobserved-componensochasic-volailiy specificaion is imposed on he daa, he change shows up as a noiceable increase in he variance of he high frequency componen. While i may be hard o deermine he correc represenaion of he daa, eiher kind of change should lead survey respondens o place less weigh on recen inflaion daa when predicing fuure inflaion. Households do no appear o have learned abou his change in he inflaion process, as hey do no appear o have changed he way in which hey form expecaions of inflaion. Hisorically, households have placed a large weigh on recen inflaion daa when forming inflaion expecaions, and hey coninue o do so now. The effecs of his misake show up in a marked deerioraion in forecasing performance, as he Michigan forecass have gone from being abou he mos accurae o he leas accurae. There is more reason o believe ha professional forecasers have changed he way ha hey forecas inflaion. They now seem o reac very lile, if a all, o noncore inflaion daa; a he same ime, hough, hey do no appear o have changed he way hey reac o core inflaion daa. However, he changes in he inflaion process documened above sugges ha his sraegy may be problemaic, an assessmen ha is borne ou by he noiceable deerioraion in he relaive forecasing performance of he professionals. These resuls sugges ha professionals are placing oo much weigh on recen core inflaion, jus as households are placing oo much weigh on recen headline inflaion. The evidence presened above is also consisen wih he inerpreaion ha he professionals have sopped worrying abou headline inflaion and are now focusing on core CPI inflaion. To he exen ha his is a recen swich, and possibly one encouraged by hen- Chairman Greenspan s advocacy of he core inflaion rae, i suggess ha analyses which use daa from expecaions surveys o deermine how agens learn abou he economy need o accoun for a wide variey of influences on agens. 16
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Table 1. Projecions of 1-year-ahead Realized and Expeced CPI Inflaion on Realized Inflaion Sample: 1978Q1-2009Q3 Consan Realized Inflaion 1.44 1 (0.43) Expeced Inflaion Michigan Survey 1.01 1 (0.16) D94 2.62 5 (0.87) 0.45 10 (0.24) ΣPi 0.66 1 (0.08) 0.63 1 (0.03) ΣDPi -1.24 1 (0.33) -0.09 (0.09) 2 R 0.69 0.93 Exclude ΣDPi* 2.39 1 1.29 ΣPi + ΣDPi = 0** 3.26 10 44.68 1 ΣPi is he sum of he coefficiens on realized CPI inflaion, ΣDPi is he sum of he coefficiens on he realized inflaion erms muliplied by he dummy D94, which equals 0 unil he end of 1993 and 1 afer ha. HAC sandard errors are repored in parenheses. 1 denoes significan a 1 percen; 5 denoes significan a 5 percen; 10 denoes significan a 10 percen. * F saisic for null ha all 8 DPi erms can be excluded from he equaion. **Chi-square saisic for null ha he sum of he coefficiens on inflaion is equal o zero in he second half of he sample. 19
Table 2. Projecions of 1-year-ahead SPF Inflaion Forecas Sample: 1981Q3-2009Q3 Consan On Headline Inflaion 2.22 1 (0.26) On Core Inflaion 1.72 1 (0.28) D94 0.13 (0.39) -0.30 (0.39) ΣPi 0.50 1 (0.05) 0.55 1 (0.04) ΣDPi -0.46 1 (0.09) -0.09 (0.15) 2 R 0.88 0.91 Exclude ΣDPi* 4.49 1 1.56 ΣPi + ΣDPi = 0** 0.32 10.53 1 ΣPi is he sum of he coefficiens on realized CPI inflaion, ΣDPi is he sum of he coefficiens on he realized inflaion erms muliplied by he dummy D94, which equals 0 unil he end of 1993 and 1 afer ha. HAC sandard errors are repored in parenheses. 1 denoes significan a 1 percen; 5 denoes significan a 5 percen; 10 denoes significan a 10 percen. * F saisic for null ha all 8 DPi erms can be excluded from he equaion. **Chi-square saisic for null ha he sum of he coefficiens on inflaion is equal o zero in he second half of he sample. 20
Table 3. Predicing 1-year-ahead headline CPI Inflaion A. Sample: 2003:Q1 2009:Q3 (27 observaions) Using: Random walk Lagged headline inflaion only Lagged core inflaion only Phillips Curve UC-SV Model Michigan SPF Mean Error -0.15 0.07 0.15 0.27 1.34-0.52 0.30 Roo Mean Square Error 2.05 1.41 1 1.59 1.47 10 2.03 2.04 1.62 Noes: 1 Beer han he SPF forecas a 1 percen (Diebold-Mariano-Wes MSE es). 10 Beer han SPF forecas a 10 percen (DMW es). B. Sample: 1996:Q2 2002:Q4 (27 observaions) Using: Random walk Lagged headline inflaion only Lagged core inflaion only Phillips Curve UC-SV Model Michigan SPF Mean Error -0.21-0.64-0.33-0.22 1.29-0.37-0.28 Roo Mean Square Error 1.13 1.11 0.99 0.98 1.50 0.90 0.89 1,5 Noes: 1 Beer han lagged core inflaion forecas a 1 percen 2 Beer han Phillips curve specificaion a 5 percen 21
Table 4. Predicing 1-year-ahead core CPI Inflaion Using: Random walk Sample: 2003:Q1 2009:Q3 (27 observaions) Lagged core Phillips inflaion Curve only UC-SV Model Michigan SPF Mean Error -0.09-0.09-0.12 1.05-1.08-0.26 Roo Mean Square Error 0.63 0.57 0.43 10 1.06 1.30 0.51 1 Noes: 1 Beer han Random walk forecas a 1 percen (DMW MSE es) 10 Beer han SPF forecas a 10% 22
12 Figure 1: 1-year-ahead Expeced Inflaion 10 8 6 Michigan Survey 4 2 SPF Survey 0 1978 1981 1984 1987 1990 1993 1996 1999 2002 2005 2008
Figure 2: Projecions on quarerly CPI inflaion 15 year rolling sample A. Dependen variable: 1-year-ahead realized CPI inflaion B. Dependen variable: 1-year-ahead expeced inflaion from Michigan Survey 1.5 Sum of coefficiens on inflaion 1.5 Sum of coefficiens on inflaion 1.0 1.0 0.5 0.5 0.0 0.0-0.5-0.5-1.0-1.0-1.5 1992 1994 1996 1998 2000 2002 2004 2006 2008 2 sandard error bands shown, based on HAC sandard errors -1.5 1992 1994 1996 1998 2000 2002 2004 2006 2008 2 sandard error bands shown, based on HAC sandard errors 1.00 Adjused R-squared 1.00 Adjused R-squared 0.75 0.75 0.50 0.50 0.25 0.25 0.00 0.00-0.25 1992 1994 1996 1998 2000 2002 2004 2006 2008-0.25 1992 1994 1996 1998 2000 2002 2004 2006 2008
Figure 3: Esimaes from unobserved componen sochasic volailiy model for CPI inflaion 1960Q1-2009Q3 3.5 Sandard deviaion of emporary innovaions 3.0 2.5 2.0 1.5 1.0 0.5 2.00 1.75 1.50 1.25 1.00 0.75 0.50 0.25 14 12 10 8 6 4 2 0-2 1960 1963 1966 1969 1972 1975 1978 1981 1984 1987 1990 1993 1996 1999 2002 2005 2008 Sandard deviaion of permanen innovaions 1960 1963 1966 1969 1972 1975 1978 1981 1984 1987 1990 1993 1996 1999 2002 2005 2008 Permanen componen 1960 1963 1966 1969 1972 1975 1978 1981 1984 1987 1990 1993 1996 1999 2002 2005 2008
Figure 4: Projecions of he 1-year-ahead SPF inflaion forecas 15 year rolling samples A. On quarerly headline CPI inflaion B. On quarerly core CPI inflaion 1.00 Sum of coefficiens on inflaion 1.25 Sum of coefficiens on inflaion 0.75 1.00 0.50 0.75 0.50 0.25 0.25 0.00 0.00-0.25-0.25-0.50 1992 1994 1996 1998 2000 2002 2004 2006 2008 2 sandard error bands shown, based on HAC sandard errors -0.50 1992 1994 1996 1998 2000 2002 2004 2006 2008 2 sandard error bands shown, based on HAC sandard errors 1.0 Adjused R-squared 1.0 Adjused R-squared 0.8 0.8 0.6 0.6 0.4 0.4 0.2 0.2 0.0 0.0-0.2 1992 1994 1996 1998 2000 2002 2004 2006 2008-0.2 1992 1994 1996 1998 2000 2002 2004 2006 2008