What's Happened to the Phillips Curve?

What's Happened to the Phillips Curve? Flint Brayton, John M. Roberts, and John C. Williams (cid:3) Division of Research and Statistics Federal Reserve Board Washington, D.C. 20551 September 1999 Abstract Thesimultaneous occurrence inthe second half of the 1990s of low and falling price inflationandlowunemploymentappearstobeatoddswiththepropertiesofastandard Phillipscurve. Wefindthisresultinamodelinwhichinflationdepends ontheunemployment rate, past inflation, and conventional measures of price supply shocks. We show that, in such a model, long lags of past inflation are preferred to short lags, and thatwithlonglags,theNAIRUisestimatedpreciselybutisunstableinthe1990s. Two alternative modifications to the standard Phillips curve restore stability. Onereplaces the unemployment rate with capacity utilization. Although this change leads to more accurate inflation predictions inthe recent period, the predictive ability ofthe utilizationrateisnotsuperior tothatoftheunemployment rateforthe1955to1998 sample as a whole. The second, and preferred, modification augments the standard Phillips curvetoincludean“error-correction” mechanisminvolvingthemarkupofpricesover trendunitlaborcosts. Withthemarkuprelativelyhighthroughmuchofthe1990s,this channelisestimatedtohavehelddowninflationoverthisperiod,andthusprovidesan explanation oftherecentlowinflation. Keywords: Inflation, NAIRU,Phillipscurve. (cid:3) TheauthorsacknowledgethecommentsandassistanceofPeterTulipandthecommentsofRobertGordonand otherparticipantsatthe 1999NBER SummerInstituteon MonetaryEconomics. Views presented arethoseoftheauthorsanddonotnecessarilyrepresentthoseoftheFederalReserveBoardoritsstaff.

1 Introduction and Summary The rise and fall of inflation in the United States during the 1970s and 1980s provided a testinggroundfor the Phillipscurvemodel of inflationdynamics. And,accordingto some observers(Fuhrer1995,Gordon1997),suchmodelsperformedadmirablywellintracking actual inflation, both within and out of sample. Based on this achievement, many became convinced of the usefulness of such models as tools in predicting inflation. Unfortunately, the main feature of empirical Phillips curve models, that is, that inflation rises when labor markets tighten, appears to be turned on its head during the economic expansion of the 1990s, when the unemployment rate fell below its long-run average of around 6 percent andthenslidunder5 percent,whileinflationfell. One objective of this paper is to ascertain whether the recent performance of inflation is surprising in a statistical sense within the context of a canonical Phillips curve in whichprice inflationdepends onthe unemploymentrate, past price inflation,andstandard measures of price supply shocks. To provide a graphical preview of our conclusion that a significant shift likely has taken place in such a baseline model, figure 1 shows forecast errors forourpreferred CPI equation.1 Theupperpanel ofthefigure contains one-quarterahead forecast errors based on successive reestimates of the equation over samples whose starting point is held fixed at 1955:Q1 and whose ending point advances one quarter at a time. The forecasts make use of the actual values of explanatory variables.2 While no individual error this decade lies outside of the 95 percent confidence range, inflation has consistentlyfallenshortofthemodel'spredictionsoverthepastfiveyears. Given the run of negativeprediction errors, multi-period forecast errors and their confidence bands provide a better graphical depiction of the probability of the equation's recent performance. The lower panel of the figure plots the sequence of four-quarter-ahead forecast errors. These errors are derived in a manner analogous to that used for the one- 1Theinflationseriesisthetheall-itemsCPI index,modifiedfrom1967to1983so thathomeownership costsareonarental-equivalentbasis,andadjustedsince1995toeliminateeffectsofmethodologicalchanges. Theexplanatoryvariablesconsistoftwenty-fourquarterlylagsofpastinflation;contemporaneousvaluesof ademographicallyweightedunemploymentrateandacompositemeasureofrelativefoodandenergyprice movements;anintercept;andavariableforthe1970swage-pricecontrols. Thestructureofthisequationis discussedinmoredetailbelow. 2TheuseofforecastsconditionalonactualvaluesofexplanatoryvariablesisappropriatebecausetheissuesbeingexaminedconcernthestructureofthePhillipscurveitself.Errorsinforecastingtheunemployment rate, forexample, arenotgermanebecauseconceptuallytheyareassociated with theperformanceofother equationsinaforecastingsystem. 1

Figure1 CPI Inflation: Forecast Errors (observations dated by end of forecast interval) (actual less predicted, annual rate) 95% confidence range one-quarter-ahead forecast error 2 1 0 -1 -2 four-quarter-ahead forecast error 1.5 1.0 0.5 0.0 -0.5 -1.0 -1.5 1978 1980 1982 1984 1986 1988 1990 1992 1994 1996 1998 2

step-ahead errors, except that within each four-quarter forecast interval, the forecast is a dynamic simulation in which inflation lags are set equal to simulated values. The most recent four-quarter forecasts have overpredicted inflation by as much as 1.3 percentage points,welloutsideofthe95percentconfidencerange,whichencompassesforecasterrors ofupto0.9percentage points. A tendency to overpredict inflation starting in the middle of this decade characterizes baselineequationsforallsixmeasuresofinflationwestudy. Forallbutone,themagnitude of the prediction errors is sufficient to reject the hypothesis of stability of the equation's intercept at a significance level of 10 percent or lower. In the framework of these equations,instabilityoftheinterceptcanbeinterpretedasinstabilityoftheNAIRU—thatis,the rate of unemployment consistent with stable inflation (Non-Accelerating Inflation Rate of Unemployment). Wealsofindacloseassociationbetweenthenumberoflagsofinflationincludedinthe baseline equations and whether or not evidence of significant structural change is found. Equations such as ours with long inflation lags (up to twenty-four quarters) are generally unstablewhilethosewithshort lags are not. Inessence, estimatesoftheNAIRU are much more precise in long-lag equations than in short-lag equations, and consequently the level of the unemployment rate over the past few years is well below the 95 percent NAIRU confidencerange oflong-lagequationsbut notthatofshort-lagequations. The relationship between inflation lag length and NAIRU precision has been documented by Staiger, Stock, and Watson (1997a)—hereafter, SSW—but they emphasize the wideconfidenceintervalsfortheNAIRUfoundinshort-lagequationsongroundsthatsuch lag lengths are optimal according to either standard hypothesis tests or the use of information criteria to select lag lengths. Our long-lag equations are the outcome of using an information criteria to choose simultaneously lag lengths and coefficient smoothing restrictions. Permittingsmoothingrestrictionsleads toequations that havemuchlonger lags on past inflation than is the case when lag coefficients are unrestricted, but with only a fewindependentlyestimatedparametersbecausethelagcoefficientsarerestrictedtolieon low-orderpolynomials. Weshowthattheselong-lagPhillipscurves,inadditiontoyielding muchmorepreciseestimates oftheNAIRU,havebetterout-of-sampleforecastingpropertiesthandotheshort-lagones. MonteCarloevidenceindicatesthattheprocedureofjointly searching overlag lengths and smoothingrestrictions is reasonably accurate at finding the 3

“correct” model,whetherornotitcontainssmoothedinflationcoefficients. Our baseline analysis provides support for the type of Phillips curve long favored by RobertGordonwhoformanyyearshasreportedaspecificationwithtwenty-fourquarterly lags of past inflation.3 The tendency of our baseline equations to significantly overpredict inflation since the mid-1990s, however, is an indication of structural change—perhaps a declineoftheNAIRU—orofmisspecification. Because thebaselineequationscontainthe relative rates of import price inflation and food and energy price inflation, the statistical evidence also permits the conclusion that recent declines in the relative prices of these supplyvariablesarenotsufficient toaccount fullyforthelowrate ofinflation. We investigate two possible explanations for the breakdown or near-breakdown of the standardPhillipscurve. Oneis thepossibilitythatthe capacityutilizationrate—whichhas been near its historical average during the past few years—is a better measure of macroeconomic slack than the unemployment rate, in which case the recent behavior of inflation would not be that extraordinary. From a conceptual perspective, the unemployment rate mightbepreferredbecauseofitsbroadersectoralcoverage. Butasitturnsout,movements of the utilization and unemployment rates are sufficiently similar over the past forty or so years that the goodness of fit of equations based on one is quite similar to the fit of equationsbasedontheother. Nonetheless,wefindthatPhillipscurveequationsthatincludethe unemploymentratefitsomewhatbetteroverthepostwaryearsthandothoseusingcapacity utilization. Theoutcomeisclosertoatossupinout-of-sampleforecasts,however. Alltold, the evidence does not provide strong support for the use of capacity utilizationbut neither does itsuggestthattheutilizationrateisdominatedbytheunemploymentrate. Our preferred explanation is based on an augmented Phillips curve that includes the level of the markup of price relative to trend unit labor costs as an error correction term. We find that the level of the markup in the nonfarm business sector is highlysignificant in equations for all measures of inflationexamined, with a high markup estimatedto restrain inflation and a low markup putting upward pressure on inflation. Equations that include the markup display much weaker evidence of instability. In particular, a high level of the markup in the mid-1990s is estimated to have depressed price inflation through the late 1990s. 3ThemostrecentexpositionisGordon(1998). 4

2 Baseline equations WeexaminetheperformanceofstandardPhillipscurvesforsixmeasuresofinflation, CPI Consumerpriceindex,allitems, CPIX Consumerpriceindex,excluding foodandenergy, PCE Personalconsumption expenditures chain-weight price PCEX Personal consumption expenditures, excluding food and energy, chain-weight price, GDP GDPchain-weight price, NFB Nonfarmbusiness, excluding housing, chain-weight price, over a sample period that extends most frequently from 1955:Q1 to 1998:Q4. Data availabilitylimitsthestartofestimationperiodsforCPIXandPCEXequationsto1963:Q3and 1965:Q3, respectively, after making allowance for the maximum number of inflation lags weconsider. Asimilarstrategyofestimationandtestingisappliedtoeachmeasureofinflation. First, a list of potential explanatory variables is chosen, and then a data-based testing procedure is used to select which variables and how many lags to include in each inflation equation. Finally,to examinewhether the inflationprocess has changed in somesignificant way,the coefficientsofeachestimatedequationaretestedforconstancyusingaprocedurethatdoes notrequireapriorbeliefabouttheprecisedateofthechange. 2.1 Selecting explanatory variables and lag lengths In the baseline specification, the list of potential explanatory variables consists of lags of inflation, a demographically weighted unemployment rate, and two measures of supply shocks: therates ofrelativepriceinflationofimportsanda food-energyaggregate.4 When initiallyconsidering howto determine lag lengths for explanatory variables,we noted that Gordon for many years has reported equations with twenty-four inflation lags while SSW (1997a)focustheirattentiononequationswithonlyayear'sworthofquarterlyormonthly lags. These two specifications represent very different approaches to economizing on the number of freely estimated parameters on lagged inflation. Gordon achieves parsimony 4Allequationsalsoincludeaconstantandadummyvariableforwageandpricecontrolsinthe1970s. 5

through the use of successive four-quarter averages of lags of inflation. Thus, his twentyfour lags require the estimation of only six coefficients (on lags 1-4, 5-8, etc.). SSW, on theotherhand,estimatemodelsinwhicheachlagofinflationhasaindependentcoefficient andfrequentlyuseaninformationcriteriontochoosethe“best”numberoflags. Our method of choosing lag specification—on inflation, unemployment, and the two supply variables—draws on both of these approaches. Similar to SSW, we use an information criterion to choose optimal lag lengths. And in the spirit of Gordon, we permit smoothing of the lag coefficients, but by constraining the coefficients to lie on a polynomialfunctionofthelagindex—PDLrestrictions. TheSchwartz criterionisusedtochoose theoptimallaglengthanddegreeofPDLsmoothing.5 A maximum of twenty-five lags of inflation is permitted, the unemployment rate and relativeimportprice inflationmayenter contemporaneouslyandwithuptothreelags,and relative food and energy price inflation may enter with up to four lags. The contemporaneous value of the food and energy price measure is excluded from CPIX and PCEX equations and included in the others. We constrain coefficients on lagged inflation to sum toone,arestrictionthatisconsistentwiththe(near)unitrootbehaviorofpostwarinflation. Moreover,estimationofourequationswithouttherestrictionresultsincoefficientsumson lagged inflation that in all but a few instances are statistically and economically close to one. Inflationdataareadjustedtoremoveestimatedeffectsofrecentmethodologicalchanges inmeasuringconsumerprices.6 Theunemploymentrate isafixed-weightaggregateofunemployment rates of five age and gender categories using 1993 labor force shares. Definitions of the two supply variables vary by equation. For the four consumption price equations, a core measure of import prices is used that excludes oil, computers, and semiconductors. Oil is excluded because energy prices are taken account of through the other supplyvariable; and the smallshare of “high-tech” goods inpersonal consumptionexpenditures suggests excluding computers and semiconductors. The two product prices have bigger high-tech shares than does consumption, but the shares are still well short of the 5Thelargenumberofpossiblecombinationsoflaglengthsandsmoothingrestrictionsprecludesasearch ofallcombinationsfortheonewiththesmallestSchwartzcriterion.Rather,weuseaniterativeprocedurethat alternatesbetweenfindingthebestspecificationofinflationlags, giventhelagstructureforunemployment andthesupplyvariables,andfindingthebestspecificationoflagsforunemploymentandthesupplyvariables, given the lag structure for inflation. The procedurestarts by optimizing inflation lags while including the maximumnumberoflagspermittedontheothervariableswithoutanycoefficientsmoothingrestrictions. 6Adescriptionofalldataseries,includingtheadjustmentstoinflation,isprovidedintheappendix. 6

contribution of such goods to imports. Roughly speaking, GDP has about one-tenth the computer and semiconductor share of imports. Consequently, the import price series we use in the product price equations includes one-tenth the contribution of computers and semiconductorstoimportprices. Relativeimportpriceinflationisconstructedbysubtracting from the appropriate measure of import price inflation the once-lagged value of the aggregate inflation series being explained. The second supply variable, relative food and energypriceinflation,ismeasuredasthedifferencebetweenoverallandcoreCPIinflation in the two CPI equations and as the difference between overall and core PCE inflation in theothers.7 2.2 Estimation results We present baseline Phillips curves estimated over two sample periods. The first set excludesthe1990sfromtheestimationperiodandservesasapointofreferenceinevaluating the second set, which is estimated through the end of 1998. Common to the Baseline-89 equations (table 1) are NAIRU estimates clustered around 6 percent with small standard errors that lie between 0.12 to 0.24 percentage points.8 Lag lengths on inflation are long (ranging from seventeen to twenty-five quarters) and coefficients on lagged inflation are highlysmoothed. All equationsincludetherelativeprice offoodandenergy,but onlyhalf containimportprices. We find no evidence of coefficient instability at significance levels of 10 percent or smaller in the Baseline-89 equations for data through 1989. We test for two aspects of stabilityusingtheexponentialFstatisticforstructuralchangeatanunknowndate.9 Oneis ajointtestthatallcoefficients arestable;theotherisforstabilityoftheintercept,whichin the baseline equations can be interpreted as examining the stability of the NAIRU. In the 7Anadequateaccountoftheshort-rundynamicsofNFBinflationalsorequirestheinclusionofthecontemporaneous value of relative farm sector price inflation to capture the tendency of NFB prices to move initiallyin theoppositedirectionof achangeinthepriceoffarmsector output. TheNFBpriceis a valueadded measure whose construction entails the subtraction of farm prices, and so the negative relationship NFBandfarmsectorpricesmayrepresenteithermeasurementerrorinfarmpricesoratendencyforthecost offarmsectorinputstonotbeimmediatelypassedthroughtothepriceoffinishedfoodproducts. 8We measurestandarderrorsof the NAIRU as one-halfthewidth of the70 percentconfidenceinterval computedbytheGaussianmethodadvocatedbySSW(1997a). 9TheexponentialFstatisticequals l o g R e x p ( :5 F ( s ) ) d s ,whereFisthevalueofthestandardChowtest forcoefficientstability attimes. Andrews, Lee, andPloberger(1996)concludethatthistest generallyhas propertiesthataresuperiortothoseofothertestsforstructuralchangeatan unknowndate. Criticalvalues fortheexponentialFstatisticarereportedinAndrewsandPloberger(1994). 7

Table1: Baseline-89Equations CPI PCE CPIX PCEX GDP NFB EquationSpecification:a inflationlags p d l d e g r e e 25 2 24 2 24 2 24 2 19 2 17 2 unemployment rate x x x x x x foodandenergy price x x x x x x importprice x x x NAIRU 6.05 6.04 6.19 6.30 5.94 5.90 (std. err.b) (.12) (.15) (.22) (.24) (.16) (.19) aCoefficientestimatesandregressionstatisticsarepresentedintheappendix. bOne-halfofthe70percentconfidencerange. absence ofa prioraboutthetypeof structuralchange that mighthaveoccurred, testingthe stabilityofallcoefficientssimultaneouslyisappropriate. Ifwebelievethatanyinstabilityis confinedtotheconstantterm,however,thejointtesthaslowpowerandthetestofintercept stabilityispreferred. From the point of view of 1989, an analyst would have been well justified in claiming that thePhillipscurvewas a stablerelationship,witha constantNAIRU.We nowconsider whethertheexperienceofthe1990swouldleavetheanalystequallysanguine. Asshownin the toppart of table 2, the longer samplegenerally has onlyminoreffects on the preferred specifications. Inflation lag lengths become shorter in three instances, but the change is substantialonlyinthecase ofPCEX forwhichthelaglengthfallsfrom twenty-fourtoten quarters. Estimates of the NAIRU are slightly lower, but remain close to 6 percent, and have standard errors that, except for the PCEX equation, are little changed from those in theshortersample. Importprices appear infourofsixequations,ratherthanthree. As shown earlier, out-of-sample forecast errors for the baseline CPI equation indicate a persistent overprediction of the rate of inflation starting in 1994. We now formally test the stability of this equation over a time span that includes the period of surprisingly low inflation. Althoughmanyhave come tobelievethat factors suchas increased international competitionorlowerwagedemandsarisingfromheightenedjobinsecurityhaverestrained inflation recently, our view is that these hypotheses have been motivated primarily by the ex post observation that inflation has been low relative to predictions.10 Moreover, the 10Inarecentpaper,KatzandKreuger(1999)donotfindanyevidencethatsupportstheworkerinsecurity 8

Table2: Baseline-98Equations CPI PCE CPIX PCEX GDP NFB EquationSpecification:a inflationlags p d l d e g r e e 24 2 24 2 23 2 10 2 15 2 17 2 unemployment rate x x x x x x foodandenergy price x x x x x x importprice x x x x NAIRU 5.98 5.88 5.99 5.86 5.88 5.84 (std. err.b) (.12) (.15) (.18) (.30) (.17) (.19) Stabilitytests:c allcoefficients ** *** - - ** intercept only *** *** ** - ** * NAIRUshift:d mostlikelydate 94.4 95.1 93.3 92.2 95.2 97.3 pre-shift NAIRU 6.09 6.06 6.21 6.17 6.01 5.93 post-shift NAIRU 4.83 4.04 4.85 4.72 4.47 3.20 aCoefficientestimatesandregressionstatisticsarepresentedintheappendix. bOne-halfofthe70percentconfidencerange. cSignificancelevel: > .10(-),.10(*),.05(**),or.01(***). dFromtheequationwhosedatingofan interceptshiftyieldstheChowstatisticwith thelowestp-value. ForGDPandNFB,theentriescorrespondtothelowestp-valueafterthe1950s. 9

conjectures do not provide any independent information about the likely date of a shift in the inflation process. Thus, in the absence of a specific prior, we assess the stability of the CPI equation at all dates in the full estimation period, which runs from 1955:Q1 to 1998:Q4. For the CPI equation, the test for stability of all coefficients rejects constancy at the 5 percent level, as shown in the bottom panel of table 2. An even stronger case for a shift in the Phillips curve is found when only the intercept is allowed to change. Here, the test indicates a probability of no shift that is less than 1 percent. Based on the shift date that provides the best fit (and for which the Chow statistic attains its lowest p-value), the shift in the intercept most likely occurred at 1994:Q4, with the NAIRU estimated to fall from 6.1percent upuntil1994to4.8percent thereafter. The other baseline inflation equations also tend to show instability of the intercept, with the probability of no structural change being less than 10 percent for NFB, less than 5 percent for CPIX and GDP, and less than 1 percent for PCE. In these equations, the most likelydate for an intercept shift ranges from late 1992 tomid1997, withthe NAIRU estimatedtofallfromabithigherthan6percenttoaslowas3.2percentinthecaseofNFB toas highas 4.9percent in thecase of CPIX. Onlythe PCEX equationshowsnoevidence ofashiftat asignificancelevelof10percent. 2.3 Other estimates of time variation of the NAIRU ThebaselineinflationequationstendtobestructurallyunstableandindicatethattheNAIRU has declined in the 1990s. The assumption used to pin down the timing of the NAIRU shift—thatitoccurredinasinglequarter—maybeunrealistic,however. As acheckonour results,weestimatevariantsofthebaselineequationsusingtwootherstatisticalmodelsof time variation in the NAIRU that have appeared in the recent literature on Phillips curves. Gordon(1997,1998)andSSW(1997a)usetheKalmanfiltertoestimateinflationequations inwhichtheinterceptfollowsarandomwalk,andSSW(1997a,1997b)allowtheintercept tomovealongacubicspline. Figure2comparesestimatesoftheNAIRUbasedontheKalmanfilterandcubicspline with the estimates derived from intercept shifts presented above. The Kalman filter series hypothesis,buttheydoconcludethattheNAIRUhasfallensincethemid-1980sbecauseoftherisingfraction ofthepopulationinprisonandtheincreasingsizeofthetemporaryhelpindustry. 10

Figure2 Time-Varying NAIRUs CPI PCE 7 7 6 6 5 5 intercept shift 4 cubic spline 4 Kalman filter 3 3 1960 1970 1980 1990 2000 1960 1970 1980 1990 2000 CPIX PCEX 7 7 6 6 5 5 4 4 3 3 1960 1970 1980 1990 2000 1960 1970 1980 1990 2000 GDP NFB 7 7 6 6 5 5 4 4 3 3 1960 1970 1980 1990 2000 1960 1970 1980 1990 2000 11

Figure3 Effect of Changing Demographics on the NAIRU (percentage points) 0.8 0.7 0.6 0.5 0.4 0.3 0.2 0.1 0.0 -0.1 -0.2 1955 1960 1965 1970 1975 1980 1985 1990 1995 usethemedianunbiasedestimateofthevarianceoftherandomwalkcomponentoftheinterceptofthePhillipscurve.11 Thecubicsplineestimatesassumetwo“knot”pointswhose location divides the estimation period into three segments of equal size. The unemployment rate entering the estimationequations is demographically weighted as are the values of the NAIRU plotted in figure 2. The Kalman filter and cubic spline thus allowfor variationin theNAIRU beyondthat predicted bychanging demographics. (The contributionof changingdemographytotheNAIRUis showninfigure3.) AccordingtotheKalmanfilterestimates,theNAIRUstartstodeclineinthelate1980s andfallsgraduallythroughoutthe1990s. Therateofdeclinediminishesinthemostrecent year or so, leavingtheNAIRU at theend of 1998inthe range of 4.5to5.4 percent, values that in all cases are higher than those estimated by intercept shifts. In contrast, the spline estimatesfallmorerapidlythisdecadeandendatvaluesthatinmostcasesarelessthanthe intercept-shiftvalues. Thesedifferences notwithstanding,allapproaches pointto adecline 11Stock and Watson (1998) derives the median unbiased estimator and provides a mapping for several testsofcoefficientstabilityfromthevalueofeachstatistictothevarianceoftherandomwalkprocessinthe Kalmanfilter. OurvarianceestimatesarebasedonthevaluesoftheexponentialFstatisticforconstancyof theintercept. 12

intheNAIRUinthe1990sthatinalmosteverycaseislargerinmagnitudethanmovements intheNAIRUat anyearliertimeintheperiodunderconsideration. 2.4 Import prices A common belief is that low import prices have been a substantial restraint on domestic inflationin the late 1990s. Over the four years from 1995to 1998, the measures of import priceinflationweusehaveincreasedbetween2and3percentage pointsmoreslowlyat an annual rate, on average,than havetheconsumptionandproduct prices underexamination. Given the estimated coefficients on the relative rate of increase of import prices (between .04 and .12), these declines reduce the average (static) inflation prediction only about a tenthofapercentagepointinthePCE,PCEX,andGDPequations,andabouttwotenthsof a percentage point in the NFB equation. However, because these effects are small relative to the mean residuals of these equations over the 1995-1998 period (from 0.4 to 0.7 percentage points), we conclude that import prices have made a modest, but not substantial, contributiontoholdingdowndomesticinflation.12 An alternative analysis of the contribution of import prices focuses not only on the decliningrelativepriceofimportsbutalsoonthepossibilityofanincreaseinthesensitivity ofdomesticpricestothepriceofimports. And,indeed,statisticaltestsrevealthatconstancy of import price coefficients is rejected at the 1 percent level for PCE, at the 5 percent level for GDP, and at the 10 percent level for NFB. Two observations suggest the strong probabilitythat these results are spurious,however. One is that it is difficult to distinguish inthemid-1990sashiftintheinterceptfromashiftintheimportpricecoefficients,because of a downward shift in the mean of the relative rate of import price inflation that occurred aroundthattime. Conditionalontherebeinganinterceptshift,evidenceforashiftinimport pricecoefficientssignificantlyweakens,andsimilarly,conditionalonashiftinimportprice coefficients,evidenceforashiftininterceptssignificantlyweakens. 12Asnotedearlier,computersandsemiconductorsarewhollyexcludedintheimportpricemeasureused inconsumptionpriceequationsandlargelyexcludedinthemeasureenteringproductpriceequations. Given rapid declines in the prices of computers and semiconductors and their relatively large share in imports, import prices inclusive of these goods fall about 3 percentage points more rapidly at an annual rate, on average, overthe 1995-1998periodthan do measures thatexcludethem. If the modelselection procedure isrunwiththebroadermeasureofimportpricesinthesetofexplanatoryvariables,wefindthat,compared withtheBaseline-98results,importpricesareincludedinthesamefourequations,butthatinthoseequations recenterrorsareslightlysmallerandthestatisticalsignificanceofaninterceptshiftismodestlyreduced. 13

The second observation calling into question a primary role of a shift in import price coefficients is that, when such a shift is allowed, the coefficients increase to implausibly large values after the shift date. In the equations with significant shifts, import price coefficients rise from 0.03 to 0.31 (PCE), 0.01 to 0.20 (GDP), and 0.10 to 0.48 (NFB). Of these, only the PCE contains prices of imported goods directly, and its post-shift import pricecoefficientisthreetimeslargerthananestimateoftheimportshare(.09)basedonthe 1998 ratio of imports excluding oil, computers, and semiconductors to GDP. While some additional influence of import prices is likely on the price of that part of domestic productionwhichcompetes withgoods from abroad, such an effect seems unlikelytoexplain the large magnitude of the PCE coefficient. A similar argument holds for the import price coefficients inthe GDP and NFB equations,in whichthe estimatedeffect of import prices mustbeentirelyfromimportcompetition. 3 Inflation lag length and smoothing restrictions Anaturalquestiontoaskiswhetherourconclusionsaboutthestabilityofbaselineinflation equations are sensitive to the use of long inflation lags and coefficient smoothing restrictions. Evidence about NAIRU uncertainty suggests that this may be the case. Standard errors of NAIRU estimates in the Baseline-98 equations, which range from 0.12 to 0.24 percentage points, are much smaller than those others have reported using equations with shorter lags on inflation. SSW (1997a,p. 196) statethat “a typical estimateof the NAIRU in 1990 is 6.2 percent, with a 95 percent confidence interval for the NAIRU in 1990 being 5.1percentto7.7percent.” TheirresultimpliesastandarderrorfortheNAIRUthatisfour timeslargerthanouraverage estimate. 3.1 Estimates without smoothing restrictions When our specification selection procedure is modified so that coefficient smoothing restrictions are not permitted (table 3), we estimate equations that are similar to those of SSW in that they have relatively short inflation lag lengths—from four to seven quarters. Point estimates ofthe NAIRU are littlechanged, but the standarderrors are about twice as large as those in the Baseline-98 set of equations. The less precise NAIRU estimates are associatedwiththeresultthatthestabilityofinterceptscannotberejectedatthe10percent 14

Table3: NoSmoothingRestrictions CPI PCE CPIX PCEX GDP NFB EquationSpecification:a inflationlags p d l d e g r e e 4 4 5 5 4 7 unemployment rate x x x x x x foodandenergy price x x x x x importprice x x x x x x NAIRU 6.04 5.95 5.96 5.80 5.92 5.86 (std. err.b) (.34) (.38) (.27) (.48) (.31) (.26) Stabilitytests:c allcoefficients - - - - - ** intercept only - - - - - ** aCoefficientestimatesandregressionstatisticsarepresentedintheappendix. bOne-halfofthe70percentconfidencerange. cSignificancelevel: > .10(-),.10(*),.05(**),or.01(***). significance level, except for NFB inflation for which a shift in the NAIRU appears likely, butoccurringinthelate1950s. Thepaucityofevidenceforaninterceptshiftintheseequations is consistent with Stock and Watson (1999), who find that Phillips curves with up to eleven monthly lags on inflation and unemployment show little sign of instability jointly amongtheinterceptandunemploymentcoefficients. We use CPI equations to illustrate in more detail the strong negative relationship betweenthe laglengthoninflationandthe standarderror oftheNAIRU. Forthis measureof inflation,thestandarderroroftheNAIRUfallsfrom0.34percentagepointsintheequation without smoothing restrictions and four lags of inflation to 0.12 percentage points in the Baseline-98equationwithtwenty-fourlags ofinflationwhosecoefficients are restrictedto lie on a second degree polynomial. Figure 4 demonstrates that the relationship between themaximuminflationlagandthestandarderroroftheNAIRUisnearlymonotonicasthe maximumlagvariesbetweenthreeandtwenty-seven,withthestandarderrorfallingsteeply as thelag lengthinitiallyincreases andthendecliningverygraduallybeyondthirteenlags. ThestandarderroroftheNAIRUat twenty-fourlags,wheretheSchwartzcriterionisminimized, is not that much less than the standard error at thirteen lags. A similar pattern is found for the other measures of inflation: The precision of the NAIRU increases substantially as the inflation lag length rises from short to moderate values (8-12 lags) and then 15

Figure4 Precision of NAIRU Estimates (CPI) 0.6 Standard Error of NAIRU (left scale) Negative of Schwartz Criterion (right scale) 0.45 0.5 0.4 0.3 0.30 0.2 0.1 0.0 0.15 4 8 12 16 20 24 Maximum Lag of D ependent Variable Note: Standard Error of NAIRU computed as one-half of 70% confidence interval tendstoflattenoutas additionallags ofpast inflationareincluded. 3.2 Out-of-sample forecasts Giventhestarkcontrast inresultsdependingontheinflationlaglengthandwhether ornot smoothingrestrictionsareimposed,wenowcomparetheaccuracyofthelong-lagequations and the short-lag specifications in out-of-sample forecasts. Three variants of the selection procedure are used in this analysis. The first (max = 25), which allows PDL smoothing restrictions and permits up to twenty-five inflation lags, is the approach used to derive the Baseline-89 and Baseline-98 sets of equations, except that now the selection procedure is run over a sequence of estimation periods whose terminal date advances one quarter at a time. The second alternativedoes not permit smoothing(no-pdl). The last case (max = 12) shortensthefeasibleinflationlaglengthtotwelvequarterswhilestillpermittingcoefficient smoothing, an intermediate case which is motivated by the frequent use of twelve lags of inflationinestimatedPhillipscurves(e.g.,Fuhrer(1995),Tootel(1994)). The first out-of-sample forecast interval starts in 1975:Q1 based on models selected andestimatedthrough1974:Q4,except for PCEXwhoseinitialforecast startsat 1977:Q1, 16

Table4: Out-of-SampleForecast RMSEs (percent) CPI PCE CPIX PCEX GDP NFB Four-Quarters-Ahead maxlag=25 .60 .72 1.25 .93 .73 1.02 maxlag=12 .77 .74 .76 .76 .76 1.04 no-pdl .85 .82 1.04 .76 .95 1.53 Eight-Quarters-Ahead maxlag=25 1.23 1.45 2.63 2.04 1.42 1.86 maxlag=12 1.82 1.51 1.60 1.48 1.33 1.79 no-pdl 2.14 1.78 2.77 1.68 2.24 3.42 giventhe shorter historical timespan overwhichdata on this measure of inflationis available. For all inflation measures, the last forecast period ends at 1998:Q4. The results in table 4, which reports root mean squared percentage forecast errors for the price level at horizonsoffourandeight quarters,confirm theconclusionbasedonin-sampleresults that long-lag inflation equations tend to be superior to short-lag ones. In nine of twelve cases, ourmodelselectionprocedure(max=25)yieldsprice-levelforecasts thathavesmallerroot meansquarederrorsthandoestheprocedurenotpermittingcoefficientsmoothing(no-pdl). Insomecases,however,theintermediateprocedure(max=12),inwhichsmoothingrestrictions are permissible but inflation lag lengths are constrained to be no more than twelve quarters,yieldsmoreaccurate forecasts thandoes thelonger-lagvariant. 3.3 Monte Carlo analysis Inthissection,wereportfourexperimentswithmodelsofCPIinflationdesignedtoaddress the question of whether model-selection criteria can discriminate between long-lag and short-lag models of the Phillips curve in samples such as the one we are examining. In thefirsttwoexperiments,werepeatedlygenerateartificialdataassumingthatourlong-lag, low-order model for own-lags in the Phillips curve is the correct model (table 2, column 1) and then run two different model-selection procedures, one of which allows for the possibility of polynomial smoothing restrictions, and the other of which does not. In the next pair of experiments, we generate sets of artificial data assuming the true model is such that inflation lags are short and unrestricted (table 3, column1). We then run the two differentmodel-selectionexercisesoneach setofartificial data. 17

Figure5 True Model: n = 24 (PDL) Model Selection Rule: PDL 0.2 0.15 0.1 0.05 0.0 4 8 12 16 20 24 28 Maximum Inflation Lag (n) ycneuqerF Model Selection Rules Results from the Monte Carlo Exercise True Model: n = 24 (PDL) Model Selection Rule: No PDL 0.6 0.5 0.4 0.3 0.2 0.1 0.0 1 3 5 7 9 11 Maximum Inflation Lag (n) ycneuqerF True Model: n = 4 (No PDL) Model Selection Rule: PDL 0.2 0.15 0.1 0.05 0.0 1 3 5 7 9 11 13 Maximum Inflation Lag (n) ycneuqerF 0.4 0.3 0.2 0.1 0.0 1 3 5 7 9 Maximum Inflation Lag (n) ycneuqerF True Model: n = 4 (No PDL) Model Selection Rule: No PDL 18

We usea six-lagVARtogenerate simulateddatafor theotherendogenous variablesin themodel,namely,theunemploymentrate;therelativefood-and-energyprice;andrelative importprices. Weassumethattheunemploymentrateisunaffectedinthecurrentperiodby anyoftheothervariablesinthemodel;thatrelativefood-and-energypricesareaffectedby theunemploymentratebutnotbyanyoftheothervariables;andthatrelativeimportprices are affectedbyunemploymentandfood-and-energyprices butnotaggregateinflation. Basedononethousanddraws,wefindthatwhenthemodelusedtogeneratetheartificial data is the long-lags version of the Phillips curve, the specification-search procedure that allows for smoothing restrictions generally chooses long lags (figure 5, upper left panel), and that the search procedure which does not allow for smoothing restrictions selects a short-lag model (upper right panel). In particular, the median lag length when smoothing restrictions are allowed is twenty-three, compared to the true lag length of twenty-four (withthecoefficientsconstrainedtolieonasecond-orderpolynomial). In75percentofthe draws,thechosenlaglengthistwentyormore. Inonly5percentofthedrawsisthechosen laglengthfourorless. By contrast,when onlyunconstrainedlags are allowed,themedian lag length chosen is three, and in 99 percent of cases the chosen lag length is ten or less. When the true model involves low order and long lags, a model-specification procedure thatdoes notallowforthispossibilitywillchoosea specificationwithfar toofewlags. As noted previously, when we run the model-specification search for a model for the CPI allowing only for unconstrained own-lag specifications, the procedure chooses four lags. Usingthis specification to generate artificial data, the mediannumber of lags chosen when the model search procedure is limited to consider only unconstrained lags is three (lower right panel), and in 95 percent of the cases, the number of lags is five or fewer. When reduced-order polynomials are allowed, the median number of lags selected is six whiletheninety-fifthpercentileofthedistributionisfourteenlags(lowerleft panel). Onthewhole,themore-generalmodel-selectionprocedurethatallowslow-orderpolynomials out-performs the procedure that permits only unrestricted lags. The median lag estimated by the first method is close to the inflation lag length used to generate the artificial data in all experiments, while the median lag estimated by the second method is severelybiaseddownwhenthetruemodelhas longlags. 19

Table5: CapacityUtilizationEquations CPI PCE CPIX PCEX GDP NFB EquationSpecification:a inflationlags p d l d e g r e e 24 2 10 4 9 4 24 2 19 2 17 2 capacityutilization x x x x x x foodandenergyprice x x x x x x importprice x x x x x x NAICU 81.31 81.62 81.70 81.92 81.72 81.79 (std. err.b) (.43) (.62) (.66) (.76) (.46) (.54) Stabilitytests:c allcoefficients *** - - - * interceptonly * - - - * aCoefficientestimatesandregressionstatisticsarepresentedintheappendix. bOne-halfofthe70percentconfidencerange. cSignificancelevel: > .10(-),.10(*),.05(**),or.01(***). 3.4 Summary of baseline equations Viewingthe completeset of baseline equations,out-of-sampleforecasts, and Monte Carlo analysis, the evidence favors the long-lag inflation equations in which the NAIRU is estimated precisely (but appears to have been unstable recently) over the short-lag equations withwideconfidence bands andnoevidenceof instability. We next turntothequestionof whether there are economic explanations other than a decline in the NAIRU for the recent lowrates ofinflation. 4 Capacity Utilization Much has been made of late of the divergent signals about resource utilization coming from the labor and production markets in the late 1990s. Although utilization rates in the two typically move together fairly closely, labor utilization has been higher relative to its historicalaveragethanhascapacityusage. Thus,therateofcapacityutilizationseemsmore consistent with the recent inflation picture than does the unemployment rate. We use the Schwartz criterion to develop a set of equations that include capacity utilization in place of the unemployment rate. As reported in table 5, only the CPI and GDP equations show 20

Table6: UnemploymentRate(U)vs CapacityUtilization(CU): InSample t-statistic EquationsbasedonU Equations basedonCU U CU U CU CPI 5.0 0.9 4.3 1.1 PCE 3.7 0.6 1.8 1.4 CPIX 3.1 0.7 2.2 0.9 PCEX 1.6 1.1 1.6 1.3 GDP 2.4 1.8 2.3 2.1 NFB 1.3 2.4 1.3 2.4 significant evidence of coefficient instability when capacity utilization is the measure of demand pressure. And, the instability in these instances is associated with the early part of the estimation period, not the 1990s. The conclusion that inflation equations are more stablewhentheycontaincapacityutilizationthanwhentheycontaintheunemploymentrate coincideswithestimatespresentedbyGordon(1998)showingmuchless movementinthe 1990s in a time-varying NAICU (Non-Accelerating Inflation rate of Capacity Utilization) thaninatime-varyingNAIRU. Although capacity utilization has an edge in explaining recent inflation, that is not the case for the whole estimation period. We reestimated the unemployment rate equations with capacity utilization added as an explanatory variable while also reestimating the capacity utilization equations with the unemployment rate added. In terms of statistical significance, the unemployment rate dominates capacity utilization in all but the NFB equations—irrespective of whether the specification was initially tuned to contain the unemploymentrateorcapacityutilization(table6). A further comparison of unemployment and capacity utilization makes use of out-ofsample forecast errors (table 7). Based on forecasts of equations chosen by our preferred model selection procedure (max=25), the equations with the unemployment rate are more accurate at forecasting three measures of inflation, while equations with capacity utilization are more accurate at forecasting the other three inflation series. The outcome of this experimentisadraw. All told, while conventional statistical testing suggests that the unemployment rate dominates capacity utilization in terms of in-sample fit, out-of-sample forecasting exer- 21

Table7: UnemploymentRate (U)vsCapacityUtilization(CU): OutofSampleRMSEs CPI PCE CPIX PCEX GDP NFB Four-Quarters-Ahead U(maxlag=25) .60 .72 1.25 .93 .73 1.02 CU(maxlag=25) .65 .77 .94 .77 .84 1.00 Eight-Quarters-Ahead U(maxlag=25) 1.23 1.45 2.63 2.04 1.42 1.86 CU(maxlag=25) 1.37 1.69 1.79 1.54 1.77 1.83 cises suggestthat neithermeasure is superior. This result is perhaps less surprisingonce it isrecalledthatbyconstructiontheout-of-sampleanalysisputsgreaterweightontherecent experience. 5 The Markup Thus far, the Phillips curves we have examined have clearly been reduced-form relationships. A more structural perspective might view prices as a function of costs. To pursue this approach, we add the the markup of prices in the nonfarm business sector over trend unitlaborcosts—wherethelatteriscompensationperhourfromtheBLSProductivityand Cost release, relativetoameasure ofthetrend inproductivitythatallows asinglebreakin its slopein1973—as a potential determinantof price inflation. As shownbythe solidline infigure6,themarkupovertrendunitlaborcostshas nodiscernabletrendhistoricallyand has been relatively high over much of the past five years—the period of “unusually” low inflation.13 Our analysis starts with the specification selection procedure used earlier, but with the set of potential explanatory variables augmented to include the first lag of the log of the markup over trend unit labor costs—which we will refer to as the “trend markup.” In an earlier stage of our research, the lagged level as well as several lagged growth rates of the trend markup were part of the set of potential regressors, but the growth rates were never selected for inclusion in the final equations. Note that the nonfarm trend markup is used in equations for all six measures of inflation. One reason for not having markup variables 13IftheEmploymentCostIndexmeasureofhourlycompensation,whichbeginsin 1980,issplicedwith theProductivityandCostseries,asimilarpatternisfound. Inaddition,thestatisticalconclusionspresented belowareunaffectedifthesplicedseriesisused. 22

Figure6 Price Markup Over Trend Unit Labor Costs (deviation from mean, percent) 4 3 2 1 0 -1 -2 -3 1955 1960 1965 1970 1975 1980 1985 1990 1995 thatarespecifictoeachinflationseriesisthedifficultlyinconstructingconsistentlydefined markups for consumption and GDP. Even without this practical consideration, however, the fact that the nonfarm markup is a broad measure of labor cost pressure on the price of domestic production makes it a plausible determinant of each inflation series. The unemploymentrate isthemeasureofslackincludedintheset ofexplanatoryvariables. Accordingtotheselectioncriterion,thelaggedlevelofthetrendmarkupappears inall inflation equations, as shown in table 8. This variable has the implication that, when the price level is high relative to trend unit labor costs, downward pressure is exerted on all the measures of inflation investigated. Given the relatively high level of the markup over muchofthisdecade, residualsofall equationscontainingthelaborcost measureare small until very recently, and only the PCEX equation shows significant evidence of intercept instability. However, the most likely date for a shift of the intercept in this instance is during1978,notinthe1990s. Because the compensation component of the markup varies with the unemployment 23

Table8: MarkupEquations CPI PCE CPIX PCEX GDP NFB EquationSpecification:a inflationlags p d l d e g r e e 24 3 24 2 23 2 24 2 15 2 17 2 unemployment rate x x x x x x foodandenergy price x x x x x x importprice x x x trendmarkup x x x x x x NAIRUb 5.97 5.88 6.05 6.01 5.88 5.84 (std. err.c) (.10) (.13) (.16) (.18) (.15) (.18) Stabilitytests:d allcoefficients - - - - - intercept only - - - * - aCoefficientestimatesandregressionstatisticsarepresentedintheappendix. bMeasuredassumingthemarkupisatitssamplemean. cOne-halfofthe70percentconfidencerange. dSignificancelevel: > .10(-),.10(*),.05(**),or.01(***). rate, the NAIRU is not uniquely defined by the structure of equations for price inflation when they contain the markup. Rather, such equations onlypin downa linear relationship betweentheNAIRUand theequilibriumvalueof themarkup. Nonetheless,for illustrative purposes, we report estimates of the NAIRU based on setting the markup to its sample mean. Asis shownintable8,theseestimatesare closeto6percent andare verysimilarto theNAIRUvaluesintheBaseline-98equations. The improvement in coefficient stability that characterizes the markup equations is highlighted in figure 7, which contrasts Kalman filter estimates of time-varying NAIRUs for the markup specifications with those shown earlier for the Baseline-98 equations.14 Indeed, for the CPIX markup equation, the median unbiased estimate of the variance of innovationsto the intercept is zero and its time-varyingNAIRU is constant. And NAIRUs in the CPI, PCE, GDP and NFB equations with the markup fall only 0.12 to 0.21 percentagepointsfrom 1989to1998. OnlythePCEXequationsexhibitsimilarmovementsofthe NAIRUovertimeinthemarkupandBaseline-98specifications. 14Thecharacteristicsoffigure7wouldbeunchangedifestimatesoftime-varyinginterceptswereshown ratherthantime-varyingNAIRUs. 24

Figure7 Time-Varying NAIRUs CPI PCE 7 7 6 6 5 5 Kalman filter, Baseline 98 4 Kalman filter, Markup 4 3 3 1960 1970 1980 1990 2000 1960 1970 1980 1990 2000 CPIX PCEX 7 7 6 6 5 5 4 4 3 3 1960 1970 1980 1990 2000 1960 1970 1980 1990 2000 GDP NFB 7 7 6 6 5 5 4 4 3 3 1960 1970 1980 1990 2000 1960 1970 1980 1990 2000 25

Figure8 NFB Markup Equation: Residuals (actual less predicted, four-quarter average) 1.5 1.0 0.5 0.0 -0.5 -1.0 1960 1965 1970 1975 1980 1985 1990 1995 The case for the markup is bolstered by the finding that our results are not dependent on having the decade of the 1990s in the sample: The selection procedure includes the markup variable in all inflation equations when they are estimated through 1989. Hence, ourhypothetical1989analystwouldhaveincludedthemarkupas well. The markup story is not without caveats, however. First, the results are sensitive to theparticularmeasureofproductivityenteringthemarkupcalculation. Althoughourmain results go through when the trend is estimated with the HP filter, the markup variable is generallyinsignificantwhenactualproductivityisused. Also,wedonothaveaclearstory for the rise of the markup in the early 1990s. The residuals of the markup equation for NFB inflation are generally positiveduring this period (figure 8), suggesting that some of theriseinthemarkupmayhavebeena resultof unexplainedprice increases. Lowrates of increase of hourly compensationin the first half of this decade may also have contributed, but an analysis of compensation developments is beyond the scope of this paper. Finally, as shown in figure 6, the markup has recently fallen back to a “normal” level and thus has not been much of a restraint on predicted inflation over the past year or so—a period in which the markup equations overpredict inflation by a substantial (but not unprecedented) 26

amount(figure8). Becausetheoverpredictionepisodeisasyetfairlyshort,itistoosoonto saywhethertheerrors are transitoryorevidenceofsomeotherfactorrestraininginflation. One possible restraint on recent inflation not captured in our markup equations would be a pickup in the trend rate of growth of labor productivity. If this were the case, the level of the trend markup might be higher than our measure, reducing the predicted rate of inflation. Much speculation has arisen concerning possible effects of booming investment in computers and related equipment on labor productivity, but as yet no consensus has emerged. And in one study pointing to an increase in the trend rate of growth of labor productivity in the nonfarm sector, the level of the trend is only slightly above our measure—based on the single kink at 1973—at the end of 1998, and thus would not have substantiallydifferentimplicationsforinflation.15 6 Conclusions ThebaselineversionofthePhillipscurvecannotadequatelyexplainwhyinflationhasbeen solowinthesecondhalf of the1990s. Whileimportprices, whichare part ofthe baseline specification,are estimatedinmostequationstohaverestrainedinflationoverthepastfew years,afullattributionofinflationdevelopmentstothesepriceswouldrequireamany-fold increase intheircoefficients. Lookingbeyondthebaselineframework,capacityutilization predictsinflationintherecentperiodmoreaccuratelythandoestheunemploymentrate,but the reverse tends to holdfor the estimationsample as a wholeon an in-samplebasis. Outof-sampleforecastaccuracyprovidesnobasisfordiscriminatingbetweenthetwomeasures ofutilization. We find that evidence favors a view in which price developments are, in part, determined by an “error-correction” mechanism involvingthe markup of prices over trend unit labor costs. A high markup puts downward pressure on price inflation and the reverse obtainswhenthemarkupislow. Withmarkupsrelativelyhighthroughmuchofthe1990s,the error-correction channel isestimatedtohavehelddowninflationovermuchofthis period. Thereasonforthepastriseinthemarkupissomewhatunclear. However,markuplevelsat theendof1998areclosetotheirhistoricalaveragesandthusshouldnotrestraininflationin the near future, unless, for somereason, firms are under pressure to reduce margins below 15Gordon (1999). We adjust Gordon's estimate of trend productivity growth to be consistent with our assumptionabouttheeffectofchangesinpricemeasurementmethodsonlaborproductivity. 27

historicalnormsortrendlaborproductivityis risingfasterthanoursimplecalculation. Additionalsupportforthemarkupstorycomesfromtheobservationthatnotonlydoes it have a long history as a theoretical model of price determination but also that we find it empiricallyto be a stable part of inflation dynamics overtime. The markup is an explanationofwhathashappenedtoinflationthisdecadethatcouldhavebeenidentifiedaspartof theinflationprocesspriortothisdecade. 28

References Andrews,Donald,InpyoLee,andWernerPloberger(1996)OptimalChangepointTests forNormalLinearRegression. JournalofEconometrics,70,9-38. Andrews, Donald, and Werner Ploberger (1994) Optimal Tests When a Nuisance Parameteris Present OnlyUndertheAlternative. Econometrica,62,1383-1414. Council of Economic Advisors (1999)Economic Report of the President. Washington D.C.: UnitedStates GovernmentPrintingOffice. Fuhrer,JeffreyC.(1995)ThePhillipsCurveisAliveandWell. NewEnglandEconomic ReviewoftheFederalReserveBankofBoston,March/April,41-56. Gordon,RobertJ.(1997)TheTime-VaryingNAIRUanditsImplicationsforEconomic Policy. JournalofEconomicPerspectives,11,11-32. Gordon,RobertJ.(1998)FoundationsoftheGoldilocksEconomy: SupplyShocksand theTime-VaryingNAIRU. BrookingsPapersonEconomicActivity,297-333. Gordon, Robert J. (1999) Has the 'New Economy' Rendered the Productivity SlowdownObsolete? NorthwesternUniversity,mimeo. Katz, Lawrence F., andAlanB. Krueger(1999) TheHigh-PressureU.S. LaborMarket ofthe1990s. BrookingsPapers onEconomicActivity,forthcoming. McIntire, Robert J. (1996) Revisions in Household Survey Data Effective February 1996. EmploymentandEarnings,March,8-16. Polivka, Anne E., and Stephen M. Miller (1995) The CPS After the Redesign: RefocusingtheEconomicLens. Bureau ofLaborStatistics,Mimeo,March. 29

Staiger,Douglas,JamesH.Stock,andMarkW.Watson(1997a)HowPreciseAreEstimatesoftheNaturalRateofUnemployment? ReducingInflation: MotivationandStrategy, ed. ChristinaD.RomerandDavidH.Romer. UniversityofChicagoPress. Staiger, Douglas, James H. Stock, and Mark W. Watson (1997b) The NAIRU, UnemploymentandMonetaryPolicyJournalofEconomicPerspectives,11,33-49. Stock, James H., and Mark W. Watson (1998) Median Unbiased Estimation of Coefficient Variance in a Time-Varying Parameter Model. Journal of the American Statistical Association,93,349-58. Stock, James H., and Mark W. Watson (1999) Forecasting Inflation. NBER working paper7023. Tootell, Geoffrey (1994) Restructuring, the NAIRU, and the Phillips Curve. New EnglandEconomicReviewoftheFederalReserve Bankof Boston,September/October,31-44. 30

Appendix Tables TableA1 Baseline-89Equations CPI PCE CPIX PCEX GDP NFB Estimatedcoefficients:a inflationlagsb 1.00 2 1 2; 5 1.00 2 1 2; 4 1.00 2 1 2; 4 1.00 2 1 2; 4 1.00 2 1 1; 9 1.00 2 1 1; 7 (0.5) (0.1) (1.9) (0.1) (0.9) (0.1) unemployment rate -.54 -.45 0 0 1; -.37 -.36 0 0 3; -.47 0 0 1; -.48 0 0 1; (11.7) (8.9) (7.5) (6.2) (8.0) (7.0) foodandenergy price .89 .94 .50 .57 (contemporaneous) (21.4) (15.2) (6.1) (6.3) foodandenergy price .45 0 1 4; .50 0 1 3; -.21 1 1; (lags) (7.5) (5.7) (2.6) farmprice -.02 (8.1) importprice .03 .07 0 0 3; .11 0 0 3; (2.8) (4.5) (5.9) Equationstatistics: sampleperiod 55.1-89.4 55.1-89.4 63.3-89.4 65.3-89.4 55.1-89.4 55.1-89.4 (cid:22) R 2 .9410 .9320 .8903 .8565 .9042 .8934 SSR 74.48 73.37 57.12 56.44 92.14 137.53 regression se .7455 .7427 .7557 .7832 .8355 1.0207 Durbin-Watson 1.81 1.61 1.80 1.52 1.83 1.84 aForeachregressor,theestimatedcoefficient,orcoefficientsum,andt-statisticarereported. Entriesthat arecoefficientsumsareindicatedbysubscriptsindexingtheminimumandmaximumlags,and,ifpolynomial restrictionsareimposed,byasuperscriptreportingthepolynomialdegree.Equationsalsoincludeanintercept andwage-pricedummy. bThe reported t-statistic is associated with the deviation from one of the sum of coefficients on lagged inflationwhenitisnotrestricted. 31

TableA2 Baseline-98Equations CPI PCE CPIX PCEX GDP NFB Estimatedcoefficients:a inflationlagsb 1.00 2 1 2; 4 1.00 2 1 2; 4 1.00 2 1 2; 3 1.00 2 1 2; 4 1.00 2 1 1; 5 1.00 2 1 1; 7 (0.1) (0.2) (2.3) (0.2) (0.0) (0.2) unemployment rate -.50 0 0 1; -.40 0 0 1; -.35 -.27 0 0 3; -.37 -.41 0 0 1; (11.3) (8.3) (8.0) (5.0) (6.8) (6.3) foodandenergy price .89 .90 .38 .54 (contemporaneous) (23.1) (15.0) (5.6) (6.6) foodandenergy price .45 0 1 4; .36 0 1 3; (lags) (8.2) (3.8) farmprice -.02 (8.5) importprice .04 0 0 1; .04 0 0 1; .05 1 0 1; .11 0 0 2; (3.8) (3.3) (3.8) (6.9) Equationstatistics: sampleperiod 55.1-98.4 55.1-98.4 63.3-98.4 65.3-98.4 55.1-98.4 55.1-98.4 (cid:22) R 2 .9350 .9223 .8909 .8796 .8962 .8845 SSR 89.48 94.48 68.80 71.51 114.73 166.58 regression se .7255 .7477 .7112 .7504 .8264 .9958 Durbin-Watson 1.66 1.51 1.74 1.53 1.76 1.74 aForeachregressor,theestimatedcoefficient,orcoefficientsum,andt-statisticarereported. Entriesthat arecoefficientsumsareindicatedbysubscriptsindexingtheminimumandmaximumlags,and,ifpolynomial restrictionsareimposed,byasuperscriptreportingthepolynomialdegree.Equationsalsoincludeanintercept andwage-pricedummy. bThe reported t-statistic is associated with the deviation from one of the sum of coefficients on lagged inflationwhenitisnotrestricted. 32

TableA3 NoSmoothingRestrictions CPI PCE CPIX PCEX GDP NFB Estimatedcoefficients:a inflationlagsb 1.00 3 1 4; 1.00 3 1 4; 1.00 4 1 5; 1.00 4 1 5; 1.00 3 1 4; 1.00 6 1 7; (1.2) (1.7) (0.6) (1.0) (2.8) (3.0) unemployment rate -.19 2 0 2; -.17 -.24 -.15 -.23 -.32 (3.8) (3.5) (4.9) (3.0) (4.2) (4.7) foodandenergy price .88 .95 .34 .47 (contemporaneous) (17.4) (13.2) (4.5) (5.3) foodandenergy price -.69 3 1 4; -.81 3 1 4; .17 1 1; -.25 1 1; (lags) (10.1) (8.2) (2.5) (3.3) farmprice -.02 (7.3) importprice .04 .05 .05 .04 .07 1 0 1; .12 2 0 2; (3.4) (4.7) (5.3) (4.2) (5.0) (6.3) Equationstatistics: sampleperiod 55.1-98.4 55.1-98.4 63.3-98.4 65.3-98.4 55.1-98.4 55.1-98.4 (cid:22) R 2 .9273 .9154 .8755 .8785 .8844 .8674 SSR 95.40 99.83 77.37 71.00 126.31 184.49 regression se .7674 .7802 .7599 .7536 .8723 1.0672 Durbin-Watson 2.02 2.04 2.03 2.01 2.02 1.74 aForeachregressor,theestimatedcoefficient,orcoefficientsum,andt-statisticarereported. Entriesthat arecoefficientsumsareindicatedbysubscriptsindexingtheminimumandmaximumlags,and,ifpolynomial restrictionsareimposed,byasuperscriptreportingthepolynomialdegree.Equationsalsoincludeanintercept andwage-pricedummy. bThe reported t-statistic is associated with the deviation from one of the sum of coefficients on lagged inflationwhenitisnotrestricted. 33

TableA4 CapacityUtilizationEquations CPI PCE CPIX PCEX GDP NFB Estimatedcoefficients:a inflationlagsb 1.00 2 1 2; 4 1.00 4 1 1; 0 1.00 4 1 9; 1.00 2 1 2; 4 1.00 2 1 1; 9 1.00 2 1 1; 7 (1.8) (2.4) (0.0) (0.1) (0.8) (0.8) capacityutilization .14 0 0 1; .09 0 0 3; .09 0 0 3; .09 0 0 3; .14 0 0 3; .15 0 0 3; (9.1) (5.0) (5.4) (5.2) (7.2) (6.7) foodandenergy price .89 .87 .35 .49 (contemporaneous) (19.4) (13.3) (5.1) (5.9) foodandenergy price -.24 0 1 4; -.38 1 1; .28 0 1 4; .36 0 1 4; (lags) (3.2) (4.8) (4.0) (3.7) farmprice -.02 (8.7) importprice .03 .04 .02 .04 .05 1 0 1; .11 0 0 2; (2.6) (3.9) (2.4) (3.6) (4.2) (6.8) Equationstatistics: sampleperiod 55.1-98.4 55.1-98.4 63.3-98.4 65.3-98.4 55.1-98.4 55.1-98.4 (cid:22) R 2 .9305 .9247 .8953 .8786 .8950 .8872 SSR 94.53 90.01 64.57 72.11 116.01 162.75 regression se .7501 .7364 .6968 .7535 .8310 .9843 Durbin-Watson 1.61 2.01 2.09 1.53 1.74 1.79 aForeachregressor,theestimatedcoefficient,orcoefficientsum,andt-statisticarereported. Entriesthat arecoefficientsumsareindicatedbysubscriptsindexingtheminimumandmaximumlags,and,ifpolynomial restrictionsareimposed,byasuperscriptreportingthepolynomialdegree.Equationsalsoincludeanintercept andwage-pricedummy. bThe reported t-statistic is associated with the deviation from one of the sum of coefficients on lagged inflationwhenitisnotrestricted. 34

TableA5 MarkupEquations CPI PCE CPIX PCEX GDP NFB Estimatedcoefficients:a inflationlagsb 1.00 3 1 2; 4 1.00 2 1 2; 4 1.00 2 1 2; 3 1.00 2 1 2; 4 1.00 2 1 1; 5 1.00 2 1 1; 7 (0.1) (0.4) (1.3) (0.8) (0.3) (1.4) unemployment rate -.56 0 0 1; -.42 0 0 1; -.36 -.37 0 0 3; -.41 0 0 1; -.43 0 0 1; (12.0) (9.4) (8.7) (7.3) (7.4) (6.9) foodandenergy price .88 .87 .36 .51 (contemporaneous) (22.6) (15.7) (5.5) (6.5) foodandenergy price .41 0 1 4; .49 0 1 4; (lags) (7.7) (5.8) farmprice -.02 (8.8) importprice .03 .04 1 0 1; .10 0 0 2; (3.0) (3.0) (6.0) trendmarkup .22 1 1; .25 1 1; .17 1 1; .24 1 1; .19 1 1; .26 1 1; (4.9) (5.7) (3.7) (5.0) (3.7) (4.1) Equationstatistics: sampleperiod 55.1-98.4 55.1-98.4 63.3-98.4 65.3-98.4 55.1-98.4 55.1-98.4 (cid:22) R 2 .9430 .9343 .9002 .8899 .9032 .8947 SSR 77.51 79.46 62.47 65.35 106.36 151.01 regression se .6793 .6877 .6802 .7174 .7980 .9509 Durbin-Watson 1.83 1.69 1.88 1.63 1.84 1.82 aForeachregressor,theestimatedcoefficient,orcoefficientsum,andt-statisticarereported. Entriesthat arecoefficientsumsareindicatedbysubscriptsindexingtheminimumandmaximumlags,and,ifpolynomial restrictionsareimposed,byasuperscriptreportingthepolynomialdegree.Equationsalsoincludeanintercept andwage-pricedummy. bThe reported t-statistic is associated with the deviation from one of the sum of coefficients on lagged inflationwhenitisnotrestricted. 35

Data Appendix Inflationrates Inflation data for CPI, CPIX, PCE, PCEX, GDP and NFB are measured as annualized rates of change in percentage points. Data for CPI and CPIX are modified from 1967 to 1983 to place homeownershipcosts on a rental-equivalent basis. All inflation series are adjustedtoremoveeffectsofrecentchangesinpricemeasurementmethodology. Estimates of methodological effects on CPI and GDP are taken from Council of EconomicAdvisors (1999, table 2-4). For CPI the reported methodological effects are: 1995, -0.12; 1996, - 0.22; 1997, -0.23; 1998, -0.44. For GDP the effects are: 1994, -0.06; 1995-98, -0.21. In eachcase,weaddbacktheeffectsofmethodologychangestocreateconsistentlymeasured inflation time series. We apply the CPI adjustment to CPIX and use adjustments to PCE andNFBthatarerespectively1.47and1.34timestheadjustmenttoGDP,wherethescaling factors are theaverageratios ofnominalGDPtonominalPCE andNFB over1995-98. Publisheddatastartsin1957:Q1forCPIXin1959:Q1forPCEX,whichsetsthebeginning of the CPIX and PCEX estimation intervals at 1963:Q3 and 1965:Q3, after allowing for a maximum of twenty-five inflation lags. We construct approximate values for CPIX andPCEXfortheperiodpriortothepublisheddataforuseindefiningthefoodandenergy price series. Early values of PCEX are constructed by removing from PCE an estimate of the price of food and energy. For the two components of the latter which are not available before 1959 (electricity and natural gas), estimates of prices are taken from the CPI and estimates of nominal values (needed for chain aggregation) are obtained by interpolating annual data publishedin various issues of the Survey of Current Business. Early values of therateofCPIXinflationareestimatedbysubtractingfromCPIinflationfittedvaluesfrom a regression of the difference between CPI and CPIX inflation on the difference between PCE andPCEX inflation. Rates ofunemployment and capacityutilization The demographicallyfixed-weightedunemploymentrate an average of unemployment ratesformalesandfemalesaged16-19,malesaged20-24,femalesaged20-24,malesaged 25 and older, and females aged 25 and older, with weights equal the labor force share of eachgroupin1993. Thefinalseriescontainstwoadjustments. First,0.08percentagepoints is added to the unemployment rate for all dates prior to 1994 to eliminate a discontinuity associated with the 1994 redesign of the Current Population Survey (Polivka and Miller, 36

1995). Second, an additional 0.10 percentage point is added to the unemploymentrate for all dates prior to 1990 to offset an adjustment associated with the undercount in the 1990 Census (McIntire,1996). Therate ofcapacityutilizationis forthemanufacturingsector. Foodand energyprice inflation For CPI and CPIX equations, the food and energy price variable is measured as CPI inflation less CPIX inflation. For the other equations, the variable is measured as PCE inflationlessPCEX inflation. Importprice inflation EquationsforCPI,CPIX,PCE,andPCEXcontaintheannualizedrateofincreaseofthe NIPA price of merchandiseimportsexcludingpetroleum,computers,and semiconductors. The adjustment for semiconductors makes use of unpublished data from the Bureau of Economic Analysis. Equations for GDP and NFB contain an import price series that is a weighted average of this measure of import price inflation and import price inflation for merchandise excluding only petroleum, with weights of 0.90 and 0.10, respectively. The weights are based on the nominal ratio of computer final sales to GDP, which averages 0.10from 1987to1998. Relativeimport price inflationis constructedby subtractingfrom the appropriate measure of import price inflation the once-lagged value of the aggregate inflationseries beingexplained. Data for the price of imports excluding petroleum, computers, and semiconductors is available from 1969:Q3. Earlier values are based on the price of merchandise imports excludingpetroleum,anapproximationthatisprobablygoodgiventherelativeunimportance of trade in computers and semiconductors at that time. The price of merchandise imports excludingpetroleumisavailableonlyfrom1967:Q1,however. Earliervaluesofbothmeasures of import prices used in the Phillips curves are based on the price of overall imports excludingpetroleum(from 1956:Q2)andthepriceofimports(priorto1956:Q2). Trend markup The trend markup is l o g ( p (cid:26) = w ) , where p is the chain-weight price index for output of thenonfarmbusinessoutputexcludinghousing, w iscompensationperhourinthenonfarm businesssectorfromtheBLSProductivityandCostrelease,and (cid:26) istrendlaborproductivity. The latter is based on the fitted values of a regression of the logarithm of actual labor productivityinthenonfarmsectoronaconstant,atimetrend,andasecondtimetrendthat starts in 1973:Q1. The estimationperiod is 1955:Q1-1998:Q4. Data on p and actual labor 37

productivity are adjusted for changes in price measurement methodology by cumulating overtimetheadjustmenttoNFB inflationdescribedabove. Thetrendmarkupismeasured relativetoits1955-98mean. Wage-pricecontrol variable Allequationscontainavariablethataccountsfortheeffectsofwageandpricecontrols in the 1970s. The series, which has a mean of zero, equals 1.0 from 1971:Q3 to 1974:Q1 and-3.67from 1974:Q2-1974:Q4. 38