Inflation Dynamics When Inflation is Near Zero

Transcription

1 No Inflaion Dynamics When Inflaion is Near Zero Jeffrey C. Fuhrer, Giovanni P. Olivei, and Geoffrey M. B. Tooell Absrac: This paper discusses he likely evoluion of U.S. inflaion in he near and medium erm on he basis of (1) pas U.S. experience wih very low levels of inflaion, (2) he mos recen Japanese experience wih deflaion, and (3) recen U.S. micro evidence on downward nominal wage rigidiy. Our findings quesion he view ha sable long-run inflaion expecaions and downward nominal wage rigidiy will provide sufficien suppor o prices such ha deflaion can be avoided. We show ha an inflaion model fied on Japanese daa over he pas 20 years, which accouns for boh shor- and long-run inflaion expecaions, maches he recen U.S. inflaion experience quie well. While he model indicaes ha U.S. inflaion migh be subjec o a lower bound, i does no rule ou a prolonged period of mild deflaion going forward. In addiion, our micro evidence on wages suggess no obvious downward rigidiy in he firm s wage coss, downward rigidiy in individual wages nowihsanding. As a consequence, downward nominal wage rigidiy may provide lile offse o deflaionary pressures in he curren U.S. siuaion, despie some circumsanial evidence ha his channel migh have been a work in he pas. JEL Classificaions: E31, E52, E12 Keywords: inflaion, anchored expecaions, survey expecaions, downward nominal wage rigidiy, Phillips curve Jeffrey C. Fuhrer is an execuive vice presiden and senior policy advisor a he Federal Reserve Bank of Boson; his address is jeff.fuhrer@bos.frb.org. Giovanni P. Olivei is a vice presiden a he Federal Reserve Bank of Boson, where he oversees he macroeconomic/finance secion of he research deparmen. His address is giovanni. olivei@bos.frb.org. Geoffrey M. B. Tooell is a senior vice presiden and direcor of research a he Federal Reserve Bank of Boson. His address is geoff.ooell@bos.frb.org. Bill Dickens and Peer Hooper provided very helpful commens and suggesions. This paper presens preliminary analysis and resuls inended o simulae discussion and criical commen. The views expressed herein are hose of he auhors and do no indicae concurrence by he Federal Reserve Bank of Boson, or by he principals of he Board of Governors, or he Federal Reserve Sysem. This paper, which may be revised, is available on he web sie of he Federal Reserve Bank of Boson a hp:// /economic/wp/index.hm. This version: Sepember, 2011

2 a series. 1 While here are many possible approaches o exploring hese quesions, we pursue a few 1. Inroducion In he wake of he longes poswar recession in U.S. hisory, inflaion declined noiceably from is 2008 peak (see able 1 for changes in a variey of inflaion measures). A abou a 1 percen annual rae a he ime of wriing (he sar of 2011), U.S. inflaion is as low as i has been since he early 1960s. Wih mos economiss esimaing ha significan economic slack remains in he American economy, i is reasonable o wonder abou he fuure rajecory of inflaion. Will wellanchored expecaions pull inflaion up as he recovery proceeds? Will slack resources pull inflaion oward or below zero? Is he Unied Saes headed for a Japanese-syle period of proraced, albei modes deflaion? Will downward nominal wage rigidiy provide an offse o disinflaionary forces? A key difficuly in answering hese quesions is ha he Unied Saes has had very lile recen experience wih very low inflaion raes. A number of researchers have examined he behavior of inflaion over he pas 20 years, as i fell from an annual rae noiceably above 2 percen o a yearly average of abou 2 percen from he lae 1990s hrough he mid-2000s. Bu his paper is concerned wih how inflaion behaves as i drops below 2 percen, and he U.S. experience in his range is quie limied. One migh wish o look for a breakpoin in he ime-series properies of inflaion daa in recen years, bu i is nearly impossible o deec a breakpoin in he las few years of specific acks. We consider a relaively wide array of Phillips curve specificaions. In several insances hese specificaions rade off micro-foundaions and/or raional expecaions for empirical relevance, and hroughou he paper we highligh he similariies and differences wih he more sandard models. Firs we examine he period from 1954 o 1963, a ime when U.S. inflaion was low. The evidence from his early episode suggess a relaively benign oucome for curren inflaion developmens, a resul of well-anchored long-run inflaion expecaions and a very mild radeoff beween inflaion and resource slack when slack is sizable. This laer effec could be he resul of downward nominal wage rigidiies. Ye he res of he paper quesions wheher sable long-run inflaion expecaions can preven deflaion and wheher downward nominal wage rigidiy can provide an imporan offse o price deflaion in he curren environmen. For his purpose, we 1 While no repored here, we also conduc convenional unknown breakpoin ess for changes in he auoregressive properies of a variey of U.S. inflaion measures. Simple auoregressive and reduced-form models of he core and headline inflaion measures examined in able 1 above ypically find eiher one or no breaks in he series from 1970 o he presen, wih he breakpoins falling in he period beween 1975 and

3 analyze he parallels beween Japan s long experience wih low inflaion over he las wo decades and he relaively recen experience in he Unied Saes. We hen examine some preliminary disaggregaed daa on wages o explore he exen o which firms are able o adjus heir wage coss downward; if here is downward rigidiy in he firm s wage bill, his may ac o limi he fall in inflaion ha migh oherwise occur. The relaively shor samples we are examining make any inflaion forecasing exercise even more difficul han usual. Neverheless, our findings cas doub on he now fairly widespread noion ha sable long-run inflaion expecaions will provide sufficien suppor o prices o avoid a prolonged period of low inflaion, or even deflaion. Indeed, recen U.S. inflaion dynamics do no seem o differ much from he Japanese experience of he pos-1990s. While in Japan a deflaionary spiral has no maerialized, here is also lile in he daa ha would lead us o confidenly rule ou he possibiliy of a prolonged period of mild deflaion in he Unied Saes. In addiion, our microeconomic evidence on wages suggess ha downward nominal wage rigidiy may provide lile offse o deflaionary price pressures. This lack of a counerweigh resuls from he fac ha downward nominal wage rigidiy in individual wages may no necessarily ranslae ino significan downward nominal rigidiy in firms wage bills. The res of he paper is srucured as follows. Secion 2 examines an opimisic scenario for near-erm inflaion developmens in he Unied Saes. In his scenario, inflaion is anchored by long-run inflaion expecaions and he correlaion beween real aciviy and inflaion is nonlinear, so ha a large degree of resource slack has a disproporionaely smaller influence on inflaion han does a more modes amoun of slack. This opimisic model, based on esimaing a sable nonlinear relaionship beween inflaion and he oupu gap in he 1950s and early 1960s, predics U.S. inflaion booming ou a a value slighly below 1 percen and, herefore, no deflaion. The res of he paper examines more closely he wo key feaures of his simple model, namely he role of longrun inflaion expecaions as a driver of inflaion and downward nominal wage rigidiy as a poenial buffer o declining inflaion. Specifically, secion 3 examines he Japanese experience, wih an emphasis on assessing he role ha inflaion expecaions a differen horizons (shor- and long-run) play in driving inflaion. Secion 4 draws parallels beween Japanese and U.S. inflaion dynamics over he pas wo decades. On he basis of his comparaive analysis, secion 5 reaches more pessimisic conclusions abou he oulook for U.S. inflaion in he near- and medium-erm. Secion 6 examines micro wage daa, focusing on preliminary evidence abou he presence of downward rigidiy (or lack hereof) in he firm s overall wage bill. Secion 7 provides some concluding remarks. 2

4 We consider differen specificaions of inflaion because U.S. episodes wih very low levels of inflaion in he pos-wwii period are scan. Therefore, saisical ess for choosing one model over anoher have limied power. Moreover, sources of insabiliy in he inflaion process have been documened exensively in he lieraure. These insabiliies have made inflaion difficul o forecas over ime. I is also possible ha he dynamics of inflaion a 2 percen or lower will urn ou o differ fundamenally from pas experiences wih low inflaion. For all of hese reasons, i is imporan o acknowledge model uncerainy under curren circumsances, and broaden he analysis o more han jus a single inflaion model. 2. An Opimisic Scenario: A Nonlinear Trend-Inflaion Model of U.S. Inflaion In his secion we revisi he one U.S. poswar episode (oher han he mos recen period) when inflaion was very low. From 1954 o 1963, 2 annual consumer price inflaion averaged abou 1.6 percen and flucuaed wihin a relaively narrow range. The privae consumpion expendiures deflaor s maximum year-over-year increase over his period was 3.25 percen. The conduc of moneary policy in hese years was reevaluaed in favorable erms by Romer and Romer (2002). Afer examining he FOMC records of he ime, Romer and Romer claim ha he Federal Reserve showed he same overarching concern abou inflaion ha is he hallmark of pos-paul Volcker moneary-policy orhodoxy. In paricular, hey argue ha policy ighening in response o increases in expeced inflaion was more aggressive han in he lae 1960s and in he 1970s. Moreover, he episode is poenially ineresing no jus because inflaion was low, bu also because here were some relaively large flucuaions in real aciviy. I is apparen from figure 1 ha over he period 1954:Q1 o 1963:Q4 here were some runups in inflaion during expansions, followed by declines in inflaion immediaely afer recessions. This paern is consisen wih a Phillips curve-ype relaionship. Figure 2 plos an esimae from he Congressional Budge Office (CBO) of he oupu gap agains he four-quarer-ahead inflaion rae, as measured by he PCE deflaor. 3 While no especially igh, he daa show a posiive relaionship beween inflaion and he oupu gap. The daa also sugges he presence of a nonlineariy, wih inflaion increasing a a faser rae for a given increase in he oupu gap when he oupu gap becomes more posiive. This nonlineariy mimics, muais muandis, he one found by Phillips (1958) 2 We exclude he early 1950s from he analysis because of he 1951 and 1952 price conrol amendmens associaed wih he Korean War. 3 The CBO oupu gap in his secion s figures is depiced as a four-quarer moving average wih declining weighs o smooh ou some shor-erm volailiy. 3

5 in his original sudy of he relaionship beween wage inflaion and he unemploymen rae in he Unied Kingdom. In he U.S. conex, such a feaure of he daa is he resul of a few quarerly observaions and, as a resul, i should be aken wih cauion. The observaions over he period from 1954 o 1963 sugges a modes radeoff beween inflaion and resources slack overall, and especially so when here is a large amoun of slack. This is confirmed by esimaing he following relaionship beween inflaion and he oupu gap: 4 LR 2 ln( *( π+ 4 π )) = *ln( * y ), n= 40, R = 0.46, (2.1) (0.0118) (0.0071) where sandard errors for he esimaes are in parenheses. 4 In he equaion, π is he four-quarerahead inflaion rae, while y denoes he oupu gap. 5 The inflaion rae is expressed as a deviaion LR from long-run inflaion expecaions, π, as of ime. Since survey expecaions of inflaion for his period are no available, we assume hem o be consan and equal o he average annual rae of inflaion (1.6 percen) prevailing over he period. We apply a linear ransformaion o he oupu gap before aking logs, as he oupu gap can ake negaive values. 6 This linear ransformaion can be hough of as providing an unemploymen rae equivalen of he oupu gap by means of a simple Okun s law. 7 The esimaed consan in equaion (2.1) is consrained o yield inflaion equal o is long-run expeced rae when he oupu gap is zero. The esimaed log-relaionship (2.1) allows he radeoff beween inflaion and resource slack o vary a differen levels of he oupu gap. This specificaion is very similar o he relaionship considered in Phillips s original aricle. The esimaed nonlineariy in U.S. daa over he period 1954 o 1963 is fairly small. An increase in he oupu gap from 2 o 4 percen raises annual inflaion by seven-enhs of 1 percen (0.70). The same improvemen in he oupu gap, bu from 4 o 2 4 Sandard errors are correced o accoun for a moving average componen in he esimaed error erm. 5 4 JC + 4 In equaion (2.1), four-quarer-ahead inflaion is compued as: π + 4 = 100* 1, where JC is he oal JC PCE deflaor. The oupu gap is: * * y = 100*ln( Y / Y ), where Y is he acual GDP level and Y is he CBO esimae of poenial GDP. 6 For he same reason, a linear ransformaion before aking logs is also applied o he difference beween inflaion and long-run expeced inflaion. 7 The consan in he linear ransformaion (which we se o 5.3) can be inerpreed as he equilibrium unemploymen rae, while he value of he slope (se a 0.5) implies ha a posiive oupu gap of 1 percen yields an unemploymen rae 50 basis poins below he naural rae. These values are consisen wih he esimaes obained from a simple level Okun s law relaionship over he sample 1954:Q1 o 1963:Q4. 4

6 percen, raises inflaion by four-enhs of one percen (0.40). We noe ha he roo mean squared error (RMSQE) from his esimaed nonlinear relaionship is abou 20 percen lower han he RMSQE from esimaing a compleely backward-looking sandard linear Phillips curve over he same sample. In oher words, over his sample period an acceleraionis Phillips curve specificaion does no perform especially well. We now use he esimaed relaionship (2.1) o fi curren inflaion developmens in he Unied Saes. Figure 3 plos acual core PCE inflaion and prediced inflaion from 2008:Q4 onward. To measureπ LR, we use he Hoey-Philadelphia survey s median 10-year inflaion expecaions. 8 The figure shows ha while he simple esimaed relaionship (2.1) fails o capure some shor-erm inflaion dynamics, i does capure he magniude of he decline in core PCE inflaion winessed since he end of The CBO esimae of he oupu gap indicaes ha resource slack peaked over he course of Since hen, slack has been decreasing modesly. Therefore, according o he nonlinear Phillips curve (2.1), inflaion boomed ou over he course of 2010 a a value slighly below 1 percen. Wih some improvemen in he oupu gap, inflaion is expeced o rever back o is long-run level. Given he esimaed nonlineariy, he reversion is exremely gradual. Core PCE inflaion is expeced o say below 1.3 percen as long as he oupu gap remains below 3 percen. The projeced pah for inflaion according o (2.1) over he course of is remarkably close o he range of esimaes provided by Sock and Wason (2010), who examine he relaionship beween inflaion and unemploymen by looking exclusively a recession episodes over he pos-1960 sample. In addiion o using a differen sample period, resource slack is defined differenly and eners he specificaion linearly. Sill, here are some more fundamenal similariies beween he approach we employ and he one used by Sock and Wason. Mos noably, inflaion in boh exercises is a funcion of long-run (rend) inflaion and an aciviy gap. Wheher his is an accurae reduced-form represenaion of he inflaion process is an issue ha will be considered more closely in he nex secion. While i may seem far-feched o projec he near-erm evoluion of inflaion based on a Phillips curve relaionship esimaed over he period 1954 o 1963, we noe ha recen movemens in inflaion fall well wihin he range experienced during his earlier period. Figure 4 depics he 8 This series is available from he Board of Governors of he Federal Reserve Sysem in he conex of he FRB/US model. The series adjuss he Survey of Professional Forecasers 10-year measure of inflaion expecaions o ake ino accoun he differenial beween PCE and CPI inflaion. The mnemonics for his series in FRB/US is PTR. 5

7 unemploymen rae vis-à-vis he four-quarer-ahead inflaion rae, expressed as a deviaion from long-erm inflaion. The char superimposes observaions from he period 1954:Q1 o 1963:Q4 wih observaions spanning he period 2003:Q1 o presen. As before, rend inflaion in he earlier period is given by he average inflaion rae prevailing over ha sample. For he mos recen period, inflaion is measured by he core PCE index, and rend inflaion is given by he Hoey-Philadelphia survey measure of 10-year inflaion expecaions. Merging hese wo periods yields he following esimae of he nonlinear Phillips curve: (2.2) 4 LR 2 ln( *( π π )) = *ln( * y ), n= 69, R = 0.50, + 4 (0.0060) (0.0036) where sandard errors for he esimaes are in parenheses. These esimaes are very similar o he ones obained using only he earlier sample. The slope of he curve is somewha shallower, bu he implied near-erm evoluion of inflaion is no maerially differen from he pah depiced in figure 3. When compared o simple benchmarks, he esimaed nonlinear relaionship is no devoid of empirical conen. Using he esimaes in (2.2), he RMSQE of he forecas for inflaion over he period 2003:Q1 o presen is 33 percen smaller han he RMSQE from a naïve forecas à la Akeson and Ohanian (2001). In Akeson and Ohanian s seup, he forecas for four-quarer-ahead inflaion is given by he curren value of four-quarer inflaion. The RMSQE from he nonlinear specificaion is also 40 percen smaller han he RMSQE from forecasing four-quarer-inflaion by jus posiing an expeced value equal o he curren level of long-run inflaion expecaions. 9 The modes decline in U.S. inflaion implied by he simple nonlinear Phillips curve given he curren large amoun of slack in he economy is he resul of wo main feaures of he model. Firs, he process for inflaion is anchored by rend inflaion (or long-run inflaion expecaions). In his respec, he nonlinear specificaion generaes dynamics ha are similar o purely forward-looking New Keynesian Phillips curve models (see Fuhrer and Olivei 2010). There are oher specificaions of he inflaion process ha do find some suppor in he daa and which enail a less benign inflaion oulook, as he nex secion will show. Even wihin he confines of his simple seup, he sabiliy of long-erm inflaion is a crucial facor in limiing he decline in inflaion, as no feedback is assumed from he curren low readings of inflaion o long-run expeced inflaion. If long-run expecaions 9 Williams (2006) noes ha since he mid-1990s core inflaion has remained remarkably close o a sable long-run arge, and ha inflaion forecass based on his long-run arge bea random-walk forecass à la Akeson and Ohanian. 6

8 were o decline, hen he implied decline in inflaion would be larger. In his regard, i is imporan o noe ha during he period from 1954 o 1963, he recessionary episodes were fairly shor-lived. For example, in he recession of , he oupu gap was closed in he firs half of Wih relaively shor downurns, i may no be unreasonable o assume lile change in long-run expeced inflaion, oher hings equal. Bu in a siuaion like he curren one in which slack in resource uilizaion may persis for a long ime, such an assumpion may prove inaccurae. The oher feaure a play in generaing a small projeced addiional decline in inflaion is he nonlinear radeoff beween inflaion and resource slack. In his original aricle, Phillips argued ha when he unemploymen rae is low and labor demand is high, firms will bid wage raes up quie rapidly. Conversely, Phillips conjecured ha wih high resource slack, wages will fall only very slowly because workers are relucan o offer heir services a less han he prevailing raes. The noion of an asymmeric response of wage changes o shocks in he economy was exploied by Akerlof, Dickens, and Perry (1996) o derive ime-series implicaions for inflaion. One imporan difference in Akerlof, Dickens, and Perry s model compared o a specificaion feauring a nonlinear relaionship beween inflaion and he oupu gap is ha in heir model high resources slack is sill compaible wih rapid disinflaion whenever he saring poin for inflaion is elevaed. Wih high inflaion, downward nominal wage rigidiy is in fac no binding. When he saring poin for inflaion, insead, is low as in he curren siuaion, heir model has implicaions for inflaion similar o he nonlinear specificaion considered in his secion, as downward nominal wage rigidiy limis firms abiliy o cu prices. 10 While his feaure of Akerlof, Dickens, and Perry s model may be desirable, we noe here ha he nonlineariy in he relaionship beween inflaion and he oupu gap which appears o be presen in he 1954 o 1963 period may have been a work in oher circumsances as well. Figure 5 shows a scaerplo of he CBO esimae of he oupu gap vis-à-vis he four-quarer-ahead core PCE inflaion rae less he 10-year inflaion expecaions. The figure merges he periods 1964:Q1 o 1969:Q4 and 1981:Q1 o 1997:Q4. 11 Figure 6 shows he same ype of scaerplo, bu over he period 1973:Q1 o 1980:Q4. Boh figures, wih he imporan small- 10 In order o generae a projeced pah for inflaion as he one depiced here in figure 3, Akerlof, Dickens, and Perry s model, oo, needs some anchoring of inflaion expecaions o a long-run arge. Absen such anchoring, heir model would predic a mild deflaion a levels of he unemploymen rae persisenly above 7.5 percen (see heir figure 3, page 32). 11 The 10-year expecaion measure was no available for he earlier period, and i is consruced by fiing he esimaed evoluion of he 10-year Hoey-Philadelphia survey measure over he period 1981 o 2006 o ha earlier sample. The esimaed process for he series is highly persisen, wih some addiional influence coming from acual core inflaion, he moneary policy sance, and he oupu gap. This series is consruced by he Board of Governors of he Federal Reserve Sysem. See foonoe 9. 7

9 sample cavea we already menioned, are suggesive of a sacrifice raio increasing when he oupu gap is negaive. For his ype of relaionship o emerge, i is crucial o consider he deviaion of inflaion from long-run expeced inflaion. Through his lens, recessions are periods when inflaion reliably falls, bu he change in he inflaion gap when oupu is below poenial appears o be smaller han he change in he inflaion gap when oupu is above poenial. Sill, i is imporan o sress ha over he periods represened in figures 5 and 6, long-run inflaion expecaions were moving as well. The change in he inflaion gap may well be mued wih high resource slack, bu if long-run inflaion expecaions are moving considerably so will acual inflaion. The oher implicaion is ha for hese periods i could prove more appropriae o appeal o some form of real, raher han nominal, wage rigidiy in order o jusify a nonlinear relaionship beween inflaion and real aciviy. 3. Inflaion in a Low-Inflaion Environmen: The Japanese Example As discussed above, over he pas 50 years he Unied Saes has had relaively lile experience wih an annual inflaion rae below 2 percen. Consequenly, i is difficul o garner much evidence ha would help policymakers gauge wheher he inflaion rae may behave differenly as i approaches zero. However, Japan provides a poenially useful recen example of a developed counry ha has experienced a prolonged recession and an exended period of very low (indeed negaive) inflaion. While one mus be cauious abou drawing parallels oo closely beween he Unied Saes and Japan, he Japanese experience may provide some clues as o how U.S. inflaion migh evolve in he years o come. We begin by examining key macroeconomic daa for Japan over he pas 30 o 40 years. Figure 7 displays some of he daa cenral o our analysis. The op panel shows boh headline and core CPI inflaion for Japan, where core is defined as all consumer iems excluding food and energy, along wih a measure of he oupu gap. Esimaes of Japan s oupu gap are hard o come by. Some esimaes sugges ha oupu reurned above poenial in he mid-o-lae 1990s, alhough his seems implausible. The oupu gap presened here was kindly provided by Sachihiro Hayashi a he Cabine Secrearia in Japan. Unlike mos oher published esimaes, i suggess wha we consider a plausible hisory for he Japanese oupu gap ha is, a gap ha implies proraced periods in which oupu falls significanly below poenial and performs reasonably well in an array of esimaes presened below. 8

10 In some of he Phillips curves ha we consider, we also use esimaes of real marginal cos (proxied by he labor share of income, as is convenional in he Phillips curve lieraure), he relaive price of impored energy goods, and he exchange rae. These daa are readily available and obained from sandard sources. 12 Of more ineres and less readily available are measures of inflaion expecaions. The boom panel of figure 7 displays boh shor-run (one year) and long-run (six o 10 years) inflaion forecass, aken from he Consensus Forecas daabase. 13 These daa are available only from he second half of 1989, and are colleced semi-annually. Oher horizons (2 5 years) are included in he daase, as are forecass for a limied se of oher macro variables. We use he oupu growh forecass for forecas horizons of 1 5 years o creae esimaes of he expeced oupu gap. Noe immediaely a few feaures of he daa: 1. Over he 1998 o 2010 period, inflaion has clearly fallen significanly and persisenly below zero. 2. This decline in inflaion occurred despie long-run inflaion expecaions ha have remained around 1 percen for he pas 15 years. 3. However, inflaion did no spiral downward, despie he presence of an (esimaed) negaive oupu gap hroughou mos of his period. 4. While he 6-10 year forecas has been wrong (on he opimisic side) for many years, he one-year forecas racks acual inflaion reasonably well. Reduced-Form Models: Old-Syle Phillips Curves and he Phillips Correlaion Consider a sandard backward-looking Phillips curve, where inflaion depends on lagged inflaion, usually wih a coefficien of one, and on he oupu gap, hus: (3.1) π = + ay π 1 Lagged inflaion serves as a proxy for expeced inflaion, or for fricions in he price-seing mechanism. The logic of his specificaion implies ha inflaion will coninue o rise (fall) as long as he oupu is posiive (negaive). This dynamic has been dubbed he acceleraionis Phillips curve, as i posis a relaionship beween he change in inflaion (and hus he second-difference or acceleraion in he price level) and he gap. Examining he op panel of figure 7, i would seem 12 See he daa appendix for deails. 13 Noe ha in he boom panel of he figure, he forecass are displayed on he dae he forecas is made. 9

11 difficul o reconcile such a specificaion wih Japanese inflaion experience of he pas 30 years. Despie a persisenly negaive oupu gap since he early 1990s, inflaion appears o have been bounded below by 2 percen. More formally, sandard backward-looking Phillips curves show a marked deerioraion in fi in recen decades. Table 2 provides a simple illusraion of his poin. The firs se of columns displays he esimaed backward-looking Phillips curve for Japanese core inflaion from 1971 o As he esimaes sugges, he uni sum resricion on lagged inflaion (hree quarerly lags) is no rejeced, and he oupu gap displays a sizable and significan coefficien sum. The second se of columns show he esimaed shif in hese parameers from 1990 o he presen. The effec of he oupu gap is essenially eliminaed, wih grea precision. 14 The able suggess oher significan shifs as well, bu he change in he esimaed effec of he oupu gap is economically quie imporan, and we consider i in more deail below. 15 Figure 8 displays he in-sample and ou-of-sample fi for he same Phillips curve over a variey of subsamples from 1980 o he presen. The Phillips curve includes hree lags of core inflaion, he change in he relaive price of impored energy goods, and lags of he esimae of he oupu gap displayed in figure 7. As he figure indicaes, forecass made employing a Phillips curve esimaed hrough he mid-lae-1990s consisenly and significanly underforecas he level of inflaion in ensuing years. The implicaion is ha he persisen negaive oupu gap would have implied more pronounced declines in inflaion, bu hese evidenly did no occur. Noe ha he rajecory of he inflaion forecas is consisen wih a coninued downward spiral as long as he oupu gap remains negaive, inflaion coninues o fall in he forecas. Why does Japan s Phillips curve miss so badly during he more recen decades? As suggesed by he shif es above, he basic acceleraionis naure of he relaionship is no presen anymore. The recen daa migh sugges a purely forward-looking raional expecaions model of inflaion in which inflaion depends on he average (discouned) fuure oupu gaps, so ha as he level of he expeced oupu gap increases, inflaion would rise. This possibiliy is examined in more deail below. 14 A flaening of he Phillips curve in Japan since he 1990s is also observed by De Veirman (2009). 15 A some economeric risk, we splice he OECD s esimaed oupu gap for wih he Cabine Office s gap from 1980 o he presen. We allow for shifs in he paern of lagged inflaion coefficiens as well, bu hese are no individually significan. They are consrained o sum o zero o preserve he uni sum consrain on lagged inflaion. Noe ha unknown breakpoin ess of he Japanese Phillips curve sugges a break in he sandard relaionship in he lae 1970s, well before he asse price collapse in he lae 1980s ha preceded Japan s grea recession. 10

12 Models ha Include Survey Expecaions The concep of anchored expecaions plays an imporan role in discussions of he expeced pah of U.S. inflaion. As highlighed in rend inflaion models such as hose proposed by Cogley and Sbordone (2008), sufficienly anchored inflaion expecaions can ac as an offse o he downward pull from a significan oupu gap and/or declining marginal coss. The following subsecions examine he role of expecaions in he inflaion process in Japan, using boh surveys of professional forecasers and raional expecaions models as alernaive means of measuring expecaions. The goal is o derive implicaions from he Japanese experience ha may cas ligh on he fuure course of U.S. inflaion. Reurning o figure 7, he boom panel suggess ha long-run inflaion expecaions (he red line) have remained well-anchored in Japan, flucuaing relaively lile around heir average of 1.2 percen over he pas 15 years (he average is shown in he dashed red line). This observaion raises he quesion of how long-run inflaion expecaions are formed. I is difficul o arrive a a fully saisfacory explanaion, bu one hypohesis is ha Japanese forecasers place considerable faih in he Bank of Japan o ulimaely deliver posiive inflaion more faih han migh be warraned given he consrains under which i labors. Since he incepion of he survey in 1989, long-run expecaions have always foreseen posiive inflaion in he 6 10 years ahead. Tha forecas has had he wrong sign for mos of he pas 15 years, ye even he mos recen reading, in he afermah of a prominen drop in Japanese oupu, expecs inflaion o recover o abou 1 percen on average six o 10 years from now. While he accuracy of he long-run Japanese forecas is of ineres, of more relevance o his paper is he role ha hese expecaions play in influencing realized inflaion. To be sure, anchored long-run expecaions have no prevened Japanese inflaion from falling below zero and remaining here for he las dozen years. Bu as already discussed before, Japanese inflaion has no coninued o decline, and his observaion raises he possibiliy ha anchored long-run expecaions have kep inflaion from dropping furher han hey migh have in he presence of a large oupu gap. To examine he influence on realized inflaion of boh shor- and long-run expecaions, we esimae simple Phillips curves ha explore he relaionship among core inflaion, expecaions, he 11

13 oupu gap, marginal cos, and imporan relaive price shifs. 16 The Phillips curves ake he form (3.2) π = aπ + bπ + cπ + dy + es + fx LR 1 1 a+ b+ c = 1, where s denoes marginal coss, y represens an esimae of he oupu gap, and x represens relaive price variables (energy prices and he exchange rae). We enerain boh he oupu gap and marginal coss as driving processes, as he lieraure is somewha unseled on his maer. The sum of he coefficiens on survey expecaions and lagged inflaion are consrained o sum o one, alhough we es he significance of ha consrain hroughou. In preliminary ess, we find ha marginal coss ofen ener hese regressions significanly; he oupu gap never does, so we exclude i from he resuls presened below. In addiion, he relaive price variables are rarely significan, so we exclude hese from he analysis. We presen boh full-sample (able 3) and rolling regression esimaes (figure 9). Noe ha as highlighed above, now-common specificaions for inflaion ypically express inflaion relaive o rend inflaion, see Cogley and Sbordone (2008). If inflaion exhibis a rend componen, perhaps aribuable o a ime-varying inflaion goal, hen i is appropriae o wrie he inflaion model so ha all inflaion erms are expressed as deviaions from he rend erm. In he conex of hese daases, long-run inflaion expecaions could serve as a reasonable proxy for rend inflaion. While he heory supporing such specificaions is compelling, he daa for his sample is much less so. Consider a rend-inflaion version of he equaion above: (3.3) π π π π π π LR 1 ( y LR ) (1 )( LR = a + a 1 1) + es. This equaion implies resricions on he way in which long-run expecaions ener: Re-arranging his equaion, i can be shown ha he coefficiens on long-run inflaion in periods and 1should be (1 a) and (1 a) respecively. A es of his resricion fails o rejec i, yielding a p-value of However, he coefficiens for long-run inflaion expecaions ener insignificanly, boh individually and joinly, likely explaining he inabiliy o rejec he opposie-sign resricion implied by he rend 16 The working paper version of his paper provides simple VAR analysis of he covariaion among hese key variables. The resuls are consisen wih he esimaes presened here. 12

14 inflaion model. 17 Alogeher, i seems empirically well-jusified o absrac from he issues implied by rend inflaion for Japanese Phillips curves over his period. The resuls ha follow employ he simpler specificaion, ha is equaion (3.2) wih b = 0 and d = 0. The esimaes in he op panel of able 3, along wih rolling regression resuls (no shown), sugges ha long-run expecaions play lile or no role in he evoluion of Japanese core inflaion. For his reason, we repor esimaes ha exclude long-run inflaion expecaions. Esimaion resuls for he full sample are presened in he boom panel of able 3, and rolling regression resuls are shown in figure 9. Our findings sugges a srong role for he one-year expecaion, boh for he full sample and for he subsamples covered by he rolling-regressions of figure 9. The p-value (no shown in he figure) for he one-year expecaion is always near zero. Lagged inflaion plays a small bu moderaely significan role hroughou mos of he sample. For he las dozen years, he role of lagged inflaion becomes insignifican, he marginal coss variable gains significance, and he p-value of he uni sum resricion drops oward zero, suggesing his resricion is violaed in he mos recen decade. The finding of a srong role for he one-year expecaion is robus o concerns abou mulicollineariy beween he oupu gap and he one-year expecaion. In he boom panel of able 3, subsiuing he oupu gap for he one-year expecaion resuls in an insignifican coefficien on he oupu gap, and a decline in he R 2 from 0.79 o The one-year expecaion appears o capure an imporan and independen effec on inflaion. While he backward-looking acceleraionis Phillips curves of he preceding secion are poor predicors for he Japanese inflaion experience of he pas 20 years, he survey expecaions models ha use real marginal coss as a driving variable achieve more success. For his model, figure 10 displays he in-sample fi for he full-sample esimaes repored in able 3, and he ou-of-sample fi for he las five years of he sample. The ou-of-sample fi suggess he model is reasonably sable (given he limied number of semi-annual observaions available o es his hypohesis), and cerainly far more sable han he Phillips curve resuls presened in figure The relaive sabiliy of he 6 10-year inflaion expecaion over he pas 20 years also suggess ha his variable will add lile o he model. Equaions esimaed in he deviaion form (3.3) produce resuls ha are very similar o hose in ables 4 and 5. Specifically, in able 3 he esimaed coefficiens on he one-year expecaion and lagged inflaion are 0.92 and 0.08 respecively; he coefficien on marginal coss is In able 5, he esimaed effec of he raional expecaions erm is once again zero, and he weighs on he one-year expecaion and lagged inflaion are 0.7 and 0.3, respecively. The marginal coss esimae, a 0.22, is a bi higher han he OLS esimae. 18 The working paper version of his paper conains a more complee se of resuls, including he rolling-regression esimaes of equaion (3.2) referenced in he ex. 13

15 Because he success of his model ress heavily on he inclusion of he one-year survey expecaion of inflaion, i is imporan o beer undersand wha informaion is incorporaed in he one-year survey. Reduced-form regression models of he one-year expecaion reveal ha one-year inflaion expecaions are well-explained by he following regression equaion: (3.4) π = aπ + bπ + cs + dy + c The esimaed equaion using semi-annual daa from 1990:H1 o 2009:H2 is (HAC sandard errors in parenheses) π = 0.31π π s y R (0.13) (0.11) (0.039) (0.035) (0.11) = The one-year expecaion is correlaed wih lagged inflaion, real marginal coss and he curren oupu gap, and exhibis very modes persisence, as evidenced by he significan bu small coefficien on he lagged dependen variable. The in-sample fi of his equaion, which is quie igh, is displayed in he boom panel of figure 10. Noe ha inclusion of he 6 10-year inflaion expecaion adds marginally o he fi of he equaion in he firs five years of he sample. For he period since 1995, he coefficien for he long-run expecaion is esimaed very imprecisely, and adds nohing o he fi of he one-year equaion. Once again, we exclude long-run inflaion expecaions for he balance of his secion. The implicaion of his simple depicion of one-year Japanese inflaion expecaions is ha hey need no be well-ied he long-run expecaions of inflaion as measured by he Consensus forecas survey. Expecaions respond o realized inflaion and o he oupu gap wih a lag. As he oupu gap improves, inflaion improves, bu wih a lag, given he dependence on is own lag and on realized inflaion. How well such an expecaions mechanism, coupled wih he inflaion equaion esimaed above, can explain he Japanese inflaion experience in a more fully fleshed-ou model remains o be seen. Srucural Models 14

16 While he old-syle backward-looking Phillips curve fis he Japanese inflaion daa quie poorly, a model wih survey expecaions achieves some success. How well would he curren generaion of forward-looking models explain Japanese inflaion behavior? We consruc a simple raional expecaions model ha encompasses boh he NKPC model wih and wihou indexaion and a survey expecaions-based model. An ineresing aspec of his exercise is ha i allows us o examine he exen o which he survey expecaions mimic he expecaions implied by he raional expecaions NKPC model for Japanese daa. The inflaion equaion is (3.5) π = ae π + bπ + (1 a b) π + cs If a = 1and b = 0, hen he raional expecaions NKPC is a reasonable approximaion for Japanese inflaion daa. If a = 0 and b = 1, hen he model wih one-year survey expecaions serves as a beer depicion of Japanese inflaion. Wih a = 0 and b = 0 he model depends only on lagged inflaion, as in an old-syle Phillips curve model. A hos of inermediae combinaions are of course 19, 20 possible. Noe ha we have revered o marginal coss as he driving variable in he Phillips curve. This is largely a maer of empirical fi iniial esimaes sugges ha he oupu gap eners insignificanly and ofen wih he wrong sign in his model. Thus we use model-consisen forecass of marginal coss, in conras o he previous exercise, which uses Consensus survey forecass of he fuure values of he driving variable. Since we need o generae model-consisen expecaions of inflaion for period +1 and we need o be concerned abou he possible simulaneous deerminaion of marginal cos (and poenially of he survey variable) and inflaion, we close he model wih he reduced-form equaion for one-year inflaion expecaions as described above, and wih VAR equaions for marginal coss and he oupu gap esimaed over he full sample (1990 o 2009). Thus he full model ha we employ for esimaion, wih error erms suppressed, is: 19 Using somewha differen models, samples, and mehods, Robers (1997) examines he role of survey expecaions in forward-looking Phillips curves for he Unied Saes. 20 In preliminary esimaion exercises, he lag of oal inflaion, raher han core, eners significanly in he inflaion equaion. Thus we allow inflaion o respond o lagged oal inflaion, and link oal inflaion o core inflaion via an esimaed error-correcion equaion. 15

17 (3.6) π = ae π + bπ + (1 a b) π + cs + c T π = dπ + eπ + f π + gy + g π π = j( π π ) + k( π π ) s T T T = Β X i i i= 1 y 2 = Γ X i i i= 1, T where π 1 is he lagged value of overall inflaion (which performs beer han lagged core inflaion in iniial regressions), and X is he vecor of variables in he wo-lag VAR (inflaion, oupu gap, marginal coss). The driving variable for he one-year expecaion is he oupu gap, as iniial esimaes find an insignifican role for marginal coss. This resul is somewha puzzling, as we find he opposie resuls for he Phillips curve. The reduced form inflaion equaion esimaed above suggesed some role for boh marginal cos and he oupu gap; his sysem parses hose roles ino effecs on inflaion and inflaion expecaions respecively. We esimae he VAR coefficien marices B and Γ joinly wih he oher parameers via maximum likelihood. 21 The resuls for he firs hree equaions in (3.6) are presened in able The esimaes find he weigh on he forward-looking (model-consisen or raional expecaions) componen o be small and imprecisely esimaed. There appears o be a small role for indexaion or lagged inflaion, while wo-hirds of he weigh on he expecaions erms falls on he one-year expecaion. This resul mirrors he resuls in he reduced-form equaions presened above. The conribuion of he shor-erm expecaions is again significan: The likelihood raio es for he hypohesis ha b = 0 is rejeced wih a p-value of For some purposes, i would be reasonable o collapse he resuls for he one-year expecaion ino he single-equaion Phillips curve of equaion (3.4). The significan esimaed coefficien for he one-year expecaion would imply an augmened role in he Phillips curve for 21 The working paper version conains esimaes in which we hold he VAR parameers a heir OLS esimaed values. There is no qualiaive difference in he resuls from he join esimaion. The sandard errors for he VAR parameers and some of he srucural parameers are larger, bu he resuls are oherwise he same. This resul is no surprising given he lack of feedback from he srucural equaions ino he VAR equaions. 22 Nunes (2010) also explores he role of survey expecaions in New Keynesian Phillips curves. His resuls differ somewha from ours; for his GMM esimaes, his may be due o weak insrumens (see Fuhrer 2011). 23 The specificaion appears well-behaved in mos dimensions. For example, he esimaion residuals are approximaely whie noise, wih Q(12) p-values for he five errors of 0.60, 0.72, 0.89, 0.61 and 0.51 respecively. The in-sample fis are all igh. As noed above, a version of his model ha expresses he inflaion variables as deviaions from long-run expecaions does no differ qualiaively from he version presened in able 5. 16

18 lagged inflaion and he oupu gap. 24 Bu his is jus he equivalen in a raional expecaions framework of solving for he model-consisen expecaions in erms of observables o arrive a a single-equaion reduced-form represenaion for inflaion ha is consisen wih he resriced srucural model. While one could hen use he reduced-form inflaion equaion as a forecasing vehicle, he poin of he modeling in his paper is o undersand he way in which expecaions survey -based or model-consisen ener srucural Phillips curves, no o arrive a a beer reducedform forecasing equaion for inflaion. 25 In sum, Japanese inflaion appears o be bes modeled no as a backward-looking acceleraionis Phillips curve, nor as a forward-looking NKPC, nor as a hybrid NKPC. Insead, inflaion depends on he one-year survey expecaions, which evolve according o he dynamics described above, and do no replicae eiher old-syle or NKPC-syle Phillips curves. 4. How Much Does he Unied Saes Look Like Japan? Up o his poin, our inflaion modeling has been suggesive, in he sense ha an economically developed counry like Japan clearly can experience a susained bou of deflaion despie long-run expecaions ha are well-anchored above zero. More imporan o he evoluion of inflaion is he shor-run (one-year) expecaion, which in Japan appears o be driven by recen realizaions of inflaion and he oupu gap. How well would such a model fi he Unied Saes in recen years? Surprisingly, he answer appears o be quie well. While we will explore he dynamics of U.S. inflaion and inflaion expecaions in more deail shorly, he spiri of he firs exercise in his secion is o simply apply he Japanese inflaion model o U.S. daa o see how well he model explains recen hisory. Panel A of able 5 presens esimaes of a Phillips curve ha closely parallels he esimaed model in able 3 for Japan. 26 Noe ha in iniial regressions, as in he Japanese daase, long-run (10-year average) expecaions from he SPF survey ener wih a very small coefficien (0.01), which is imprecisely esimaed (sandard error 0.25), also paralleling he evidence from Japan. Thus we exclude long-run inflaion expecaions from he regressions in able 5. The issues ha arise from considering socalled rend inflaion models are presen here as hey were in he case of Japan. The daa for he 24 The posiive coefficien on lagged expeced inflaion implies addiional lags of all he variables in he Phillips curve as well, alhough his lagged coefficien is relaively small. 25 In a raional expecaions framework, one can also solve for he single-equaion reduced form for inflaion, expressed in erms of observables. 26 See he daa appendix for deails on daa consrucion and sources. 17

19 Unied Saes also fail o rejec he resricion implied by he rend inflaion model, wih a p-value of Bu like Japan, he long-run (10-year) expecaions are esimaed very imprecisely, and are far from significan eiher individually or joinly. As a consequence, we exclude 10-year inflaion expecaions from he equaion deermining inflaion for he Unied Saes. The esimaes ha follow employ he simpler, non-rend-inflaion specificaion oulined above. The one-year expecaion akes on a similar coefficien of abou wo-hirds. Excluding he one-year expecaion from he regression decreases he R 2 from 0.69 o The one-year expecaion clearly explains a quaniaively significan and saisically independen source of inflaion variaion. 27 Panel A of able 5 also displays esimaes for he one-year expecaion for U.S. inflaion, which is pivoal in deermining U.S. inflaion, jus as i is for Japan. The parallels are sriking. In he core inflaion equaion, he coefficiens on he one-year (SPF) survey expecaion and lagged inflaion are exremely close o hose esimaed for Japan. The coefficien on marginal coss is smaller, bu sill likely plays an imporan role. The one-year expecaion similarly depends on lags of realized inflaion and he oupu gap. 28 Figure 11 displays he fied values for boh of hese regressions, wih he pos-2006 ou-of-sample fi for he core inflaion regression depiced in he op char. 29 There is no obvious sign of ou-of-sample degradaion. In parallel wih he exercises conduced for Japan, we esimae a version of he model for U.S. daa ha allows he raional expecaion of nex period s inflaion o ener he inflaion equaion. The model parallels he Japanese model in he previous secion, and is displayed in panel B of able 5. Broadly speaking, he resuls are quie similar o he OLS esimaes above, which is no surprising given he absence of a raional expecaions effec in he equaion. 30 Inflaion is well- 27 A version of he model in which we express inflaion as he deviaion from rend inflaion in his case, as a deviaion from he SPF 10-year inflaion expecaion produces resuls ha are qualiaively similar. Specifically, he coefficiens on he one-year lagged inflaion and marginal cos are 0.73, 0.27, and 0.057, remarkably close o he esimaes in able 6. The relaive sabiliy of he SPF 10-year expecaion suggess ha his adjusmen is close o subracing a consan from he inflaion measures, which of course should no affec he resuls much. 28 One can improve he fi of he equaion by including he lagged one-year expecaion, bu he esimaed coefficien in his case is abou 0.7, which seems like an undue reliance on lagged expecaions. 29 The esimaes in panel A of able 5 are OLS esimaes. GMM esimaes of he same model yield very similar resuls, wih he sum of coefficiens on he inflaion and oupu gap erms insignificanly differen from he OLS esimaes. The J-saisic fails o rejec he over-idenifying resricions. Full informaion esimaes appear in panel B of he able. The ou-of-sample fi is generaed by esimaing he regression from 1990 o 2006, and hen dynamically simulaing he model wih hese esimaed coefficiens for :H1. 30 Noe, however, ha he maximum likelihood echnique employed in hese esimaes akes full accoun of he simulaneiy implied by he presence of he conemporaneous inflaion and oupu erms in he equaion for one-year inflaion expecaions. The esimaes for a, b and c are consrained o be greaer han or equal o zero, as i is difficul o develop a srucural inerpreaion in which any of hese expecaions proxies would ener negaively. Esimaes for he model in which inflaion variables are expressed as deviaions from he 10-year expecaion deliver remarkably similar resuls. The esimaes for a, b and c are 0.00, 0.78 and 0.52 respecively. In he one-year expecaion equaion, he sum of 18