Empirical Estimates of Changing Inflation Dynamics

Transcription

1 No Empirical Esimaes of Changing Inflaion Dynamics Jeff Fuhrer, Giovanni Olivei, and Geoffrey M. B. Tooell Absrac: This paper provides an array of empirical evidence bearing on poenially imporan changes in he dynamics of U.S. inflaion. We examine he overall performance of Phillips curves relaive o some well-known benchmarks, he efficiency wih which he Federal Reserve s Greenbook forecass of inflaion use real aciviy informaion, and shifs in he key deerminans of he reduced-form riangle model of inflaion. We develop a srucural model-based inerpreaion of observed reduced-form shifs and conduc a reduced-form assessmen of he relaionship beween core and headline measures of inflaion, cenering on he persisen pass-hrough of relaive price changes ino core and headline inflaion measures, and a parallel exercise ha examines he pass-hrough of key relaive price changes ino wage and compensaion measures. JEL Codes: E5, E31, E37 Jeff Fuhrer is an execuive vice presiden and he direcor of research, Giovanni Olivei is a vice presiden and economis, and Geoff Tooell is a senior vice presiden and he depuy direcor of research, all a he Federal Reserve Bank of Boson. Their addresses are Jeff.Fuhrer@bos.frb.org, Giovanni.Olivei@bos.frb.org, and Geoff.Tooell@bos.frb.org, respecively. We would like o hank Todd Clark for helpful commens and suggesions. Denny Lie, Chad Secher, and Rachel Sern provided excellen research assisance The views expressed in his paper are hose of he auhors and do no necessarily represen he views of he Federal Reserve Bank of Boson or of 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:// This version: May 2009

2 Inroducion This paper provides a baery of empirical ess of Phillips curves. The ess examine he sabiliy of various aspecs of he Phillips curve, including: (1) is slope (he coefficien(s) on he real aciviy measure), (2) he influence of key relaive prices ha shif he curve, (3) he influence of pas inflaion dynamics on he formaion of inflaion expecaions, and (4) general equilibrium influences ha arise from he conduc of moneary policy and he I-S curve linking real aciviy o real ineres raes. The paper uses boh single-equaion, reduced-form versions of he Phillips curve and muliequaion, consrained raional expecaions models ha incorporae a Phillips curve. The paper suggess he following conclusions: (1) There have indeed been shifs in Phillips curve parameers. This conclusion is validaed in all forms of he Phillips curve ha we examine. (2) The shifs are mos pronounced for he effec of he relaive price of oil on core inflaion. (3) The effec of he real aciviy variable may have diminished in recen decades. However, i is no zero, and we provide evidence suggesing ha he Federal Reserve s Greenbook forecas may have under-weighed he conribuion of he unemploymen rae in recen years. (4) The shifs appear o be concenraed in he early 1980s. The Phillips curve has been relaively sable over he pas wo decades. (5) Accouning for a change in parameers in he 1980s dramaically improves he ou-of-sample forecasing performance of he Phillips curve. In fac, incorporaing his shif in parameers overurns he resuls of Akeson and Ohanian (2001). (6) In a srucural model of he New Keynesian variey, he source of he shifs in he more reduced-form Phillips curves is a combinaion of a smaller effec of he relaive price of oil in he Phillips curve, a smaller Phillips slope coefficien, and a downward shif in he ineres sensiiviy of he I-S curve, all of which occurred in he early 1980s. In more recen years, he share of backward-looking or indexing agens in he Phillips curve appears o have declined, alhough he idenificaion of ha effec is difficul in recen years. The srucure of he paper is as follows. Secion I discusses he Phillips curve forecasing performance, especially relaive o he Akeson-Ohanian benchmark. Secion

3 II examines he inflaion-unemploymen radeoff implici in recen Greenbook forecass. Secion III looks a reduced-form and srucural esimaes of shifs in key Phillips curve parameers. Because a key finding from Secion III is a clear shif in he influence of he relaive price of oil, Secion IV looks in more deail a poenial changes in he passhrough of key relaive prices ino core and headline inflaion, and ino wages. Secion V offers some concluding remarks. I. Why use a Phillips curve? Some new resuls on forecas accuracy In his secion we revisi he forecasing performance of he radiional backward-looking Phillips curve. The main reason o perform his exercise is o provide an inerpreaion of some of he negaive findings in he lieraure (see Akeson and Ohanian 2001, and Sock and Wason 2008) on he usefulness of backward-looking Phillips curves o forecas U.S. inflaion. While increasingly complemened by more srucural models of inflaion, backward-looking Phillips curve specificaions ofen play an imporan role in shaping he inflaion oulook and he conduc of moneary policy. We show ha he relaionship beween inflaion and unemploymen is igher han some of he previous sudies sugges, hough here are periods when he Phillips curve relaionship failed o maerialize. We discuss changes in he relaionship ha have occurred over ime, and in so doing we illusrae specificaions ha improve on he forecasing performance of well-known benchmarks. Exan lieraure on ou-of-sample inflaion forecasing cass doub on he usefulness of backward-looking Phillips curves for forecasing U.S. inflaion in he pos period. While several sudies have reached more nuanced conclusions, he essence of Akeson and Ohanian s (2001) resuls abou he inabiliy of Phillips curve specificaions o improve upon a simple univariae benchmark (whereby he forecas of inflaion in he nex four quarers is he value of four-quarer inflaion oday) has proved difficul o overurn. In he mos comprehensive sudy o dae, Sock and Wason (2008) corroborae Akeson and Ohanian s findings, wih he imporan qualificaion ha when 3

4 he unemploymen rae is sufficienly differen from he NAIRU, Phillips curve specificaions improve subsanially upon a univariae benchmark. To illusrae some imporan issues concerning he usefulness of radiional backward-looking Phillips curves in forecasing inflaion, we sar by comparing he insample versus he ou-of-sample performance of he Phillips curve. We show ha here is a deerioraion in he performance of he Phillips curve when moving from in-sample o ou-of-sample evidence. There are several poenial reasons for his finding. For example, i has been noed ha ou-of-sample ess have low power in small samples. 1 Anoher poenial explanaion is model insabiliy. Shifs in he parameers over ime may weaken he ou-of-sample performance of he Phillips curve. We provide evidence ha parameer insabiliy is likely o have played a role in he weakening of he ou-ofsample relaive o he in-sample evidence over he period 1984 o Ou-of-sample forecass were generally worse han in-sample forecass in he firs par of he sample, bu performed beer in he laer par of he sample. This paern in he relaive performance of in-sample versus ou-of-sample forecass suggess a shif in parameers in he early 1980s. We hen show how he ou-of-sample performance of he Phillips curve can be improved by aking ino accoun poenial changes in he Phillips curve s parameers. The backward-looking Phillips curve specificaion we consider is sandard in he lieraure. Curren inflaion is a funcion of pas inflaion, he unemploymen rae, and oher conrol variables (supply shocks) ha ac as shifers in he inflaion-unemploymen rae relaionship. Le rae of inflaion a an annual rae, P denoe he average price index in quarer. Then he quarerly π, can be wrien as π = 400 * ln( P / P 1). Fourquarer inflaion, ha is, he percenage growh in prices over four quarers, is given 4 by π = 100*ln( P / P 4 ). We consider inflaion forecass a he four-quarer horizon, which is widely sudied in he lieraure and of ineres o policymakers. As a resul, our Phillips curve specificaion akes he form: 1 See Inoue and Kilian (2004). For evidence on he low power of ou-of-sample ess in backward-looking Phillips curve specificaions, see Clark and McCracken (2006). 4

5 4 (1) π + 4 π = α + γ ( L) π + β ( L) u + δ ( L) x + ε, where α is a consan, γ (L), β (L), and δ (L) are lag polynomials wrien in erms of he lag operaor L, and he unemploymen rae, π is he firs difference in inflaion. The variable u denoes x is a vecor of supply shock variables, and ε is an error erm. As wrien, he specificaion imposes he condiion ha he coefficiens on quarerly inflaion π sum o one. These ime and lagged quarerly inflaion erms proxy for expecaions of inflaion over he nex four quarers a key feaure of he backwardlooking Phillips curve. We compare he four-quarer-ahead forecas of inflaion using he Phillips curve specificaion in equaion (1) wih he Akeson-Ohanian benchmark, whereby expeced 4 inflaion over he nex four quarers, π 4 quarers, π, plus noise: +4, is equal o inflaion over he previous four 4 4 (2) π + 4 = π + η, where η is an i.i.d. error erm. This random-walk benchmark is no as naïve as i firs appears. Sock and Wason (2007) documen ha from 1984 on, he univariae process for inflaion, π, is well described by an IMA(1,1) process. Over his period, he esimaed coefficien for he moving average erm in he IMA (1,1) represenaion is such ha a he four-quarer (or longer) horizon, he Akeson-Ohanian benchmark well approximaes a forecas made wih he IMA(1,1) process. As such, he Akeson-Ohanian benchmark can be hough of as an effecive shorcu o a non-naïve univariae represenaion of he inflaion process. We consider wo measures of prices, he core CPI and he core PCE indexes. Core measures of consumer prices are of paricular ineres o policymakers. Also, by 5

6 miigaing he role of energy and food price shocks, a Phillips curve relaionship specified on core inflaion measures should provide a beer assessmen of he role of economic aciviy in generaing common price movemens. The civilian unemploymen rae (16 yr. +) is specified eiher in levels or as a deviaion from a ime-varying NAIRU. Specifying he unemploymen rae in levels is equivalen o assuming a consan NAIRU in equaion (1) over he chosen esimaion period. We use he CBO measure as our imevarying esimae of he NAIRU. 2 As supply shock conrols, we include in (1) lags of he change in he relaive price of oil and lags of he change in he relaive price of non-oil impors. We use he roo mean squared forecas error (RMSE) as our meric o evaluae each forecas. The RMSE over he period 1 o 2 is RMSE = 1 1, = 1 ( ) π + 4 π, 4 where π is he forecas of +4 4 π +4 made a ime. Table I.1 compares roo mean squared errors for four-quarer inflaion forecass for core CPI and core PCE inflaion, respecively. The able provides he RMSE for he Akeson-Ohanian forecas benchmark, and he RMSE from differen Phillips curve specificaions relaive o he Akeson-Ohanian benchmark. The sample period is 1984 o We consider Phillips curve specificaions wih eiher a ime-varying NAIRU or a consan NAIRU, and wih or wihou supply shocks. We also disinguish beween insample forecass and (pseudo) ou-of-sample forecass. The in-sample forecass are obained from esimaing a Phillips curve over he period 1984:Q1 o 2007:Q4. The ouof-sample forecass, insead, simulae a real-ime forecasing exercise. 3 This involves 2 We experimened wih oher esimaes of he NAIRU, consruced as eiher one-sided or wo-sided filers of he unemploymen rae. The resuls are no sensiive o he chosen measure. 3 To fully simulae a real-ime forecasing exercise, pseudo ou-of-sample forecasing should use real-ime daa. Here, as in some previous sudies, we use final daa. This, among oher hings, reduces he measuremen error bias ha a ruly real-ime exercise enails. 6

7 esimaing a Phillips curve up o dae, making he four-quarer ahead forecas for dae + 4, hen moving forward o dae + 1 and repeaing he esimaion o generae he nex four-quarer ahead forecas. This process is repeaed over he enire sample period, and a each poin in ime he Phillips curve is esimaed over a rolling window of 40 quarers. This means ha when we generae he firs forecas in he sample, ha is, he forecas for inflaion over he four quarers 1984:Q1 o 1984:Q4, we esimae a Phillips curve over he period 1973:Q4 o 1983:Q4. Thus, in he earlier par of he sample, he ou-of-sample forecass use daa ha pre-dae 1984 when esimaing he Phillips curve. These daa are no used when generaing he in-sample forecass, which are based on a Phillips curve esimaed over he forecasing sample 1984 o For simpliciy, he Phillips curve specificaion we esimae in he ou-of-sample exercise a each poin in ime always mainains he same lag lenghs. Specifically, we use he same lag lenghs as in he Phillips curve specificaion esimaed over he full forecasing sample. The resuls in he able show ha he in-sample Phillips curve forecass perform well relaive o he Akeson-Ohanian benchmark. The Phillips curve RMSEs are 13 o 42 percen below he Akeson-Ohanian benchmark, depending on he paricular specificaion and he inflaion measure used. The performance of he Phillips curve, however, deerioraes when we consider he ou-of-sample forecasing exercise. The deerioraion occurs across all differen specificaions and measures of inflaion, bu is much more pronounced for core CPI inflaion han for core PCE inflaion. For he core CPI inflaion measure, he RMSE is higher han he Akeson-Ohanian benchmark across all specificaions. I should also be noed ha esimaing a Phillips curve wih he same lag lenghs as he in he in-sample specificaion migh allow he ou-of-sample exercise o undersae he deerioraion in he RMSE relaive o he in-sample exercise. This is so because in real ime he forecaser also faces model specificaion uncerainy, which we may have arificially reduced by imposing he (bes fiing) in-sample specificaion. In sum, while he in-sample performance of he Phillips curve in he pos 1984 sample is good relaive o he Akeson-Ohanian benchmark, he resuls for he ou-ofsample forecasing exercise are in line wih he exising lieraure. These laer resuls 7

8 show ha he performance of he Phillips curve over he period 1984 o 2007 relaive o he Akeson-Ohanian benchmark is, a bes, mixed. Our findings of a deerioraion in he ou-of-sample vis-à-vis he in-sample performance of he Phillips curve are also similar o he findings in Clark and McCracken (2006). Wha accouns for he ou-of-sample forecasing performance deerioraion of he Phillips curve? A possible answer can be gleaned by comparing he evoluion of he insample RMSE versus he ou-of sample RMSE over ime. This is shown in Figures I.1a and I.1b for core CPI and core PCE inflaion, respecively. A each poin in ime, he RMSE is compued over he mos recen eigh quarers. From he figures, i is eviden ha he ou-of-sample forecass are worse han he in-sample forecass in he early par of he sample, ha is, from 1984 o he early 1990s. In he mos recen years, he ou-of sample forecass have been as good as when no beer han he in-sample forecass. Noe ha daa from he early 1980s are used in esimaing Phillips curves for he ou-of sample forecass ha cover he period 1984 o he early 1990s bu ha hese observaions do no ener in he laer period, as he window over which Phillips curves are esimaed in he ou-of-sample forecasing exercise is 40 quarers. This paern in he RMSE suggess ha parameer insabiliy in he early 1980s is likely o have adversely affeced he ou-of-sample forecasing performance of he Phillips curve. Laer in he paper, we provide formal ess on parameer insabiliy, which, overall, confirm his view. The low power of ou-of sample forecasing relaive o in-sample forecasing could sill play some role, bu his explanaion seems somewha harder o reconcile wih he way in which he ou-of-sample forecas has evolved over ime relaive o he in-sample forecas. An imporan quesion is wha feaures of he Phillips curve could be responsible for parameer insabiliy. Is he insabiliy in he specificaion coming from he lags of inflaion, he unemploymen rae, or he supply shocks? Again, we will provide formal ess laer, bu some insigh can be gained by looking a he evoluion of he RMSE in he ou-of-sample forecass relaive o he in-sample forecas when only some coefficiens in he Phillips curve specificaion are esimaed in he ou-of-sample exercise, while he 8

9 oher coefficiens are kep fixed a he values esimaed in he in-sample exercise. This is shown in Figures I.2a and I.2b for core CPI and core PCE inflaion, respecively. The figures depic he RMSE of he in-sample forecass and he RMSE of ou-of-sample forecass when only he subse of coefficiens peraining in urn o he lags of inflaion, he unemploymen rae, and he supply shocks are esimaed, wih he remaining coefficiens se equal o he full-sample (1984 o 2007) esimaes. The figures show ha insabiliy in he supply shocks coefficiens a he very beginning of he sample is likely o have played a role. There is also some evidence ha a shif in he parameers on lagged inflaion conribued o he deerioraion of ou-of-sample forecass. The evidence on shifs in he unemploymen rae coefficiens is somewha weaker, hough earlier in he sample he RMSE for core CPI inflaion when only he unemploymen rae coefficiens are esimaed is generally above he RMSE for he in-sample exercise. We will show ha hese findings align well wih more formal ess presened laer in he paper. So far we have shown, as in previous lieraure, ha ou-of-sample forecass of inflaion using Phillips curves are no always beer han simple univariae benchmarks. The changing dynamics of inflaion make reliance on he Phillips curve difficul, bu before discarding he framework enirely one should firs invesigae wheher Phillips curve specificaions ha accoun for shifs in dynamics are useful for forecasing inflaion. This avenue of research is sill in is infancy. Sock and Wason (2007, 2008) illusrae a simple univariae model for inflaion where parameers adap o accoun for breaks. The model has appeal from an economic sandpoin in ha i decomposes inflaion ino a permanen and a ransiory componen. The model s forecasing performance is similar o he Akeson-Ohanian benchmark over he sample we consider, and we are no aware of any work ha checks wheher he performance of he model improves once aciviy variables are included. In principle, here are several ways o accoun for shifs in inflaion dynamics. A simple way ha preserves he sandard feaures of he Phillips curve framework is a ime-varying coefficiens version of equaion (1), which we wrie as follows: 9

10 4 (1 ) π + 4 π = γ ( L) π + β ( L)( u nairu ) + ε, where we ake he unemploymen rae as a deviaion from he NAIRU, so ha he consan erm can be dropped from he specificaion. Here, he coefficiens on he lag polynomials (L) γ and (L) β are ime-varying and follow random walk processes. In order o keep he specificaion relaively simple, we omi supply shocks. The ime-varying coefficiens Phillips curve in (1 ), esimaed via sandard Kalman-filer echniques, seems o capure inflaion dynamics fairly well in ou-ofsample forecass. Table I.2 compares he ou-of-sample performance of he Phillips curve (1 ) relaive o he Akeson-Ohanian benchmark for core CPI and core PCE inflaion, respecively. As before, equaion (1 ) is esimaed over a rolling window of 40 quarers. We allow for only small ime variaion in he coefficiens, bu even so he RMSEs for boh core CPI and core PCE inflaion are more han 50 percen lower han in he Akeson-Ohanian benchmark. Figures I.3a and I.3b depic he evoluion of he RMSE for he Akeson-Ohanian benchmark and for he Phillips curve specificaion (1 ). The RMSE for he Phillips curve forecas is generally below he RMSE for he Akeson-Ohanian random walk forecas. The above findings illusrae ha i is possible o specify processes for inflaion ha, by aking ino accoun changing inflaion dynamics, improve noiceably upon widely used univariae benchmarks. In erms of a Phillips curve framework, however, we sill need o assess he imporance of including he unemploymen rae gap in (1 ) vis-à-vis specifying a relaionship, as shown below, in which inflaion follows he imevarying univariae auoregressive process: 4 (1 ) π 4 π = γ ( L π + ε + ), where, as before, he ime-varying coefficiens on quarerly inflaion are consrained o 10

11 sum o uniy. The ou-of-sample RMSEs of he Phillips curve specificaion (1 ) relaive o he RMSEs of he univariae process (1 ) when considering core CPI and core PCE inflaion are 0.76 and 0.83, respecively. The evoluion of he RMSE of he univariae process (1 ) versus he RMSE of he Phillips cure specificaion (1 ) is also depiced in Figures I.4a and I.4b. The figures show ha he RMSEs of he Phillips curve specificaion end o be below he RMSEs of he simple auoregressive specificaion. Sill, over some periods he forecasing performance of he Phillips curve does no differ from he forecasing performance of he ime-varying univariae auoregressive process. This is rue for he lae 1990s, and for he mos recen period (in his las insance, more so for core PCE han for core CPI inflaion). These episodes highligh ha no all is well wih he simple backward-looking Phillips curve. For example, from mid-2003 unil mid- 2005, he Phillips curve specificaions we have considered in his secion would have prediced a fall in inflaion, as he unemploymen rae was relaively far away from he NAIRU. Conrary o he Phillips curve predicion, inflaion picked up over his period. While some omied conrol variables could in principle accoun for he rise in inflaion, i is no clear wha hese variables are. To summarize, in his secion we have shown ha he forecasing performance of he backward-looking Phillips curve is no as poor as some sudies indicae. We have highlighed, however, ha o improve noiceably over well-known univariae benchmarks one has o explicily ake ino accoun changes in inflaion dynamics for ou-of-sample Phillips curve forecass of inflaion. The mos imporan changes in inflaion dynamics are likely o have occurred in he early 1980s, as will be shown more formally laer in he paper. The bes way o accommodae changing inflaion dynamics in he Phillips curve specificaion, however, is sill an open quesion ha deserves more sudy. I is likely, hough, ha even wih improved specificaion some episodes in he pos-1984 sample will remain hard o explain in he ligh of an inflaion-unemploymen radeoff. 11

12 II. The inflaion-unemploymen radeoff: A view from he Greenbook Even when one adops a Phillips framework o model inflaion dynamics, considerable debae remains abou he size of he unemploymen-inflaion radeoff. This link from he nominal o he real side of he economy is obviously crucial, in ha i informs he conduc of moneary policy in he pursui of is dual mandae. Is here evidence ha his radeoff has changed over ime? Figure II.1 shows he relaionship beween he change in core PCE inflaion and he unemploymen rae gap over he period 1994:Q1 o 2007:Q4 in he conex of a baseline Phillips curve specificaion such as (1). Noe ha he wo series are parialling ou he effec of oher righ-hand-side variables in he Phillips curve specificaion, so ha regressing one series on he oher gives an esimae of he slope of he Phillips curve. This relaionship, esimaed over he period 1984 o 2007, produces a saisically significan and economically meaningful slope for he unemploymen rae gap. However, over he more recen period depiced in he figure, he esimaed slope of he Phillips curve would be close o zero. The figure shows ha he correlaion beween inflaion and unemploymen is generally negaive bu for he period 2003:H2 o 2005:H1, when inflaion was rising despie a relaively high unemploymen rae. In essence, his episode urns ou o be influenial when esimaing a small slope for he Phillips curve over he period 1994:Q1 o 2007:Q4. This poin can be seen, oo, in he conex of Figures II.2a and II.2b, which show esimaes of he slope of he Phillips curve obained from he ime-varying coefficiens specificaion (1 ) for core CPI and core PCE inflaion, respecively. A each poin in ime, he figures depic he esimaed slope from a rolling regression using 40 quarers of daa, where each esimae is associaed wih he las observaion in he rolling window. I is eviden ha here is a drop in he esimaed slope when he period 2003:H2 o 2005:H1 sars enering ino he rolling window. The conclusion o be drawn from his episode in erms of he economic relevance of he radeoff beween inflaion and unemploymen over he mos recen 10 o 15 years is cerainly debaable. Bu i is imporan o noe ha he failure of he inflaion-unemploymen radeoff o maerialize during his period 12

13 seems o be concenraed in ime. The figures also show ha, pre-2003:h2, here is some evidence of a decline in he slope when using core CPI as he inflaion measure, bu no when using core PCE. As of 2003:Q1, for boh core CPI and core PCE inflaion, he esimaed slope of he Phillips curve was abou 0.3, which is economically meaningful. While his reduced-form evidence is no clear-cu in poining o a flaening of he Phillips curve, more srucural evidence suggess ha he slope of he Phillips curve may have lessened in he mos recen decade. Laer in he paper we provide some evidence o ha effec. Even more imporan, Telow and Ironside (2007) documen ha he Federal Reserve Board s workhorse macroeconomic model, FRB/US, has been modified over he course of he mos recen decade o encompass a flaer Phillips curve. From 1997 o 2003, he FRB/US esimae of he sacrifice raio doubled, essenially implying ha over his period he slope of he Phillips curve lessened by abou one half. 4 The belief ha he Phillips curve has flaened appears o be informing he Federal Reserve s Greenbook inflaion forecas as well. Figure II.3a shows he esimaed slope of he inflaion-unemploymen radeoff when we esimae a Phillips curve on Greenbook forecass of core CPI inflaion over ime. Specifically, we esimae a relaionship of he form: (2) π + ε, 4, GB RT RT RT RT + 4, π = α + γ ( L) π + β ( L) u + δ ( L) x 4, GB where π is he Greenbook forecas of core CPI inflaion over he nex four quarers, +4, and he variables indexed by RT denoe real-ime informaion available a he ime he Greenbook forecas was made. Equaion (2) is essenially he same as he Phillips curve specificaion (1), wih he difference ha (2) uses Greenbook forecass of inflaion insead of acual inflaion. In equaion (2), he unemploymen rae is expressed in levels, and we use he relaive change in crude oil prices as a conrol variable. The sample uni when 4 The slope of he Phillips curve deermines he effec ha deviaions of unemploymen (or oupu) from is equilibrium will have on inflaion. The smaller is he coefficien, he more unemploymen needs o move in order o effec a change in inflaion. Thus a smaller coefficien enails a higher sacrifice raio he number of unemploymen poin-years required o reduce he inflaion rae by one percenage poin. 13

14 esimaing (2) is given by one Greenbook forecas. In performing his exercise, we use a rolling window ha includes 10 years of Greenbook forecass. 5 The resuls indicae a decline over ime in he esimaed slope of he Phillips curve. When forecasing inflaion, he Greenbook was obviously using more informaion han he informaion included in equaion (2). Omiing relevan informaion would bias he esimaed slope whenever he omied informaion is correlaed wih he unemploymen rae. In his respec, a relevan omission in (2) could be a ime-varying NAIRU. We lack informaion abou he Greenbook s esimae of he NAIRU a he ime of each Greenbook forecas. As a check on he plausibiliy of our specificaion, we back ou from (2) an esimae of he NAIRU over he 10-year rolling window. This esimaed NAIRU is depiced in Figure II.3b, and is evoluion over ime appears o be roughly in line wih he sparse evidence we have on he Greenbook s evolving esimae of he NAIRU. The change in he perceived size of he inflaion-unemploymen radeoff ha one can infer from Greenbook forecass in addiion o he FRB/US model, which forms he basis for he Greenbook s alernaive simulaions has imporan policy implicaions. Wih a flaer Phillips curve, inflaion responds less o he unemploymen rae, and hus he coss of bringing down inflaion o he desired arge in erms of los employmen are much higher. I is no sraighforward o gauge wheher, ex-pos, he Greenbook s percepion ha he inflaion-unemploymen radeoff has flaened considerably was righ. Bu i is possible o check wheher he Greenbook has incorporaed informaion abou he unemploymen rae efficienly ino is inflaion forecas. In his regard, i is imporan o noe ha over he period 1996 o 2003, Greenbook forecass of he unemploymen rae have been fairly accurae, exhibiing no glaring bias. As a resul, Greenbook s inflaion forecass errors were, on average, no he resul of errors in forecasing he unemploymen rae. Having esablished his poin, which is essenial when examining he inflaion forecass error wihin he conex of a Phillips curve framework, we hen ask wheher he Greenbook was incorporaing informaion abou he labor marke 5 We sop he analysis in 2003 because Greenbook daa are made available o he public wih a five-year lag. 14

15 available a he ime he forecas was made efficienly ino he inflaion oulook. For his purpose, we define he Greenbook inflaion forecas error, 4 e o be: (3) 4 e = π π, , GB + 4, 4, GB where, as before, π is he Greenbook forecas of core CPI inflaion over he nex four +4, 4 quarers, and π +4 is he corresponding acual value. We hen regress he forecas error, 4 e, on informaion available a he ime he forecas was made. This informaion is given by he mos recen value of he unemploymen rae, over he mos recen quarers, π 4, RT RT u, and by core CPI inflaion. These values are in real ime, and are aken from 4, GB he same Greenbook from which he forecas π is aken. 6 We consider pas inflaion in addiion o he unemploymen rae because hese wo variables are correlaed. To he exen ha pas inflaion helps o explain he Greenbook s inflaion forecas errors, omission of pas inflaion from he regression would lead o bias in he esimaed coefficien for he unemploymen rae. +4, The regression resuls over he period 1996 o 2003 are as follows: e RT 4, RT =.233*.351* π , R 2 =. 39, N = 64, (0.066) (0.152) (0.407) 4 u where sandard errors are in parenheses. Over his sample, here is evidence ha boh he curren level of he unemploymen rae and four-quarer inflaion explain a considerable porion of he Greenbook forecas error. The regression indicaes ha when he curren level of he unemploymen rae was high, prediced inflaion ended o be higher han acual inflaion. Similarly, when he mos recen four quarers of inflaion were high, prediced inflaion ended o be higher han acual inflaion. This las resul 6 Because we consider core CPI inflaion and he civilian unemploymen rae, real-ime values are he same as curren vinage values, aside from minor seasonal adjusmens in he unemploymen rae. 15

16 suggess ha he Greenbook s percepion of inflaion persisence was likely oo high. The negaive coefficien on he unemploymen rae is consisen wih he Greenbook, mainaining a flaer Phillips curve han he one operaing on acual daa. Sill, his is no he only possible explanaion. A endency o oversae he NAIRU during his period could also have produced such a resul. While we canno disinguish beween he wo hypoheses, we noe ha he regression esimaes are no driven by he experience of he lae 1990s, when esimaes of he NAIRU were being revised downward. Figure II.4 shows acual core CPI inflaion, he Greenbook forecas, and he Greenbook forecas adjused ex-pos o correc for he inefficiency wih which lagged inflaion and he lagged unemploymen rae were facored ino he forecas. The adjusmen maers mos in he early par of he sample and over he period Bu his inefficiency in he Greenbook s inflaion forecas, if sill presen, could become relevan again in he curren conex of a rising unemploymen rae. In sum, simple backward-looking Phillips curves provide mixed evidence of a change in he inflaion-unemploymen radeoff. Bu more srucural models ofen indicae a reducion in he slope of he Phillips curve over he pas 10 o 15 years. Moreover, he Greenbook forecass of inflaion in he mos recen years appear o hinge on a relaively fla Phillips curve. While he acual size of he radeoff is sill debaable, we have shown ha, over he period 1996 o 2003, he Greenbook has no incorporaed informaion abou he unemploymen rae efficienly ino he inflaion forecas. While here is more han one poenial explanaion for his finding, he finding is consisen wih he Greenbook s posiing a slope in he Phillips curve ha is oo fla. III. Esimaes of changing inflaion dynamics A. Reduced-form Phillips curve In considering how inflaion may behave over he moneary policy horizon, i is of ineres o know he fuure effecs on inflaion of economic slack, of expecaions, and 16

17 of imporan relaive price (or oher) shocks. 7 One canno presume ha he influence of hese deerminans on inflaion has remained consan across ime; for example, here are good reasons o expec ha he effec of oil shocks on inflaion should have changed in recen decades. There has also been considerable debae abou wheher he slope of he Phillips curve has changed in recen decades, wih he leading argumen cenering on a decline in he slope of he Phillips curve ha would imply a significanly higher sacrifice raio. Finally, mos macroeconomic heories of inflaion sugges ha changes in he sysemaic response of he cenral bank o oupu and inflaion will change he behavior of inflaion. To he exen ha moneary policy behaves differenly now han i did in he 1960s and 1970s, he reduced-form dynamics of inflaion now would be expeced o differ from hose in he earlier period. In his secion we examine more formally wheher he influence of inflaion s key deerminans, as viewed hrough he Phillips curve lens, has changed in recen decades. We consider wo varians of he Phillips curve in his secion, one a radiional, backward-looking and somewha reduced-form represenaion already used in he previous secions, he oher a srucural raional expecaions represenaion, in he radiion of New Keynesian Phillips Curve models (see, for example, Galí and Gerler 1999 and Chrisiano, Eichenbaum, and Evans 2005). The radiional Phillips curve akes he form below. Inflaion, π, depends on is own lags (proxying expecaions and a variey of fricions in he price-seing process), an economic slack measure (here proxied by he unemploymen rae gap), and idenified relaive-price shifers. As before, we wrie he equaion in firs-differenced form, which implicily imposes he consrain ha he sum of he lagged inflaion coefficiens equals uniy: o o no no (4) π = γ ( L) π + β ( L)( u nairu ) + δ ( L) rp + δ ( L rp + ε ) 1 7 This axonomy of effecs loosely corresponds o Rober Gordon s riangle model of inflaion, see Gordon (1985) 17

18 As is convenional in such specificaions, we include several lags of he unemploymen rae, as well as lagged changes in he relaive price of oil and non-oil impored goods. 8 We examine wo measures of core inflaion, he CPI and PCE, and perform an array of ess of sabiliy of all he key coefficiens in he Phillips curve. 9 The op panel of Table III.1a shows he resuls for he core PCE. The firs five lines of resuls repor he p- value for he es ha he coefficiens are sable across he break a he indicaed ime. We ake a repored p-value of 0.05 or lower as saisical evidence of a change in he relaionship. The Grea Moderaion break poin is se o 1984:Q1, in accord wih an array of empirical lieraure on he reducion in he variabiliy of many macroeconomic ime series a leas up unil he curren (2008 and 2009) recession. 10 The Greenspan era breakpoin is se o he beginning of Alan Greenspan s enure as Chairman of he Federal Reserve, in 1987:Q3, and he pos-1994 break poin is chosen as represening a period of acceleraing produciviy. 11, 12 For he core PCE, he known breakpoin ess sugges ha he effec of he relaive price of oil changed significanly, someime in he mid-1980s. The ess develop no compelling evidence of a shif in he effec of inflaion s oher key deerminans. The unknown breakpoin ess uncover a breakpoin in 1982, consisen wih he known 8 Alernaive specificaions ha employ rend inflaion measures here he FRB/US measure of long-run inflaion expecaions yield somewha differen resuls, depending on he specificaion. One specificaion allows boh lagged inflaion and rend inflaion o ener, wih coefficiens summing o one. The weigh on rend inflaion was esimaed a 0.2 for PCE inflaion, and 0.06 for CPI. 9 See he complee daa definiions for Secions III and IV in he daa appendix a he end of he paper. 10 In he presen exercise, he esimaion sample ends in 2007:Q4, righ a he onse of he recession (he NBER-daed peak is December 2007). 11 In each case, we compue a Wald es ha incorporaes a heeroskedasiciy and auocorrelaion-consisen esimae of he parameer covariance marix. The es regression includes a dummy imes he variable or 1 variables for which a shif is enerained. The es saisic is consruced as W = ( Rβ )' ( RΩˆ R' ) ( Rβ ), where R is consruced so as o impose he consrain R β = 0 for he dummied regressors of ineres, and Ωˆ is he HAC esimae of he covariance marix. The saisic is disribued as a chi-square wih degrees of freedom equal o he number of coefficiens consrained. 12 Resuls for a Phillips curve ha defines he unemploymen gap as he difference beween he civilian unemploymen rae and he CBO s esimae of he NAIRU produce he same qualiaive resuls. 18

19 breakpoin es findings. 13 Wald ess for coefficien sabiliy on he individual coefficien groups develop evidence ha he effec of changes in he relaive price of oil shifed significanly in he 1980s. The sum of he coefficiens on he relaive price of oil (no repored) dropped from abou 0.1 in he 1970s o approximaely zero afer he mid- 1980s. There is also some evidence ha he paern of lags in he Phillips curve shifed in he 1980s. Because his erm in he Phillips curve proxies for a number of possible inflaion deerminans expecaions, conracing lags, indexaion i is more difficul o inerpre his shif. In he discussion of he srucural resuls below, we will aemp o uncover more of he srucure underlying hese lags, by making explici expecaions, price-seing, and moneary policy acions. For he CPI, Table III.1b, he resuls are similar. For he known breakpoins, he core CPI develops rejecions of sabiliy only for he relaive price of oil, in his case a all hree breakpoins. As wih he core PCE, he coefficien sums ha reflec he effec of oil prices on core inflaion diminish unil hey are near zero as he sample progresses oward he presen. The resuls for he unknown breakpoin are quie similar o hose for he PCE, wih a shif in The significance aached o he es for a shif in he lag coefficiens is higher han for he PCE, while sabiliy of he oil price effec is rejeced wih very high significance. As wih he PCE resuls, he esimaed sum of coefficiens on oil prices drops from a bi below 0.1 for he earlier samples o zero for he pas wo decades. In sum, he effecs of relaive oil prices have been a key source of insabiliy in inflaion dynamics, from he perspecive of his radiional Phillips curve. The esimaed impac of a change in oil prices is currenly insignificanly differen from zero, a saisically significan shif from he sizable impac in he 1970s and early 1980s. To be sure, here have likely been oher shifs as well. In he CPI Phillips curve, we develop 13 The breakpoin es uses boosrapped criical values consruced under he null of no break for he fullsample Phillips curve esimaes. The wild boosrap mehod we employ follows O Reilly and Whelan (2005). Muliple breakpoin ess using asympoic criical values sugges a breakpoin in he mid-1970s in addiion o he break deeced in he early- o mid-1980s. 19

20 some evidence ha he unemploymen effec has shifed down in he 1980s. Such a shif is less eviden in he core PCE Phillips curve. B. Srucural Phillips curve As suggesed above, inerpreing shifs in he backward-looking Phillips curve can be difficul, as he framework leaves implici many srucural feaures of priceseing. This is paricularly rue for he lagged inflaion erms in he radiional Phillips curve. In addiion, he framework is mue regarding he behavior of oher aspecs of he economy ha bear on inflaion noably he sysemaic behavior of moneary policy and he ransmission channel from moneary insrumens o oupu o inflaion. A simple example demonsraes how he combinaion of price-seing behavior, moneary policy, and he real economy joinly deermine he behavior of inflaion. A sylized version of he backward-looking Phillips curve above makes inflaion a funcion of lagged inflaion and he oupu gap: π = π + a~ 1 y, where y~ represens he deviaion of oupu from poenial. The oupu gap in urn is a funcion of he policy rae: ~ y = bi, and he policy rae i follows a sylized Taylor rule: i = cπ. Wih his much-simplified economic srucure, i is easy o see ha inflaion will follow he simple firs-order auoregressive process: 20

21 π π = A 1 1 A = 1+ abc Inflaion will more persisenly deviae from is desired level (here assumed for simpliciy o be zero) A will be larger when moneary policy arges inflaion less aggressively (c is smaller), when he policy rae s effecs on oupu (b) are smaller, and when he effec of oupu on inflaion (a) is smaller. This rivial model demonsraes simply and inuiively he way ha he key feaures of he macroeconomy ogeher deermine he reduced-form behavior of inflaion. This secion akes a somewha more srucural view on he poenially shifing dynamics of inflaion by making many of hese aspecs explici. Doing so enails some risk, as he resuling model is more resriced and in a sense places higher demands on he aggregae daa in aemping o idenify hese addiional economic behaviors. The hybrid model so-called because i includes boh forward- and backwardlooking elemens comprises hree componens, along he lines of he skeleal model skeched above: I. A Phillips curve wih explici expecaions, in he New Keynesian Phillips curve radiion. I allows for a fracion of backward-looking or indexing price seers, moivaing a lagged inflaion erm; II. An I-S curve, which one can derive from a canonical consumer opimizaion problem, which also allows for some backward-looking behavior, moivaed in many cases by habi formaion in consumer spending; and III. A moneary policy (Taylor 1993) rule, consruced along convenional lines. 14 The model is summarized in he following se of equaions: 14 We also explored an alernaive version of he model, in which he oupu gap depends on a long-erm real ineres rae, defined according o a simple erm srucure relaionship linking he long real rae o expeced shor-erm real raes. The qualiaive resuls presened in he ables below are unchanged; idenificaion of he I-S curve was superior in he version presened here. 21

22 (5) π = µπ ~ y = µ ~ y i = bi y ( β µ ) π + ( β µ ) ~ y + (1 b)[ a y + 1, π + 1, + γ~ y + ε a( i π π a ~ y + 1, 4 π ( ) + y + + ] + ρ ρ ) + υ π η Because he overall behavior of inflaion can be influenced by price-seing behavior, summarized in he op equaion, or by he moneary ransmission mechanism, summarized in he second equaion, or by he behavior of moneary policy, summarized in he hird, we look for breaks in he coefficiens of all of hese equaions. 15 The resuls in Table III.2 ake a form similar o hose in he preceding able for he backward-looking Phillips curve. 16 For he core PCE, shown in he op panel, he resuls sugges clearly ha he model overall has no been sable, eiher across known breakpoins, or looking a breakpoins deeced using unknown breakpoin mehodology. 17 Somewhere in he 1980s, a very significan parameer shif is deeced. Ineresingly, he ess sugges ha he shif is no primarily due o significan shifs in he parameers of he forward-looking Phillips curve, bu raher o a shif in he ransmission mechanism (he I-S curve) and perhaps o some change in moneary policy. For he core CPI, he resuls are similarly clear. The daa srongly rejec sable coefficiens for he enire model across he full sample. Boh known and unknown breakpoin ess indicae a break somewhere in he 1980s. The source of he break appears o be he same as ha for he PCE. The es for sabiliy of he I-S curve parameers srongly rejecs sabiliy for boh known breakpoin daes. 15 The ess repored are likelihood-raio ess for he hypohesis ha he esimaed coefficiens in he firs sample are equal o hose in he second. The likelihood raio is compued by imposing he firs-sample coefficiens on he second sample, and aking he raio of he unconsrained likelihood o he consrained likelihood for he second sample. 16 Resuls using an oupu gap based on he CBO esimae of poenial oupu differ lile from he resuls presened. 17 This mehod simply searches for he breakpoin associaed wih he larges likelihood raio. We do no know of research ha allows one o compue he criical values of his likelihood raio es for sysems of equaions wih raional expecaions. Bai (1999) discusses criical values for a likelihood-raio es for singleequaion models. 22

23 Typically, such srucural models do no accoun for he effecs of key relaive price shifs, as in he backward-looking models. In some cases, his is heoreically jusified paricularly when inflaion is linked o real marginal cos. In his case, marginal cos should capure he effec of any inpu coss on inflaion, so he addiion of energy or oher inpu prices would be superfluous. In our case, inflaion is linked o he oupu gap, as is convenional in many NKPC specificaions. Here, here may be a heoreical and empirical role for relaive prices. Thus, we consider a model ha allows for he explici effec of he relaive price of oil on inflaion, augmening he forwardlooking Phillips curve as follows: π ~ + o = µπ 1 + ( β µ ) π + 1, + γy + po rp ε. The resuls of he ess in his case are ineresing, as hey now uncover some shif in Phillips curve parameers. Again, as shown in able III.3, for boh core PCE and core CPI, he hypohesis of sabiliy of all he coefficiens is srongly rejeced for boh known and unknown breakpoins. Bu now, sabiliy of he Phillips curve coefficiens is rejeced for boh measures and boh breakpoins. Because he only change o he Phillips curve is he addiion of an oil price erm, his suggess ha he effec of he oil price on inflaion, omied in he firs specificaion, is a significan source of insabiliy in hese esimaes, echoing he resuls of he reduced-form Phillips curve models. Boh he known and he unknown breakpoin ess poin o a shif in srucure in he early 1980s. Figure III.1 provides a reasonably clear picure of he changes ha appear o have occurred over he pas 30 years. The figure displays he esimaed value of a paricular srucural model parameer a he breakpoin dae indicaed on he horizonal axis. The solid line shows he parameer s esimaed value over he firs par of he (spli) sample, and he dashed line shows he esimaed value over he second par of he sample. For example, he op-lef panel shows he esimaes for μ, he backward-looking weigh (or indexaion parameer) in he Phillips curve. The value of he solid line for 23

24 1990:Q1 is he esimae of μ for he sample 1966:Q1 1989:Q4; he value of he dashed line for he same period is he esimae of μ for he sample 1990:Q1 2007:Q4. The resuls ha emerge from his figure should be of some ineres o policymakers. Firs of all, mos of he laer sample esimaes are lower han hose of he early sample: Inflaion laely appears somewha less responsive o oupu gaps (γ ), he effec of oil prices is smaller ( p o ), and he ineres-sensiiviy of oupu is smaller. The ransmission channel of moneary policy he effec of ineres raes on real aciviy, and correspondingly he effec of real aciviy on inflaion appears somewha mued, wih he change occurring somewhere in he early 1980s. Second, many of hese key parameers are reasonably sable afer ha breakpoin. Tha is, he dashed lines, while hey vary wih normal sampling variaion, are relaively sable over he pas 25 years. Two noable excepions are he policy response o inflaion ( a π ), o which we will reurn shorly, and he backward-looking componen of inflaion ( µ ). Beginning wih he op lef panel, he backward-looking weigh in inflaion, someimes referred o as he inrinsic persisence of inflaion, is insignificanly higher in he earlier sample han in mos of he laer period. However, beginning in he early 1990s, is value drops from abou 0.5 o 0.2 or lower. This decline could reflec a change in he price-seing behavior of economic agens. In conjuncion wih beer-run moneary policy, his could explain he observaions by some of a decline in reducedform inflaion persisence in recen years. I may also reflec he difficuly in assessing he inheren persisence in inflaion during a period when inflaion has ranged beween one and hree percen. Finally, i is imporan o noe ha he decline in his parameer is no robus across alernaive model specificaions The inference here is somewha complicaed. An alernaive version of he model in which he inflaion equaion is π = µπ + µ π + γ~ 1 ( 1 ) + 1, y + ε does no display a similar decline in μ. This seemingly small change in he erm pre-muliplying expeced inflaion from β 1 o 1 appears o have imporan implicaions for his aspec of inflaion dynamics. Noe also ha he esimaed inflaion response falls below 1 in he early 1990s, an apparen violaion of he so-called Taylor principle. However, in his model, wih β < 1, inflaion sabilizes independen of he response of moneary policy, a feaure of his widely used class of models ha is no well ariculaed in mos reamens. 24

25 The response of inflaion o oupu gaps is everywhere lower in he laer samples, as shown in he op righ-hand panel of he figure. This corroboraes he widespread belief ha he slope of he Phillips curve has become quie shallow, implying a large sacrifice raio. The effec of he relaive price of oil on inflaion, shown in he middle lef panel, is clearly lower in he laer samples han he earlier, and is generally difficul o disinguish from zero for mos of he samples ha include daa from 1985 and forward. The responsiveness of oupu o he real ineres rae, shown in he middle righ panel, is clearly smaller in he recen daa han in he earlier samples. In fac, i is difficul o esimae a non-zero ineres elasiciy, hining a he general difficulies in idenifying some of hese srucural equaions in recen periods. Apar from some early sample noise, he arge rae of inflaion, shown in he lower lef panel, has behaved consisenly wih common wisdom abou he Fed s inflaion goal: I is clearly lower in he laer samples, and appears o have declined somewha in recen decades, wih he curren esimae hovering around 2 percen. 19 The rise in he moneary policy response o inflaion, shown in he boom righ panel, is sriking. I arises from he brief period in he daa from 1992 o 1995, during which inflaion was declining, bu he funds rae was rising from 3 o 6 percen. In his relaively simple model, ha episode is inerpreed as a modes decline in he inflaion goal, coupled wih a significan increase in he response of policy o inflaion. 20,21 In sum, we find reasonably consisen evidence across boh reduced-form and srucural models ha he influence of key relaive prices (paricularly oil) on inflaion has significanly diminished in recen years. We find somewha more mixed evidence 19 The overall sample begins in For breakpoins daed 1975 hrough 1980, we use 30 o 40 observaions o idenify 10 parameers. The inflaion arge is difficul o idenify in samples ha include he early 1980s, he non-borrowed reserves operaing procedure period. 20 Noe ha he verical axis of he panel is runcaed a five. The maximum response esimaed in his period is abou No shown are esimaes for he forward- and backward-looking weighs in he I-S curve; hese do no differ significanly beween esimaion periods, wih he backward-looking componen cenering on abou 0.6. In addiion, he lagged ineres rae erm in he policy rule remains reasonably sable a around 0.8 hroughou he enire sample period. 25