The Deah of he Phillips Curve? Anhony Murphy Federal Reserve Bank of Dallas Research Deparmen Working Paper 1801 hps://doi.org/10.19/wp1801
The Deah of he Phillips Curve? 1 Anhony Murphy, Federal Reserve Bank of Dallas January 018 Absrac: Are inflaion dynamics well capured by Phillips Curve models, or has his framework become less relevan over ime? The evidence for he U.S. suggess ha he slopes of he price and wage Phillips Curves he shor-run inflaion-unemploymen rade-offs are low and have go a lile flaer. For example, he recursive esimae of he unemploymen coefficien in he core PCE Phillips Curve has fallen a lile from -0.09 o -0.07 since he Grea Recession. However, he decline is no saisically significan. Dynamic forecass from he wage and price Phillips Curves esimaed using daa ending in 007q, almos 10 years ago, are prey close o inflaion oday. This suggess ha (i) low curren inflaion is no ha surprising, and (ii) facors such as increased globalizaion, increased e-commerce aciviy, changes in concenraion, he aging of he U.S. populaion and mismeasuremen of he NAIRU are no ha imporan (or offse each oher). The Phillips Curve is sill a useful, albei imprecise, framework for undersanding inflaion. Keywords: Inflaion, Wage Inflaion, Phillips Curve, Slack. JEL Codes: E31, E37 1. Inroducion Are inflaion dynamics well capured by Phillips Curve models, or has his framework become less relevan over ime? If he slope of he Phillips Curve has flaened, his may explain he missing disinflaion during he Grea Recession and missing inflaion now, in which case 1 Email: anhony.murphy@dal.frb.org. I am graeful o David Reifschneider and Jeremy Rudd for assisance wih he daa. The views expressed here are my own, and no hose of he Federal Reserve Bank of Dallas or he Federal Reserve Board. 1
low inflaion is no really a surprise. If facors such as increased globalizaion, increased e- commerce aciviy, changes in concenraion, he aging of he U.S. populaion and mismeasuremen of he NAIRU are more imporan nowadays, sandard Phillips Curve models are likely o be less relevan since hey do no ake accoun of hese facors. Of course, many of hese issues are no new see Saiger, Sock and Wason (001) for example. Many of he facors lised above are hard o measure, bu changes in he fi or sabiliy of he Phillips Curve may provide useful clues abou heir poenial conribuion o inflaion dynamics. I may well be he case ha he conribuion of omied, or poorly measured, facors has no significanly increased over ime. I examine he fi and sabiliy of he Phillips Curve using he models of price and wage inflaion discussed by Jane Yellen, he Chair of he Board of Governors of he Federal Reserve Sysem, when she spoke abou moneary policy and inflaion (Yellen, 01, 017). The wo Phillips Curve models are reasonably sandard, and represenaive of he inflaion models many policy makers implicily or explicily use, so he resuls of his paper generalize.. Core PCE inflaion The model of core PCE inflaion Phillips Curve in Yellen (01) is 3 : (1) core e core core 1 3 1 ( nru = + + + u u ) + 6rpimrpim + π β βπ βπ βπ β β ε where core e π is core PCE inflaion, π is he Survey of Professional Forecasers (SPF) measure of nru long run (10 year) inflaion, u u is he unemploymen gap (he difference beween he unemploymen rae and he CBO s esimae of he naural rae), and rpim is he relaive inflaion rae of core impors. Inflaion has a forward looking componen, even hough his is no a New Keynesian Phillips Curve. In he model, inflaion depends on expeced long-erm fuure inflaion as well as pas inflaion, labor marke slack in he form of he unemploymen A decade ago, commenaors worried abou he Walmar effec and a poorly measured NAIRU. Today, many worry abou he Amazon effec and a poorly measured NAIRU. 3 Core PCE is personal consumpion expendiure excluding food and energy. The relaive inflaion rae of core impors rpim is defined in Yellen (01).
gap and core impored inflaion. The resricion β = 1 β3 β is imposed so ha, in he long run, inflaion equals expeced inflaion (when he unemploymen gap is zero). Implicily, long run expeced inflaion equals arge inflaion, as long as moneary policy is credible. The key parameer of ineres in (1) is he slope of he Phillips Curve ( β ). The esimaed Phillips Curve for he period 1990q1 o 017q is: core e core core nru () ˆ π = 0.0π + 0.36π 1 + 0.3π 0.07( u u ) + 0.rpim SE = 0.9 R = 0. 70 (.1) (3.9) (.6) (.) (3.7) The relaive weighs on pas and expeced fuure inflaion are 60:0. The fi of he equaion is reasonable, alhough he 9% confidence bands of ˆ π core are wide (approximaely ± 1%). The esimaes sugges ha he Phillips Curve is relaively fla. Formal ess of he sabiliy of he model are somewha mixed. Recursive esimaes of he slope (and oher coefficiens) are fairly sable (Figure 1). The recursive esimaes sugges ha he slope of he Phillips Curve has become a lile flaer since he Grea Recession, alhough he decline in he slope from -0.09 o -0.07 is no saisically significan..08.0.00 -.0 -.08 -.1 -.16 -.0 -. Phillips Curve Slope 00-007 Ave = -0.09 010-016 Ave = -0.07. -.8 000 00 00 006 008 010 01 01 016 Figure 1: Recursive Esimaes of Slope of Phillips Curve wih 9% Confidence Inervals Oher Phillips Curve models, such as he Gordon riangle model, which exclude long erm inflaion expecaions display more insabiliy. NBER daed recessions are shaded. 3
A comparison of he esimaed dynamic effecs of a emporary rise in he unemploymen rae from Phillips Curves based on wo differen samples - one sample ending in 007q (represened by he blue line) and he oher ending in 017q (he red line) is informaive (Figure ). The esimaed effecs are abou wice as large before he Grea Recession as hey are now. Percen 1.6 1. 0.8 Rise in Unemploymen 0. 0.0-0. -0.8 1990q1 o 017q Parameers 1990q1 o 007q Parameers Decline in Core PCE Inflaion 07 08 09 10 11 1 13 1 1 16 17 Response of Core PCE Inflaion - 1990q1 o 007q Parameers Response of Core PCE Inflaion - 1990q1 o 017q Parameers Deviaion of Unemploymen Gap from Baseline Figure : Decline in Esimaed Effec on Core PCE Inflaion of a Rise in Unemploymen Neverheless, dynamic forecass from he Phillips Curve rack he underlying movemen in core inflaion fairly well. Figure 3 shows he pseudo ou-of-sample forecass from he Phillips Curve esimaed using daa ending in 007q. Alhough forecas core inflaion is lower han acual inflaion in many periods, he forecas racks core inflaion reasonably well over his en year period. Iner alia, he recen below arge core inflaion readings should no have come as a surprise and, according o he model, core inflaion should gradually rever o arge over ime. The forecass are dynamic, condiional forecass reaing he pahs of he unemploymen rae and relaive core impor inflaion as given.
Percen 3 Acual 1 0-1 Fied (In-Sample) Forecas (Ou-of-Sample) - 000 00 00 006 008 010 01 01 016 Figure 3: Ou-Of-Sample Dynamic Forecas of Core PCE Inflaion wih 9% Confidence Inervals, Esimaion Sample Ending 007q So wha forecas of core PCE inflaion does he model produce? The condiional forecas of core PCE inflaion from Yellen s core PCE inflaion model is shown in Figure. I is a condiional forecas given he laes SPF unemploymen pah and he CBO s esimae of he NAIRU, an unchanged SPF long-erm expecaion of % PCE inflaion, and he forecas values for relaive core impor price inflaion (rpim) from a simple AR() model. Given he srucure of he model and he SPF forecas of a igh labor marke, i should come as no surprise ha he model suggess ha inflaion is likely o sabilize around he [Federal Open Marke] Commiee s percen objecive over he medium erm. Of course, he simulaed confidence bands (which ake accoun of coefficien uncerainy) are very wide.
Percen 3. 3.0..0 1. Forecas Core PCE Inflaion (9% Confidence Bands) 1.0 0. 0.0 1 3 1 3 1 3 1 3 1 3 1 3 01 016 017 018 019 00 Figure : Condiional Forecas of Core PCE inflaion 3. Wage Inflaion A version of he wage Phillips Curve se ou in Yellen (017), is: ω= γ + γπ + γ( ω + ω + ω + ω ) + γ ( u u ) + γ ( u u ) + γ prod + v e nru nru 1 3 1 3 6 where ω is he growh of nominal compensaion (ECI wages and benefis) and prod is a measure of long run produciviy growh. 6 Compensaion growh depends on expeced long run inflaion, recen compensaion growh, slack and he change in slack (he unemploymen gap and he change in he unemploymen gap) as well as rend produciviy growh. The resricion γ = γ = 1 γ is imposed so ha, in he long run, he rae of growh of compensaion in real 6 3 erms equals he underlying rend growh in produciviy. 6 The coefficiens on he lagged compensaion erms in Yellen (017) are no resriced o be equal. ECI is he employmen cos index produced by he Bureau of labor Saisics. See Yellen (017) for he deails of how rend produciviy prod is measured. 6
The esimaed wage Phillips Curve for he period 1988q1 o 017q is: ω = 0.77+ 0.6π + 0.09( ω + ω + ω + ω ) 0.18( u u ) e nru (.1) (.) (.7) 1 3 (3.0) nru 0.6 ( u u ) 0.6 prod SE 0.76 R 0. (.) (.) + = = Unsurprisingly, he wage Phillips Curve does no fi as well as he price Phillips Curve, since he variaion in ECI inflaion is greaer han in core PCE inflaion. In addiion, he recursive coefficiens esimaes are no as sable, alhough many of he changes over ime are offseing. For example, he esimaed negaive effec of slack ( γ ) has become smaller since he Grea Recession, while he esimaed negaive effec of he change in slack ( γ ) has become larger. 7 Neverheless, he esimaed dynamic effecs of a emporary rise in he unemploymen rae is fairly sable. Figure shows he esimaed effecs using he same wo samples as before - one sample ending in 007q and he oher ending in 017q. The esimaed effecs are similar, albei a lile faser for he sample ending in 017q (he red line). Percen 1.6 1. Rise in Unemploymen 0.8 0. Decline in ECI Wage Inflaion 0.0-0. 1988q1 o 017q Parameers 1988q1 o 007q Parameers -0.8 007 008 009 010 011 01 013 01 01 016 017 Response of ECI Wage Inflaion - 1988q1 o 007q Parameers Response of ECI Wage Inflaion - 1988q1 o 017q Parameers Deviaion of Unemploymen Gap from Baseline Figure : Esimaed Effecs of a Rise in Unemploymen are Fairly Sable 7 The esimaed γ coefficien is no saisically significan before he Grea recession. 7
The dynamic / pseudo ou-of-sample forecass from he esimaed wage Phillips Curve using daa up o 007q are shown in Figure 6. The forecass rack he underlying movemens in ECI inflaion surprisingly well (declining wage inflaion during he Grea Recession, followed by very gradual rises in wage inflaion), alhough hey are a lile on he low side. This sugges ha he low ECI inflaion readings in recen years are acually no ha far off he mark. The model aribues he low raes of wage inflaion in he las few years o low rend produciviy growh and ineria. Percen 6 Acual 3 1 0 Fied (In-Sample) Forecas (Ou-of-Sample) -1-000 00 00 006 008 010 01 01 016 Figure 6: Ou-Of-Sample Dynamic Forecas of ECI Inflaion Tracks Well (Forecas and 9% Confidence Inervals, Esimaion Sample Ending 007q). Conclusion The Phillips Curve is sill a useful, albei imprecise, framework for undersanding inflaion (Blanchard, 016). Longer erm movemens in inflaion since he onse of he Grea Recession in 007 are fairly well capured by he price and wage Phillips Curves in Yellen (01, 017), even hough he shor-run response of inflaion o he unemploymen rae has declined somewha over ime. The Phillips curve is relaively fla, so recen low inflaion readings are no paricularly surprising. More conroversially, he dynamic forecass from hese models sugges ha he impac of difficul o quanify facors (such as increased globalizaion, 8
increased e-commerce aciviy, changes in concenraion, he aging of he U.S. populaion and mismeasuremen of he NAIRU) may be small. References: Blanchard, O. (016), The U.S. Philips Curve: Back o he 60s?, Peerson Insiue for inernaional Economics Policy Brief PB16-1, January. Saiger, D., Sock, J. and Wason, M. (001), Prices, Wages and he U.S. NAIRU in he 1990s, in Krueger, A. and Solow, R., The Roaring Nineies, New York: Russell Sage Foundaion, pp. 3-60. Yellen, J. (01), Inflaion Dynamics and Moneary Policy, Philip Gamble Memorial Lecure, Universiy of Massachuses, Amhers, Sepember. Yellen, J. (017), Inflaion, Uncerainy and Moneary Policy, Speech a 9 h Annual meeing of he Naional Associaion for Business Economics (NABE), Cleveland OH, Sepember 6 h. 9