The Passthrough of Labor Costs to Price Inflation

Finance and Economics Discussion Series Divisions of Research & Statistics and Monetary Affairs Federal Reserve Board, Washington, D.C. The Passthrough of Labor Costs to Price Inflation Ekaterina V. Peneva and Jeremy B. Rudd 2015-042 Please cite this paper as: Peneva, Ekaterina V. and Jeremy B. Rudd (2015). “The Passthrough of Labor Costs to Price Inflation,” Finance and Economics Discussion Series 2015-042. Washington: Board of Governors of the Federal Reserve System, http://dx.doi.org/10.17016/FEDS.2015.042. NOTE: Staff working papers in the Finance and Economics Discussion Series (FEDS) are preliminary materials circulated to stimulate discussion and critical comment. The analysis and conclusions set forth are those of the authors and do not indicate concurrence by other members of the research staff or the Board of Governors. References in publications to the Finance and Economics Discussion Series (other than acknowledgement) should be cleared with the author(s) to protect the tentative character of these papers.

The Passthrough of Labor Costs to Price Inflation Ekaterina V. Peneva Jeremy B. Rudd ∗ ∗∗ Federal Reserve Board Federal Reserve Board May 21, 2015 Abstract Weuseatime-varyingparameter/stochasticvolatilityVARframeworktoassesshow the passthrough of labor costs to price inflation has evolved over time in U.S. data. We find little evidence that changes in labor costs have had a material effect on price inflation in recent years, even for compensation measures where some degree of passthrough to prices still appears to be present. Our results cast doubt on explanationsofrecentinflationbehaviorthatappealtosuchmechanismsasdownward nominalwagerigidityoradifferentialcontributionoflong-termandshort-termunemployedworkerstowageandpricepressures. ∗E-mail: ekaterina.v.peneva@frb.gov. ∗∗Correspondingauthor. Mailingaddress: Mailstop61,20thandCStreetsNW,Washington,DC20551. E-mail: jeremy.b.rudd@frb.gov. WethankDavidLebow,DebLindner,andseminarparticipantsatAuburn Universityforhelpfulcommentsonearlierversionsofthiswork.Wealsoexpressourconsiderablegratitude to Todd Clark for providing us with his computer algorithms for estimating TVP/SV VAR models. (Any remainingerrorsareours.)Theanalysisandconclusionssetforthareourownanddonotnecessarilyreflect theviewsoftheBoardofGovernorsorthestaffoftheFederalReserveSystem.

I Introduction Manyformalandinformaldescriptionsofinflationdynamicsassignanimportantexplicit orimplicitroletolaborcosts. Intuitively,laborcompensationshouldbeakeydeterminant offirms’pricingbehavioras,intheaggregate,itrepresentsabouttwo-thirdsoffirms’total costs of production. More formally, economic theory suggests that increases in labor costs in excess of productivity gains should put upward pressure on prices; hence, many older theoretical and empirical models (including the large-scale econometric models of the 1970s and 1980s) assumed that prices are determined as a markup over unit labor costs. Similarly, many empirical implementations of the new-Keynesian Phillips curve haveusedrealunitlaborcostsasaproxyforrealmarginalcosts,whicharethetheoretical driverofinflationinthesemodels. Wage-based explanations of inflation dynamics have seen increased prominence of late, as a number of observers have sought to use developments in the labor market to explain why price inflation did not decline by as much as conventional models would have predicted following the 2007–2009 recession (the so-called “missing disinflation” puzzle).1 First, some analysts have argued that the presence of downward nominal wage rigidity has propped up aggregate wage inflation to an unusual degree in recent years, which has in turn led price inflation to decline by less than would be expected given the magnitude and persistence of the shortfall in real activity that resulted from the Great Recession.2 Second, some researchers (for example, Gordon, 2013) have argued that 1See Ball and Mazumder (2011), Watson (2014), and Coibion and Gorodnichenko (2015) for some representativediscussionsofthemissingdisinflationpuzzle. 2Forexample,PaulKrugmanhasmadethistypeofargumentinhispopularwritings. Formalmodelling suggeststhattheeffectsofdownwardnominalwagerigiditycouldbemorecomplicated: InDalyandHobijn’s(2014)theoreticalanalysis,downwardnominalwagerigiditypropsupwageinflationinarecession; as the labor market recovers, however, the existence of “pent-up” wage cuts puts downward pressure on wagesevenastheunemploymentrateisfalling. 1

recent inflation behavior can be better explained if real activity is measured in terms of the short-term unemployment rate (that is, the share of the labor force unemployed for 26weeksorless),onthegroundsthatthelong-termunemployedseemtoputless(orno) downwardpressureoninflation. Ultimately,theseproposedexplanationsfortherecentbehaviorofpriceinflationonly make sense if there is an economically significant influence of compensation costs on prices. Regarding the first explanation, it is clear that downward nominal wage rigidity can have an important effect on inflation dynamics only if price setting is closely connected to labor costs. Regarding the second explanation, we would not expect a rise in long-term unemployment to have a smaller effect on aggregate demand than a rise in short-term unemployment: Presumably, the long-term unemployed—who have suffered a relatively larger and more persistent shock to their permanent income—would reduce their contribution toaggregate demand to agreater degree than would the short-term unemployed. Hence, it seems difficult to invoke the idea that the short-term unemployment rate provides a better gauge of the level of real activity that is relevant for price inflation without simultaneously arguing that the fundamental source of this relation is the differentialeffectthattheshort-andlong-termunemployedhaveonwageinflation(and,again, thatlaborcostsareanimportant determinant ofprices). In this paper, we explore whether there is a tight—and stable—link between labor costs and price inflation. Overall, we find it difficult to discern an important independent effect of changes in average labor costs on aggregate price inflation in recent years once we account for labor market slack. In particular, we find evidence either that the passthroughoflaborcoststopriceshasfallenoverthepastseveraldecadesor—forcompensation measures where there is still evidence of passthrough—that changes in labor 2

costshavehadessentiallynomaterialeffectonpriceinflationinrecentyears. A number of authors have examined whether movements in labor costs lead changes inpriceinflation. Althoughtheresultsareoftenspecifictovariousmethodologicalchoices and data definitions, the general conclusion that emerges from this literature is that there appears to be a break in the relation between labor costs and broad price measures, with changesinlaborcostshavinglittleornopredictivepowerforpriceinflationaftertheearly 1980s. For example, Mehra (2000) divides the postwar period into three subperiods and finds that wage inflation helps predict price inflation only in the middle (high-inflation) subperiodof1966–1983;similarly,EmeryandChang(1996)findthatlaborcostsareonly useful in forecasting core consumer price inflation in the 1970s. Our work complements and extends this earlier research in two ways. First, the empirical framework that we use to gauge how the passthrough of labor costs to prices has evolved over time—a VAR modelwithtime-varyingparametersandstochasticvolatility—hasnot,toourknowledge, been previously employed for this purpose.3 This framework allows us to better identify thesourceofanychangesinpassthroughthatweobserve,aswellastheirimplicationsfor inflation dynamics. Second, our analysis covers a more-recent period, one that includes theGreatRecessionandasignificantportionofthesubsequentrecovery. While it casts doubt on explanations based on downward nominal wage rigidity or similar labor-market developments, our finding that the behavior of labor costs appears to have had little material influence on price inflation leaves unanswered the question of howtoexplaintheevolutionofinflationfollowingtheGreatRecession. Basedonourresults,weconcludethatthedynamicsofpricesandlaborcostshavechangedsignificantly in recent decades,suchthat the stochastic trends for price inflation and labor cost growth 3ClarkandTerry(2010)usethisapproachtoanalyzetimevariationinthepassthroughofenergyprice changestocoreconsumerprices. 3

have both been essentially constant since the mid-1990s. As a result, price inflation now responds less persistently to changes in real activity or costs; at the same time, the joint dynamics of inflation and compensation no longer manifest the type of wage–price spiral that was evident in earlier decades. Hence, the recent behavior of inflation (and our inability to find an important independent role for labor costs in driving inflation movements) reflects a change to the inflation process that predates the 2007–2009 recession, notsomethingspecifictotheGreatRecessionitself. II Empiricalframeworkanddata We use a time-varying parameter/stochastic volatility vector autoregression model (a TVP/SV VAR) to examine whether and to what degree the passthrough of labor costs to price inflation has changed over time. In general, an n-variable recursively identified VARcanbewrittenas y1 = a1 +A11 (L)y1 +A12 (L)y2 + ··· +A1n(L)yn +ε1 t 0 t−1 t−1 t−1 t y2 = a2 +A21 (L)y1 +A22 (L)y2 + ··· +A2n(L)yn +a2y1 +ε2 t 0 t−1 t−1 t−1 1 t t . . . yn = an +An1 (L)y1 +An2 (L)y2 + ··· +Ann(L)yn +any1 + t 0 t−1 t−1 t−1 1 t any2 + ··· +an yn−1 +εn, (1) 2 t n−1 t t where the Aij(L) terms denote lag polynomials and εi is the structural residual assot ciated with equation i. (Note that as the system is written, the variables are ordered y1,y2,...,yn.) In the TVP/SV framework we consider, the values of Aij(L) and ai and t t t j the standard deviations of the εi terms are allowed to drift over time (they are modelled t asrandom walks). Hence,byusingtherelevantsetsofparametervalueswecanexamine 4

impulse response functions at various points in time; similarly, we can use the VAR to decomposethehistoricalmovementsinagivenvariableintothecumulativecontributions of the various structural shocks. In addition, the model can be used to produce estimates of the variables’ stochastic trends. Following Cogley, et al. (2010), write the VAR in its companionform as z = µ +B z +e , (2) t+1 t t t t+1 where z stacks the current and lagged values of the variables yi, µ contains the (timet t t varying) intercepts from each VAR equation, and B contains the VAR’s autoregressive t parameters (which are also time-varying). At time t, we can obtain estimates of the stochastictrendsz¯ from t z¯ = (I −B ) −1µ , (3) t t t whereI denotestheidentitymatrix.4 The TVP/SV approach complements alternative approaches to evaluating changes over time in the passthrough of labor costs to inflation, such as examining models estimated over rolling samples or specified subperiods. In a rolling regression, coefficient estimates can fluctuate purely because of sampling variability; by explicitly modelling parameter drift and using information from the full sample, the TVP/SV approach can in principle provide a clearer picture of the amount and type of drift that is truly present. Likewise,intheTVP/SVapproachthetimingofanyparametershiftsisdeterminedbythe data, rather than by the analyst’s choice of estimation subperiods. Finally, the TVP/SV approach allows us to model changes in the volatility of shocks over time, which can be important in determining whether observed changes in passthrough actually reflect 4NotethatthetrenddefinitionbeingusedhereisanalogoustotheBeveridge–Nelsonconcept. 5

parameterbreaks.5 ThebaselineVARsystemthatweconsiderisafour-variable,two-lag,quarterlymodel consisting of weighted relative import price inflation, a measure of trend unit labor cost growth, core price inflation, and an unemployment gap, with that causal ordering.6 (All growthratesaredefinedasannualizedlogdifferences.) Weincludearelativeimportprice term to control for the effect of an important component of non-labor costs on price inflation. The unemployment gap, which we include to capture the degree of labor- and product-market slack in the economy, is defined as the difference between the total civilian unemployment rate and the Congressional Budget Office’s (CBO’s) estimate of the short-term natural rate of unemployment.7 The core inflation measure that we use is the market-based component of the core PCE price index—that is, the chain price index for market-basedpersonalconsumptionexpendituresexcludingpricesforenergyandfoodat home.8 Finally,weestimatethemodelusingClarkandTerry’s(2010)implementationof 5Ofcourse,theseadvantagescomeatacostinasmuchasaTVP/SVmodelismoredifficulttoestimate; in addition, the model’s dynamic structure will tend to be relatively parsimonious compared with other typesofempiricalinflationequations(suchasaPhillipscurve). 6OurchoiceoflaglengthisinformedbyapplyingtheSchwarzcriteriontoaconstant-coefficientVAR estimatedoverthefullsample;foreachofthemeasuresoftrendunitlaborcoststhatweuseinouranalysis, thiscriterionwasminimizedbyatwo-lagsystem. 7ThisisthesamegapdefinitionusedbyCoibionandGorodnichenko(2015)indocumentingthepresence of “missing disinflation” in the aftermath of the Great Recession. The CBO defines the natural rate as“theestimatedrateofunemploymentarisingfromallsourcesexceptfluctuationsinaggregatedemand,” withtheshort-termvariantdefinedtoincludestructuralfactorsthatacttotemporarilyboostthenaturalrate relativetoitslong-termlevel. (Forreference,notethattheCBO’sshort-termnaturalrateestimaterisesby apercentagepointfrom2008to2012,peakingat6percent.) Theshort-termnaturalrateisintendedtobe compared to the total unemployment rate to obtain a measure of aggregate labor market slack; it has no connection totheshort-termunemployment rate—which, asnoted above, isdefined asthefractionofthe laborforceunemployedfor26weeksorless. 8Weconfineourattentiontomarket-basedpricesbecauseseveralnonmarketcomponentsofconsumptionarepricedusinginputcostindexesthatareinturnderivedfromwageorcompensationmeasures. (In total,coremarket-basedpricesaccountfornearly90percentoftheoverallcorePCEpriceindex.) Notethat beforethecoreinflationmeasureisusedintheVAR,wesubtractoutBlinderandRudd’s(2013)estimates oftheeffectsoftheNixon-erapricecontrols. 6

theMetropolis-within-Gibbs posteriorsampler.9 We consider two alternative measures of trend unit labor costs for our analysis; in each case, trend unit labor cost growth is defined by subtracting an estimate of the trend growthrateofaveragelaborproductivityforthenonfarmbusinesssectorfromameasure of hourly compensation growth.10 The first compensation measure that we use, hourly compensation for the nonfarm business sector, is taken from the Productivity and Costs (P&C) report constructed by the Bureau of Labor Statistics (BLS). The P&C series includeswageandsalarypaymentstoemployees(derivedfromsourcedatathatarebenchmarked to full-universe tax records), benefit costs, and an imputation for the portion of proprietors’ income that is attributable to labor. This series therefore represents a relatively comprehensive measure of labor-related production costs. The second measure thatweuse,theEmploymentCostIndex(ECI)forprivateindustryworkers,alsoincludes wage and salary payments and benefit costs, though its coverage excludes proprietors, self-employed workers, and those with substantial discretion over their own pay. More importantly, the ECI uses fixed weights for industry and occupational groups to control fortheeffectofchangesinthemixofjobsonmeasuredhourly compensation.11 It is not clear a priori which measure of hourly compensation—the P&C measure or the ECI—provides a better estimate of the compensation costs that are relevant for firms’pricingdecisions. AlthoughtheECI,bycontrollingfortheeffectsofmix-shiftson 9SeetheAppendixforadditionaldetailsregardingtheestimationprocedureandvariabledefinitions. 10Weobtainanestimateoftrendproductivitygrowthbyapplyingalow-passfiltertoactualproductivity growth (see the Appendix for details). Our use of trend unit labor costs is informed by the fact that in othercontexts,itisdifficulttofindaninfluenceofactualunitlaborcostgrowthonpriceinflationoncewe conditionontrendunitlaborcostgrowth,likelybecauseactualproductivitygrowthisextremelynoisyata quarterlyfrequency. 11Additional background on the P&C measure can be found in a March 11, 2008 BLS note entitled “Technical Information About the BLS Major Sector Productivity and Costs Measures” (available at www.bls.gov/lpc/lpcmethods.pdf); chapter8oftheBLSHandbookofMethodsdiscusseshow theECIisconstructed. 7

compensation,mightseemtosmoothawayimportantvariationinlaborcosts,itispossible thatsuchmix-shiftsarenotoffirst-orderimportancetofirms’pricingdecisions(inwhich case an ECI-based measure of unit labor costs would potentially provide a better gauge of the labor costs that are relevant for price setting). In any case, both the P&C and ECI hourly compensation series are commonly followed aggregate measures that are broadly representativeofthecompensationcostsfacedbyalargesetofprivatebusinesses,soitis ofinteresttoexaminehoweachmeasureinfluencesobservedpriceinflation. The estimation period for our VARs ranges from 1965:Q1 to 2012:Q2 for the P&Cbasedmodels,andfrom1982:Q1to2012:Q2fortheECI-basedspecifications(thechoice of a later starting date for the ECI-based models reflects that fact that the ECI for total compensationdoesnotexistpriortothe1980s). Ouruseofa2012:Q2endingdateforour sample is informed by several considerations. First, income shifting in advance of an anticipatedtaxincreaseresultedinalarge,transitoryswinginmeasuredP&Ccompensation at the end of 2012; moreover, the implementation of federal budget sequestration provisions in early 2013 had large temporary effects on some of the medical services prices that enter the PCE price index. Hence, in order to prevent these unusual endpoint observationsfromundulyinfluencingthemost-recentparameterestimatesfromourmodel,we stopourestimationperiodinmid-2012(note,however,thatthisendingdatestillgivesus three years’ worth of data from the recovery that followed the 2007–2009 recession). In addition, at the time that we constructed the dataset for our study (in early 2014), 2012 was the last full year for which the national accounts data—from which the P&C compensationmeasureisderived—hadundergoneanannualrevision;thus,thecompensation data from 2012 and earlier should be somewhat less subject to measurement error than themost-recent availabledata. 8

III Timevariation inthepassthroughoflaborcoststoprices To gauge how the passthrough of trend unit labor costs into core inflation has changed over time, we use the parameter estimates from our TVP/SV models to evaluate impulse response functions for core market-based PCE inflation at different dates.12 Figure 1 plots the median response of core inflation following a 2.7 percentage point shock to the P&C-based measure of trend unit labor cost growth (expressed at an annual rate) at various times over the period 1975–2012, along with 70 percent credible sets. (A 2.7 percentage point shock is used because this is the standard deviation of this measure of trend unit labor cost growth over the full sample period.) As can be seen from the figure, the passthrough of unit labor costs to core inflation has diminished markedly over time; in particular, in the last year of the sample the point estimate for the response’s peakvalueisonlyaboutone-fourthaslargeasin1975(andaboutone-thirdaslargeasin 1985),andisstatisticallyindistinguishablefrom zero. Weobtainasomewhatdifferentpictureofhowthepassthroughoflaborcoststoprice inflationhasevolvedifwemeasurelaborcostswiththeECI.Figure2plotsthemedianresponseofcoreinflationatvariousdatesfollowingaone-standard-deviationshocktotrend unitlaborcostgrowthfromtheECI-basedmodels.13 Inthisspecification,thepassthrough of labor cost changes into core inflation varies little over the sample period, with a peak responsethatremainsstatisticallysignificantthroughout. Apossibleexplanationforthesefindingscanbefoundbycomparinghowthevolatility 12Alternatively,wecouldexaminethesumofthecoefficientsonthelaggedtrendunitlaborcostgrowth termsinthecoreinflationequationoftheVAR.However,becausecoreinflationisorderedbelowunitlabor cost growth, there can be a potentially important contemporaneous effect of the unit labor cost shock; in addition,timevariationinthecoefficientsonlaggedcoreinflationimpliesthatthepersistenceoftheeffect oftheseshocksoninflationcouldchangeovertimeinwaysthatwouldnotbecapturedbyonlyconsidering their (full) impact effect. Hence, in this context we believe that it is more useful to look at the impulse responsefunctions. 13Aone-standard-deviationshocktothismeasureequals0.8percentagepointatanannualrate. 9

of innovations to these two measures of unit labor cost growth has varied over time. We do this in figure 3, which plots the posterior medians for the standard deviation of the structural residuals from the unit labor cost equation of the P&C- and ECI-based VARs. Starting around 1985, the volatility of own innovations to P&C trend unit labor costgrowth(thesolidlineinthefigure)hasmovedsteadilyhigher,reachingalevelatthe end of the sample that is more than twice as large as the level that prevailed over the first half of the sample. By contrast, the volatility of innovations to ECI trend unit labor cost growth (the dashed line) changes little over the sample; if anything, a modest downward trend is evident in the standard deviation of these shocks. This difference in volatility is also apparent in the raw data on trend unit labor costs, which we plot in figure 4: There is a clear increase in the variability of the P&C-based measure, both relative to its earlier history and relative to the ECI-based series (note that the figure shows four-quarter log differences).14 Of course, such an increase in volatility should only result in a reduction in the passthrough of labor costs to price inflation to the extent that it actually reflects a rise in the degree to which (measured) compensation movements are unimportant for price setting. It is difficult, though, to pinpoint specific changes in compensation practices (or measurement) that might explain both the observed reduction in passthrough and the similarly timed rise in volatility. One possibility is that the greater use over time of employee stock options could be driving both phenomena: The ECI does not capture stock options in any form, while the employee compensation data from the national accounts 14Becausethesameestimateoftrendproductivitygrowthisusedtoconstructbothunitlaborcostmeasures, the relative volatility across the two measures reflects the relative volatility of the P&C and ECI measuresofhourlycompensationgrowth.Likewise,becausethetrendproductivitygrowthseriesisreasonablysmooth,thevolatilityofthetrendunitlaborcostmeasuresisitselfmostlyattributabletothevolatility ofthehourlycompensationseriesthatareusedtoconstructthem. 10

that are used to construct the P&C measure include the value of options when they are exercised.15 If, as seems consistent with economic theory, the grant value of a stock option is a better measure of the relevant cost to the firm, then including stock option exercises in compensation could both raise measured volatility (again because options have become more prevalent over time and because the value of exercises can be subject to large quarter-to-quarter swings) while at the same time reducing the passthrough of measured compensation changes to price inflation. However, the timing of the rise in importanceofstockoptionsincompensation,whichappearstooccurafterthemid-1990s (see Moylan, 2008, p. 7), does not line up especially well with the corresponding decline in passthrough (which, according to our estimates, appears to have occurred somewhat earlier). It is also possible that the decline in passthrough and increase in volatility for the P&C-based measure relative to the ECI-based measure reflects increased measurement error in the former, or a rise in the importance of changes in the mix of jobs (which the ECI controls for) in driving quarterly movements in compensation growth. Regarding measurement error, we are not aware of any evidence that the quality of the P&C hourly compensationserieshasdeterioratedovertime. Indeed,themeasurementofthewageand salarycomponentoftheemployeecompensationdatathatentertheP&Cmeasurehasarguablyimproved(atleastoverthepastdecade): Startingin2002,theBureauofEconomic Analysis (who are responsible for constructing the U.S. national accounts) began using full-universe tax records to measure employee compensation on a quarterly basis (previously, these tax records were only used to provide an annual benchmark, with quarterly estimates interpolated using a proxy measure of the quarterly wage bill). Regarding the 15See Moylan (2008) for a discussion of how employee stock options are treated in the U.S. national accounts. 11

second possibility, it is certainly plausible that a compensation measure such as the ECI, which controls for changes in the mix of jobs, might provide a better read of the laborrelatedcoststhatarerelevantforfirms’price-settingdecisions. Thatsaid,wearealsonot aware of any evidence that these sorts of mix-shifts have made an increasingly important contribution in recent years to the volatility of compensation growth (nor do we know of any plausible explanation as to why an increase in the importance of mix-shifts might haveoccurred).16 IV Stochastictrendsininflationandlaborcostgrowth Anotherinterestingfeatureoftheinflationprocessisrevealedbyconsideringthestochastic trends in price inflation and unit labor cost growth that we obtain from our model, which we plot (together with the four-quarter log differences of the actual data) in panelsAandBoffigure5.17 As is evident from panel A of the figure, trend price inflation (the thick dashed line) rises steadily over the 1960s and 1970s, peaking at 61⁄ percent at the end of 1979. Trend 2 inflation then drops sharply following the back-to-back recessions of 1980–1982, after which it stays roughly flat at around 4 percent for the rest of that decade. The 1990– 1991 recession results in another—though much smaller—decline in trend inflation (to around 2 percent) that is essentially complete by the mid-1990s. From then on, however, there are no persistent movements in the trend—in particular, the 2001 recession leaves 16Inprinciple, itwouldbepossibletoassesstimevariationintheimportanceofmix-shiftsbycomparing ECI-based hourly compensation with the hourly compensation measure from the Employer Costs for EmployeeCompensation(ECEC)report(veryroughly,theECECiscomputedfromthe“raw”datausedto estimatetheECI,withoutany correction forchanges inthemixofjobs). Unfortunately, quarterlyECEC dataareonlyavailablestartingin2002,whichisnotearlyenoughforthispurpose. 17We focus on the estimates from the model with the P&C-based unit labor cost measure because it allowsustoconsideralongertimeperiod;thestochastictrendsfromtheECI-basedmodelaresimilar. 12

no discernable imprint on the trend inflation rate, nor does the much more severe recessionof2007–2009. Thisbehaviorofinflation’sstochastictrendislargelymirroredbythe stochastictrendinourmeasureoftrendunitlaborcostgrowth,whichisshowninpanelB of the figure. Interestingly, the broad contour—and recent stability—of these stochastic trends is also apparent in survey measures of longer-run expected inflation, such as the expected five-to-ten-year price change from the Michigan survey (the dotted line in panelA).18 When inflation dynamics are characterized by a stable long-run trend, certain types of empirical inflation specifications will tend to fit poorly in periods that see persistent changes in the other determinants of inflation. For example, under this characterization ofinflationdynamics,apersistentwideningoftheunemploymentgap(suchasthatseenin the2007–2009recessionandsubsequentslowrecovery)willtendtopushactualinflation belowitstrendforaslongasthegappersists. Astheeconomyrecoversandthegapcloses, however,actualinflationwillmovebacktoits(unchanged)trend,withnopersistenteffect on its level. This sort of behavior will be at odds with the predictions of a traditional “accelerationist”modelofinflationoftheform π t = A(L)π t−1 +γX t +ε t , (4) in which X captures other influences on inflation (for example, the unemployment gap t or supply shocks) and where the accelerationist restriction A(1) = 1 is imposed when the equation is estimated. In this model, the presence of a persistent unemployment gap 18Thiscorrespondencebetweeninflation’sstochastictrendandsurveymeasuresoflonger-termexpected inflationwasnotedbyClarkandDavig(2008);seeFaustandWright(2013)forarelateddiscussioninthe contextofinflationforecasting. (Notethattoobtainalongertimeseriesforexpectedinflationinfigure5, priorto1990:Q2wesplicetheMichigansurveymeasuretothelonger-termexpectedinflationseriesfrom theHoeysurvey—seetheAppendixforadditionaldetails.) 13

causes predicted inflation to drift lower and lower over time; when the gap finally does close,themodelpredictsthatinflationwillbottomoutatsomenew,lowervalue(andwill shownotendencytoreturntoitspre-recessionlevel). In practice, fitting an accelerationist specification to a period where there is a large widening of the unemployment gap—and, again, where inflation dynamics are actually characterizedbyastablelong-runtrend—willtendtoattenuatethecoefficientonthegap, thereby suggesting the presence of nonlinearities in the inflation–unemployment relation (this result can obtain even if the full sample period is relatively long, since a rise in the unemployment gap similar to that seen over the previous recession will represent a large and influential outlier). Relatedly, any modification to the baseline accelerationist specification that reduces the size or persistence of the measured unemployment gap— for example, defining the unemployment gap in terms of the short-term (as opposed to the total) unemployment rate or allowing for an increase in the natural rate—will tend to improve the model’s performance over the past several years.19 Of course, an alternative explanation is simply that the inflation process has changed in a manner that makes an accelerationist-stylemodelapoordescriptionofcurrentactualinflationdynamics.20 Finally, the joint behavior of the stochastic trends for inflation and unit labor cost growthshowninfigure5alsosuggestswhyitisthatreduced-formmodelswouldtendto 19Becausethetotalunemploymentrateandtheshort-termunemploymentratebehavesimilarlyinmost previouspostwarU.S.businesscycles—itisreallyonlyinthemost-recentrecoverythatanoticeabledifferenceispresent—thisparticularmodificationneednotcompromisetheaccelerationistmodel’sabilityto fitinflationinearlierperiods. 20Itisnoteworthy,therefore,thatobserverswhohavepointedtononlinearitiesintherelationshipbetween unemploymentandinflation(suchasthoseinducedbydownwardnominalwagerigidity)inordertoexplain recentpricebehaviorappeartohavethepredictionsfromanaccelerationistmodelinmindasabenchmark. Likewise, many of the studies that have pointed to a differential role for short-term unemployment in determining price inflation—such as Gordon (2013) and the results presented in chapter 2 (pp. 82–83) of the 2014 Economic Report of the President—have made the case in the context of an accelerationist framework (this statement also applies to the analysis of Watson, 2014, inasmuch as his specification for inflationcanbethoughtofasanaccelerationistmodelwithalongdistributedlag). 14

findasmallerroleforlaborcostsindrivingpriceinflationovermorerecentperiods: Since theearly1980s,therehavebeennoinstancesofasignificantwage–pricespiralofthesort thatresultedinapersistentandroughlycontemporaneousincreaseinthestochastictrends ofinflationandlaborcostgrowthoverthe1960sand1970s. Asaresult,inrecentdecades movements in labor costs have not tended to carry much information about persistent movementsinpriceinflation(andvice-versa). V Theroleoflaborcostsinexplainingrecentinflationbehavior The results in section III suggest that the passthrough of trend unit labor costs—defined using the P&C-based measure of hourly compensation—to core inflation has declined markedly in recent years, to the point where the response of core inflation to a shock to this measure of labor costs is statistically indistinguishable from zero. Nevertheless, given that the volatility of these shocks has risen sharply over time (recall figure 3), it is still possible for this measure of unit labor costs to have a nontrivial effect on inflation. Toassesstheextenttowhichrecentmovementsininflationaredrivenbychangesinunit labor cost growth, we use the estimated VAR system to decompose actual movements in core inflation into the VAR’s baseline forecast (that is, the projected path of inflation absentanystructuralshocksbutgivenanytime-variationinthemodel’scoefficients)and thecumulativecontributionofthemodel’sestimatedstructuralshocks. Inthefiguresthat follow, we focus on the shocks to trend unit labor cost growth and the unemployment gap;notethatforagivenvariable,thecontributionofallofthemodel’sstructuralshocks (i.e.,theshockstocoreinflation,unitlaborcostgrowth,relativeimportpriceinflation,and theunemploymentgap),combinedwiththeVAR’sbaselineforecast,willbyconstruction exactlysumtothevariable’sactualvalue. Thespecificperiodoverwhichweperformthis 15

decomposition extends from 2001:Q1 to 2012:Q2, and therefore includes both the 2001 and2007–2009 recessions. Panel 1 of figure 6 gives the results from this exercise for the VAR specification that uses the P&C-based measure of labor costs. (To improve readability, the figure shows actual core inflation as a four-quarter log difference, and plots the baseline forecast and innovationcontributions asfour-quarter movingaverages.) Accordingtothemodel,very little of the movement in core inflation over this period can be attributed to innovations to trend unit labor cost growth (compare the dashed line, which gives the baseline forecast, with the dotted line, which adds in the contribution of the unit labor cost shocks). Importantly,thisresultobtainseventhoughtheseinnovationsaccountformuchoftheactual variation in unit labor costs themselves (see panel 3 of the figure, which repeats this calculation for trend unit labor cost growth), and even though unit labor cost growth is orderedbeforecoreinflationintheVAR.Bycontrast,ifweinsteadconsidertheeffectof shockstotheunemploymentgap(whichisorderedlastintheVAR),theresultingdecompositionsuggeststhatthewideningofthegapinboththe2001and2007–2009recessions made an important contribution to pushing both price inflation (panel 2) and unit labor costgrowth(panel4)belowtheirrespectivebaselines.21 WhatabouttheVARsystemthatusesanECI-basedmeasureoftrendunitlaborcosts? Here,thepassthroughoflaborcoststocoreinflationappearedtobeessentiallystableover time, which suggests that we might be able to find a more important role for labor costs inexplainingrecentinflationbehaviorifweinsteadusethisspecification. Inaddition,the stabilityofthedynamicresponsesofinflationtounitlaborcostshocksinthismodelraises 21Note that a corresponding historical decomposition of the unemployment gap (not shown) indicates that the VAR attributes almost all of the widening of the unemployment gap in each recession to owninnovationstothegap. 16

thepossibilitythatwemightbeabletoemployaconstant-coefficientspecification,solong as the other dynamic reponses implied by the VAR manifest a similar degree of stability. As it turns out, they do: In figure 7, we plot the impulse response functions for core inflation, the ECI-based measure of trend unit labor cost growth, and the unemployment gap that we obtain from the time-varying parameter VAR at various dates (the first set of panels gives the responses following an unemployment gap shock, and the second set showstheresponsesfollowingashocktocoreinflation). Noneoftheresponsesfromthis model shows any significant variation over time, mirroring the results that we obtained fortheresponseofinflationtoaunitlaborcostshock(figure2).22 One advantage of using a constant-coefficient VAR is that it allows us to indirectly test for the presence of downward nominal wage rigidity of the sort invoked by Daly and Hobijn (2014) in their interpretation of recent U.S. wage dynamics. Recall that in the Daly–Hobijn model, downward nominal wage rigidity induces a nonlinearity in the relationship between wage growth and labor market slack that causes wage inflation to decline by less than it otherwise would following an increase in unemployment; later, as the labor market recovers, the existence of “pent-up” wage cuts puts downward pressure onwages. Hence,ifweuseaconstant-coefficientVARmodel—inwhichaconstantlinear relationship between the unemployment gap and labor costs is imposed—to describe the evolution of labor costs in the wake of the 2007–2009 recession, the presence of downwardnominalwagerigidityshouldresultinourseeingasequenceofpositiveinnovations tolaborcostgrowthastherecessionproceedsandtheunemploymentgapwidens(thatis, growth in labor costs should be higher than expected over the recession period). Afterwards,asthelabormarketstartstorecover,weshouldexpecttoseeasequenceofnegative 22Theresponsesoftheothermodelvariablesfollowingashocktounitlaborcosts(notshown)displaya similardegreeofstability,asdotheresponsesfollowingashocktoimportpriceinflation(alsonotshown). 17

innovations to labor costs as compensation growth is held down by pent-up wage cuts.23 More broadly (and outside of this specific model), to the extent that downward nominal wage rigidity has had an important effect on recent price inflation dynamics, it should be possible to find an economically significant influence of labor costs on core inflation duringandafterthe2007–2009recession. In figure 8, we repeat our historical decompositions of core inflation and trend unit labor cost growth using a constant-coefficient VAR in which unit labor costs are defined using the ECI for hourly compensation.24 In contrast to the results from the P&C-based VARs, we find that shocks to labor cost growth have had a less-trivial effect on core inflation over this period (panel 1), though quantitatively their contribution remains small (generally no greater than 1⁄ percentage point) and accounts for very little of the over- 4 all movement in core inflation from 2007 to 2012. In addition, the shocks to labor cost growth have exactly the opposite pattern to what we would expect if downward nominal wage rigidity were playing an important role: Over the course of the 2007–2009 recession, a sequence of negative own-innovations pushes down the rate of growth of labor costs (see panel 3), leaving the pace of labor cost growth lower than would be expected giventheinnovationstotheunemploymentgapalone(panel4). Thelabormarketstartsto recoverafter2009(theunemploymentgapreachesitswidestpointin2009:Q4);however, instead of seeing negative innovations to labor costs (as would be expected were pent-up wagecutsholdingdowncompensationgrowth),overthenextcoupleofyearsasequence ofpositiveown-innovations putsnetupward pressureonlaborcosts. 23This discussion is loose in that it does not distinguish between compensation growth and growth in trendunitlaborcosts(recallthatthelatteristheformeradjustedfortrendproductivity). However,overthe 2007–2012periodthatisourmainfocus,virtuallyallofthemovementinourmeasureoftrendunitlabor costgrowthreflectschangesinnominalcompensationgrowth. 24ThespecificationandestimationperiodfortheVARareotherwiseidenticaltothecorrespondingtimevaryingparameterVARdescribedinsectionII. 18

Whatever conclusion one draws about the presence or absence of downward nominal wage rigidity from this pattern of labor-cost innovations, the fact remains that on average these innovations make a small negative contribution to core price inflation over this period, not the large positive contribution that would be needed were wage-related developments to be a good candidate explanation for the existence of significant “missing disinflation.” VI Additionalimplicationsandcaveats Inthispaper,wehavedocumentedthatshockstolaborcostshavemadearelativelysmall contribution to the observed behavior of price inflation in recent years. Our findings thereforecastdoubtonexplanationsofrecentinflationbehaviorthatappealtosuchmechanismsasdownwardnominalwagerigidityoradifferentialcontributionoflong-termand short-termunemployedworkerstowagepressures. Wehavealsoproposedanalternative waytounderstandtherecentbehaviorofpriceinflationthatdoesnotrelyonwage-based explanations—specifically, price inflation is currently tied down by a stable stochastic trend, to which it ultimately returns once resource utilization rates return to normal levels and the influences of any other shocks dissipate. If correct, this alternative view of the inflation process implies that most of the “missing disinflation” puzzle that has been discussed by previous analysts simply reflects the use of a model of inflation (an accelerationistspecification)thatnolongerprovidesanespeciallyaccuratecharacterizationof U.S. inflation dynamics, and that therefore generates a misleading benchmark for how we would have expected inflation to behave following the 2007 business cycle peak. In addition, our results suggest that wage developments are unlikely to be an important independentdriverof(oranespeciallygoodguideto)futurepricedevelopments. 19

We would emphasize that our results do not necessarily imply that labor costs are unimportant for pricing. Instead, a more-nuanced interpretation is that as long as the stochastic trends for inflation and labor costs remain stable—in particular, so long as the sort of wage–price spiral that characterized earlier decades does not emerge—observed year-to-year movements in price inflation are likely to mostly reflect a mix of changes in resource utilization, supply shocks, and idiosyncratic variation, not independent movements in the growth of labor costs. Indeed, it is quite possible that the greater observed stability of inflation’s stochastic trend is itself directly attributable to the greater stability that we observe in the stochastic trend for labor cost growth (even if the cause of this latterphenomenonultimately lieselsewhere). Thislastpointhighlightsanimportantquestionthatisleftunansweredhere—namely, what has caused the processes for inflation and labor costs to change in such as way as to make their long-run levels essentially constant? While a simple explanation—that the public’s expectations of longer-term inflation have become better anchored over time— certainlyseemsplausible(recallourfigure5),suchanansweritselfbegsthefurtherquestion of why this greater anchoring has taken place. (The obvious reply, that the improved conductorcredibilityofmonetarypolicyhasplayedakeyroleinanchoringexpectations, turns out to have surprisingly little hard evidence to support it—though see Clark and Davig,2011,forsomesuggestivecircumstantialevidence.) Unfortunately,untilwecome to a much better understanding of what determines the expectations of wage- and pricesetters, we are unlikely to be able to claim much certainty regarding how the inflation processwillevolveinthefuture. 20

VII References Ball, Laurence, and Sandeep Mazumder, “Inflation Dynamics and the Great Recession,” International MonetaryFundWorkingPaperno.WP/11/121(2011). Blinder, Alan S., and Jeremy B. Rudd, “The Supply-Shock Explanation of the Great StagflationRevisited,”inMichaelD.BordoandAthanasiosOrphanides(Eds.),TheGreat Inflation: TheRebirthofModernCentralBanking(Chicago: UniversityofChicagoPress, 2013). Clark, Todd E., and Troy Davig, “An Empirical Assessment of the Relationships Among InflationandShort-andLong-TermExpectations,”FederalReserveBankofKansasCity WorkingPaperno.RWP08-05(2008). Clark, Todd E., and Troy Davig, “Decomposing the Declining Volatility of Long-Term InflationExpectations,”JournalofEconomicDynamicsandControl35(2011),981–999. Clark, Todd E., and Stephen J. Terry, “Time Variation in the Inflation Passthrough of EnergyPrices,”JournalofMoney,CreditandBanking42(2010), 1419–1433. Cogley, Timothy, and Thomas J. Sargent, “Drifts and Volatilities: Monetary Policies and OutcomesinthePostWWIIUS,”ReviewofEconomicDynamics,8(2005), 262–302. Coibion, Olivier, and Yuriy Gorodnichenko, “Is the Phillips Curve Alive and Well after All? Inflation Expectations and the Missing Disinflation,” American Economic Journal: Macroeconomics7(2015), 197–232. Daly,MaryC.,andBartHobijn,“DownwardNominalWageRigiditiesBendthePhillips Curve,”JournalofMoney,CreditandBanking46:S2(2014),51–93. Emery, Kenneth M., and Chih-Ping Chang, “Do Wages Help Predict Inflation?” Federal ReserveBankofDallasEconomicReview,FirstQuarter(1996), 2–9. Faust, Jon, and Jonathan H. Wright, “Forecasting Inflation,” in Graham Elliott and Allan Timmermann(Eds.),HandbookofEconomicForecasting,vol.2A(Amsterdam: Elsevier– NorthHolland,2013). Gordon,RobertJ.,“ThePhillipsCurveisAliveandWell: InflationandtheNAIRUduring theSlowRecovery,”NBERWorkingPaperno.19390(2013). Koop, Gary, and Simon M. Potter, “Time Varying VARs with Inequality Restrictions,” JournalofEconomicDynamicsandControl 35(2011),1126–1138. 21

Mehra, Yash, “Wage-Price Dynamics: Are They Consistent with Cost Push?” Federal ReserveBankofRichmondEconomicQuarterly86:3(2000), 27–43. Moylan, Carol E., “Employee Stock Options and the National Accounts,” Survey of CurrentBusiness88:2(2008), 7–13. Staiger, Douglas, James H. Stock, and Mark W. Watson, “Prices, Wages, and the U.S. NAIRU in the 1990s,” in Alan Krueger and Robert Solow (Eds.), The Roaring Nineties: Can Full Employment Be Sustained? (New York: Russell Sage Foundation and Century FoundationPress,2001). Watson,MarkW.,“InflationPersistence,theNAIRU,andtheGreatRecession,”American EconomicReview104(2014), 31–36. 22

A Appendix This Appendix provides additional details regarding the data and estimation procedures thatweuseforourstudy. A Datadocumentation All standard data from the National Income and Product Accounts (NIPAs) were downloaded from the Bureau of Economic Analysis (BEA) website; data on unemployment, productivity, and compensation were downloaded from the Bureau of Labor Statistics website. (All data were current as of February 12, 2014.) Finally, the CBO short-term natural rate series is taken from the February 2014 edition of The Budget and Economic Outlook: 2014to2024. Market-based PCE price index: Official data for the core market-based PCE price index are published from 1987 to the present. To extend back the market-based series before 1987,weusedetailedPCEdataandaFisheraggregationprocedureroutinethatreplicates the procedure followed by the BEA in constructing the NIPAs to strip out the prices of corenonmarketPCEcomponentsfromthepublishedoverallcorePCEpriceindex,where ourdefinitionof“nonmarket”mimicstheBEA’s.25 Relative import price term: We define import price inflation as the annualized log difference of the price index for imports of nonpetroleum goods excluding natural gas, computers, peripherals, and parts, which we compute using detailed NIPA series. (As the data required to construct this series only extend back to 1967:Q1, we use the annualized log difference of total goods imports prior to that date.) The relative import price inflation term that we use in our VARs is equal to the difference between this series and core market-based price inflation (lagged one period), weighted by the two-quarter moving average of the share of nominal imports (defined consistently with the import price measure)innominalcorePCE.26 Long-run expected inflation: We splice the median response to the Michigan survey’s question on expected 5-to-10-year inflation to long-run expected CPI inflation from the Hoey survey. Specifically, we use the Hoey data from 1980:Q3 to 1989:Q4 (their first and last available dates), and the Michigan survey data starting in 1990:Q2 (the first date in which a continuous quarterly series is available). (For the 1990:Q1 observation, we extrapolate the Hoey data using the change from 1989:Q4 to 1990:Q1 in the median long-term CPIinflationforecastfrom theSurveyofProfessionalForecasters.) 25Asnotedinthetext,thecoreinflationseriesthatweuseinourVARmodelssubtractsoutBlinderand Rudd’s(2013)estimatesoftheeffectsoftheNixon-erapricecontrols. 26In constructing the relative import price term, we use the actual core market-based PCE price series (thatis,wedonotadjusttheseriesfortheeffectofpricecontrols),andscalethenominalimportshareby itssamplemean. 23

Trend productivity growth: Trend productivity growth is defined as the low-frequency component of the annualized log difference of nonfarm business output per hour, which we obtain from a band-pass filter with the filter width and cutoffs set equal to the values used by Staiger, Stock, and Watson (2001). We use an ARIMA(4,1,0) model to pad the actual productivity growth series prior to its 1947:Q2 starting point; to pad the series after its 2013:Q3 endpoint, we set the series equal to the CBO’s February 2014 forecast of average trend labor productivity growth from 2013 to 2024 (which equals 1.96 in log differences), and to the 2024 value of the CBO forecast (which equals 1.76) thereafter. (Note that the padded series is only used in the trend extraction routine, not to construct anyoftheunitlaborcostseriesthatweuseinourVARmodels.) B Additional estimationdetails We use Clark and Terry’s (2010) implementation of the Metropolis-within-Gibbs posterior sampler, which in turn follows Cogley and Sargent (2005).27 We set the number of burn-in draws equal to 50,000 and then run 50,000 additional draws, keeping every tenth draw. The priors for the initial values are computed by estimating the VAR over a training sample that runs from 1950:Q2 to 1964:Q4 (for the P&C-based models) or from 1967:Q2 to 1981:Q4 (for the ECI-based models).28 Following Clark and Terry (2010), we use an uninformative prior for the degree of time variation in the VAR coefficients (specifically, we set the prior equal to 0.001 times the variance-covariance matrix of the VAR coefficients estimated over the training sample, with degrees of freedom set equal tothenumberofcoefficientsinthesystemplusone). 27IncontrasttoCogleyandSargent(2005),wedonotsetthesamplertotruncateexplosivedrawswith a reflecting barrier or “backstep” algorithm; in line with the recommendation of Koop and Potter (2011), therefore, we generally report median values and use relatively interior percentiles (the 15th and 85th) to bound the credible sets. (An exception is in the historical decompositions, where we use mean values in ordertoensurethatthesumofthebaselineforecastandthecontributionsofallshockswillexactlyequal theactualvalueofthevariablewhosedecompositionwearedescribing.) 28In two cases, it was necessary to extend the data back to 1950:Q2 for use in the training sample; specifically,weextendedthemarket-basedcorePCEinflationseries(whichstartsin1959:Q2)withthelog differenceofapriceindexfortotalPCElesspricesforfoodandenergygoods,andextendedourmeasure oftrendproductivitygrowthpriorto1955:Q1bysettingitequaltoits1955:Q1valueof2.375. Inaddition, priorto1980:Q2(thestartingdateforourECIinflationseries),weusedP&Chourlycompensationgrowth tocomputetrendunitlaborcostgrowthinthetrainingsamplethatweconstructedfortheECI-basedVARs. (Again,alloftheseextendedserieswereusedforthetrainingsampleonly.) 24

Figure 1 Response of core inflation to P&C trend unit labor cost growth shock A. 1975 0.6 0.5 0.4 0.3 0.2 0.1 0.0 -0.1 -0.2 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 B. 1985 0.6 0.5 0.4 0.3 0.2 0.1 0.0 -0.1 -0.2 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 C. 1995 0.6 0.5 0.4 0.3 0.2 0.1 0.0 -0.1 -0.2 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 D. 2005 0.6 0.5 0.4 0.3 0.2 0.1 0.0 -0.1 -0.2 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 E. 2012 0.6 0.5 0.4 0.3 0.2 0.1 0.0 -0.1 -0.2 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 Note: Core inflation defined as log difference of core market-based PCE price index. Dashed lines denote 70 percent credible set. 25

Figure 2 Response of core inflation to ECI trend unit labor cost growth shock A. 1985 0.5 0.4 0.3 0.2 0.1 0.0 -0.1 -0.2 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 B. 1995 0.5 0.4 0.3 0.2 0.1 0.0 -0.1 -0.2 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 C. 2005 0.5 0.4 0.3 0.2 0.1 0.0 -0.1 -0.2 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 D. 2012 0.5 0.4 0.3 0.2 0.1 0.0 -0.1 -0.2 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 Note: Core inflation defined as log difference of core market-based PCE price index. Dashed lines denote 70 percent credible set. 26

Figure 3 Standard deviation of structural innovations (Annualized log differences) 4.5 4.0 3.5 P&C trend unit labor cost 3.0 2.5 2.0 1.5 ECI trend unit labor cost 1.0 0.5 0.0 1965:1 1969:1 1973:1 1977:1 1981:1 1985:1 1989:1 1993:1 1997:1 2001:1 2005:1 2009:1 Note: Estimated from VAR systems with relative import price inflation, labor cost growth, core inflation, and unemployment gap. Figure 4 Trend unit labor cost measures (Four-quarter log differences) 10 8 P&C trend unit labor cost 6 4 2 0 ECI trend unit labor cost -2 -4 1965:1 1969:1 1973:1 1977:1 1981:1 1985:1 1989:1 1993:1 1997:1 2001:1 2005:1 2009:1 27

Figure 5 Measures of trend inflation A. Core market-based PCE price index 12 10 Coreinflation 8 6 4 Michigansurvey 2 Stochastic trend 0 -2 -4 1965:1 1970:1 1975:1 1980:1 1985:1 1990:1 1995:1 2000:1 2005:1 2010:1 Note: Inflation measured as four-quarter log difference. Michigan survey is median response, spliced to Hoey data prior to 1990:Q2. B. Trend unit labor costs (productivity and costs measure) 12 Trendunit labor cost growth 10 8 6 4 Stochastic trend 2 0 -2 -4 1965:1 1970:1 1975:1 1980:1 1985:1 1990:1 1995:1 2000:1 2005:1 2010:1 Note: Trend unit labor cost growth measured as four-quarter log difference. 28

Figure 6 Effect of structural shocks from P&C trend unit labor cost model (Four-quarter log differences) A. Effect of structural shocks on core inflation 1. P&C trend unit labor cost shocks 2. Unemployment gap shocks 3.0 3.0 Baseline plus effect of trendunit labor cost shocks 2.5 Baseline forecast 2.5 Baseline forecast 2.0 2.0 1.5 1.5 Actual 1.0 1.0 Actual Baseline plus effect of unemployment gap shocks 0.5 0.5 0.0 0.0 2001:1 2003:1 2005:1 2007:1 2009:1 2011:1 2001:1 2003:1 2005:1 2007:1 2009:1 2011:1 B. Effect of structural shocks on P&C trend unit labor cost growth 3. P&C trend unit labor cost shocks 4. Unemployment gap shocks 5.0 5.0 4.0 Baseline plus effect of 4.0 trendunit labor cost shocks Baseline forecast Baseline forecast 3.0 3.0 2.0 2.0 1.0 1.0 0.0 0.0 -1.0 -1.0 Actual Actual Baseline plus effect -2.0 -2.0 of unemployment gap shocks -3.0 -3.0 2001:1 2003:1 2005:1 2007:1 2009:1 2011:1 2001:1 2003:1 2005:1 2007:1 2009:1 2011:1 Note: Core inflation defined as four-quarter log difference of core market-based PCE price index. 29

Figure 7 Impulse responses at different points in time 1. Effect of an unemployment gap shock Inflation response ECI trend unit labor cost growth response Unemployment gap response 0.00 0.00 0.4 0 2 4 6 8 10 12 14 0 2 4 6 8 10 12 14 -0.05 -0.05 0.3 0.2 -0.10 -0.10 0.1 -0.15 -0.15 0.0 -0.20 -0.20 0 2 4 6 8 10 12 14 1985 1995 2005 2012 1985 1995 2005 2012 1985 1995 2005 2012 2. Effect of an inflation shock Inflation response ECI trend unit labor cost growth response Unemployment gap response 0.6 0.6 0.20 0.5 0.5 0.15 0.4 0.4 0.3 0.3 0.10 0.2 0.2 0.05 0.1 0.1 0.0 0.0 0.00 0 2 4 6 8 10 12 14 0 2 4 6 8 10 12 14 0 2 4 6 8 10 12 14 1985 1995 2005 2012 1985 1995 2005 2012 1985 1995 2005 2012 Note: VAR system includes relative import price inflation, ECI trend unit labor cost growth, core market-based PCE price inflation, and unemployment gap. 30

Figure 8 Effect of structural shocks from ECI trend unit labor cost model (Four-quarter log differences) A. Effect of structural shocks on core inflation 1. ECI trend unit labor cost shocks 2. Unemployment gap shocks 3.0 3.0 B tr a e s n e d lin u e n i p t l l u a s b e o f r f e co ct s t o s f hocks B un as e e m li p n l e o y p m lu e s n e t f f g e a c p t o sh f ocks 2.5 2.5 Baseline forecast Baseline forecast 2.0 2.0 1.5 1.5 1.0 1.0 Actual Actual 0.5 0.5 0.0 0.0 2001:1 2003:1 2005:1 2007:1 2009:1 2011:1 2001:1 2003:1 2005:1 2007:1 2009:1 2011:1 B. Effect of structural shocks on ECI trend unit labor cost growth 3. ECI trend unit labor cost shocks 4. Unemployment gap shocks 2.0 2.0 Baseline plus effect of Baseline plus effect of trendunit labor cost shocks Baseline forecast unemployment gap shocks 1.5 1.5 Baseline forecast 1.0 1.0 0.5 0.5 0.0 0.0 -0.5 -0.5 Actual Actual -1.0 -1.0 2001:1 2003:1 2005:1 2007:1 2009:1 2011:1 2001:1 2003:1 2005:1 2007:1 2009:1 2011:1 Note: Core inflation defined as four-quarter log difference of core market-based PCE price index. 31