Real-Time Properties of the Federal Reserve's Output Gap

Finance and Economics Discussion Series Divisions of Research & Statistics and Monetary Affairs Federal Reserve Board, Washington, D.C. Real-Time Properties of the Federal Reserve’s Output Gap Rochelle M. Edge and Jeremy B. Rudd 2012-86 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.

Real-Time Properties of the Federal Reserve’s Output Gap Rochelle M. Edge Jeremy B. Rudd ∗ ∗∗ Federal Reserve Board Federal Reserve Board December 3, 2012 Abstract This note considers the reliability of Federal Reserve Board staff estimates of the output gap after the mid-1990s, and examines the usefulness of these estimates for inflationforecasting. Overthisperiod,wefindthattheFederalReserve’soutputgap is more reliably estimated in real time than previous studies have documented for earlier periods and alternative estimation techniques. In contrast to previous work, wealsofindnodeteriorationinforecastperformancewheninflationprojectionsare conditionedonreal-timeestimatesoftheoutputgap. ∗Corresponding author. Mailing address: Mail Stop 155-C, 20th and C Streets NW, Washington, DC 20551. E-mail: rochelle.m.edge@frb.gov. ∗∗E-mail: jeremy.b.rudd@frb.gov. WethankAthanasiosOrphanidesforhelpfulcommentsonanearlier versionofthiswork. TheviewsexpressedareourownanddonotnecessarilyreflecttheviewsoftheBoard ofGovernorsorthestaffoftheFederalReserveSystem.

I Introduction In a 2002 paper, Orphanides and van Norden contend that it is not possible to obtain reliable estimates of the output gap in real time. As they demonstrate, standard detrending procedures yield gap measures that are subject to large subsequent revisions, primarily because trend extraction becomes quite difficult at the endpoint of a given sample. In addition, based on data available for the 1980s and early 1990s, Orphanides (1998) concludesthatFederalReservestaffestimatesoftheoutputgaparesimilarly unreliable. The purpose of this note is to consider whether these conclusions obtain for more recentvintagesoftheoutputgapestimatesproducedbytheFederalReservestaff. Narrative evidence suggests that the Federal Reserve’s ability to recognize and quantify the mid- 1990s acceleration in trend productivity in a reasonably timely manner was an important contributortothesuccessfulconductofmonetarypolicyoverthatperiod.1 Thispointsto animproved abilitytoestimatethegap,whichshouldinturnbeevidentinthedata. A related issue concerns the usefulness of real-time estimates of the output gap for inflation forecasting. In companion work, Orphanides and van Norden (2005) find that overthepost-1983period,inflationforecastingmodelsthatusereal-timeestimatesofthe output gap typically perform worse than models that condition on final estimates of the gap. We therefore also examine whether the Federal Reserve staff estimates of the GDP gapprovideausefulpredictor offuture inflationmovements inrealtime. II Real-TimeEstimatesoftheFederalReserveBoardOutputGap Before each meeting of the Federal Open Market Committee (FOMC), the Federal Reserve Board’s staff produce a detailed projection of various U.S. economic aggregates. 1SeeMeyer(2004,ch.6)forafirsthandaccount. 1

This projection, which is known as the Greenbook forecast, is judgemental in the sense that it is not explicitly derived from a single model of the economy.2 In particular, the staff’sestimatesofpotentialGDPpoolandjudgementallyweighttheresultsfromanumberofestimationtechniques,includingstatisticalfiltersandmorestructuralmodel-based procedures.3 Our set of real-time output gap estimates starts with the June 1996 Greenbook forecast;theseestimatesextendbackto1975:Q1foreveryvintageoftheforecast. TheGreenbook projection is only made public with a five-year lag; hence, the most recent estimate ofthegapinourdatasetcomesfromtheDecember2006Greenbook. BecausetheGreenbook is produced eight times a year, there will be eight sets of output gap estimates for eachyear(typicallytwoperquarter). Define the December 2006 estimates of the gap to be the gap’s “final” value. We then define the corresponding real-time estimate of the quarter-t gap to be the estimate of the gap from the forecast round whose closing date falls in quarter (t + 1). (Obtaining the period-t gap estimate from a Greenbook in the following quarter ensures that in most cases an advance estimate of GDP—or a relatively full set of monthly indicators— would have been available for estimating the quarter-t gap.) For example, the June 1997 Greenbook forecast was completed in 1997:Q2. We therefore call the 1997:Q1 value of the gap from the June 1997 round the real-time estimate of the gap in that quarter. This means,ofcourse,thattherecanbemultiplereal-timeobservationsforagivenquarter;for instance, we will obtain real-time estimates of the 1997:Q1 gap from both the May 1997 2StartinginJuneof2010, thestaff’sforecastdocumentwasrenamedtheTealbookforecast, asitnow combines elements of the original Greenbook with topics related to the conduct of monetary policy that wereformerlypresentedtotheFOMCintheso-called“Bluebook.” (Duringtheentireperiodweconsider, thestaff’sprojectionwascontainedintheGreenbook,sowerefertoitbythistitle.) 3SeeMishkin(2007)foradescriptionofhowtheFederalReserveBoardstaffestimatepotentialoutput. 2

and June 1997 Greenbook forecasts. We ignore the informational asymmetry generated by these timing definitions—specifically, we ignore the fact that rounds that occur later inagivenquarterwillenjoyaninformationaladvantageoverthosethatoccurearlier—as such asymmetries will be roughly constant across years. (As we document in the next section,ourmainconclusionsarerobust toalternativeassumptionsregarding timing.) III TheMagnitudeofRevisionstotheFederalReserve’sGapEstimates Wedefinethegaprevisionasthedifferencebetweenthefinalandreal-timegapestimates. Lines 1 and 2 of Table 1 give the mean, standard deviation, and root-mean-square error (RMSE) for these revisions, together with two measures of the noise-to-signal ratio: the ratio of either the standard deviation or the RMSE of the gap revisions to the standard error of the final estimate of the gap.4 As can be seen from the table, the mean error over the full sample is small (less than a tenth of a percentage point). The standard deviation (andRMSE)oftherevisionsisaround0.7percentagepoint;whilethisislargeinabsolute terms, it is only about half the size of the corresponding standard deviation of the final estimateofthegap.5 These standard deviation and RMSE values are also small relative to the corresponding estimates found by Orphanides (1998) in his analysis of the Greenbook output gap: Over the 1980-1992 period, Orphanides reports a RMSE of 2.8 percentage points for revisions to the Greenbook’s real-time output gap estimates, which is actually greater than 4Recallthatthemean-squareerrorcontainsanadjustmentforthesquaredbias(here, themeanerror). Thus, whenthemeanerrorissmall, thestandarddeviationofthegaprevisionsandtheRMSEshouldbe quiteclose. 5Tocomputethemeanandstandarddeviationofthefinalgapestimate,we“duplicate”theobservations onthefinalgapinlinewiththenumberofGreenbookforecaststhatfallinagivenquarter. However, the computedmeanandstandarddeviationareessentiallyidenticalifweinsteadjustallowoneobservationon thefinalgapperquarter. 3

the2.4percentagepointstandarddeviationofhis“final”(end-of-1994)gapestimate. Part of this difference no doubt reflects our use of a different sample period: Relative to the 1980s, GDP in our sample period is less volatile. However, this explanation is tempered somewhat by the observation that the Federal Reserve appears to have had greater difficultyforecastingrealGDPmovementsinrecentdecades(seeTulip,2005). Of course, another explanation for the observed reduction in the size of gap revisions issimplythattheFederalReservestaff’sabilitytoestimatetheGDPgapinrealtimehas improved relative to the period that Orphanides examined. To assess this possibility, we usedreal-timeGDPdatatoexaminewhetherpurelystatisticalmethodsforestimatingthe output gap yield a decline in the size of gap revisions that is comparable to what we find for the Greenbook output gap. In particular, we produced real-time estimates of the output gap using each of the six univariate detrending procedures considered by Orphanides and vanNorden (2002). Theseprocedures include three deterministic approaches(fitting a linear trend, a broken-linear trend, and a quadratic trend to log real GDP) and three unobserved-componentsapproaches(theHodrick-PrescottfilterandthetrendGDPmodels of Watson, 1986 and of Harvey, 1985 and Clark, 1987). The noise-to-signal ratios that obtain for these various gap estimates—which are shown in the upper panel of Table 2—imply that for all but one of the six detrending methods, the size of the real-time gap revisions relative to the volatility of the gap itself either remains about unchanged or increases somewhat from 1980-1992 to 1992-2006. Hence, these purely statistical procedures do not yield an improvement in the reliability of real-time gap estimates that is similar to what we observe for the Federal Reserve’s measure, which in turn suggests that some element particular to the the Fed’s estimation procedure—such as the use of 4

judgementorthepooling ofresultsfrommultiple sources—isresponsible.6 In line with Orphanides (1998), however, we find that the autocorrelation of the Greenbook gap revisions is quite high: about 0.91 over the period we consider.7 It turns out that part of the autocorrelation over our sample period is attributable to a persistent string of negative errors (that diminish in magnitude) up until around 1998. Very likely, this string of errors reflects slow learning about the 1990s speedup in trend productivity growth; dropping the pre-1999 observations from the sample reduces the estimated autocorrelation coefficient to 0.70. Interestingly—and as shown in Table 3—when we compute real-time gap estimates using the univariate approaches in Orphanides and van Norden (2002), we find that the gap revision is as highly autocorrelated over the 1996-2006 period(line2)asitisoverthe1980-1992period(line1),withautocorrelationcoefficients ontheorderof0.9. Forthesegapmeasures,however,droppingthepre-1999observations from the latter period (line 3) reduces the estimated autocorrelation coefficient for only twoofthesixmethods(thelinearandpiecewise-lineardetrending procedures). As was noted above, the publication of two Greenbook forecasts per quarter implies that we will have multiple gap estimates in each quarter. In addition, even though we have obtained each time-t gap estimate from a Greenbook published in period (t + 1), there will be occasions where an advance estimate of GDP will not have been available to produce the gap estimate for a given quarter.8 We therefore considered two modifications to our timing assumptions. First, we recomputed the statistics in Table 1 using the 6One reason we are not fully willing to advance such an optimistic conclusion is that it implicitly suggests that previous techniques for estimating potential GDP were less sophisticated. However, as Solow(1982)documents,themethodologyusedbytheCouncilofEconomicAdviserstoestimatepotential outputasfarbackasthe1960swouldnotbeoutofplaceinacontemporarypolicyinstitution. 7Inhissample,Orphanides(1998)findsanautocorrelationcoefficientinexcessof0.8forrevisionsto theFederalReserve’sgapestimates. 8Forexample,oneofthetwo2006:Q3estimatesoftheGDPgapistakenfromtheOctober2006Greenbook;anadvanceestimateofthird-quarterGDPwasnotavailablewhenthisGreenbookwasfinalized. 5

time-t gap estimate from the time-(t+2) Greenbook; this ensures that a complete set of GDPdataforquartertwouldhavebeenavailableforproducingtheGreenbookestimate. Unsurprisingly, doing this (not shown) lowers the mean, standard deviation, and RMSE of the gap revisions, but only by a very small amount (on the order of 0.02 or 0.03 percentage point in each case). Next, we recomputed the statistics in Table 1 using only the gapestimatefromthesecond Greenbookineachquarter. Onceagain,themean,standard deviation, and RMSE of the gap revisions are little changed by this modification (not shown). However, the autocorrelation of the revisions declines slightly (to 0.84), and is considerablylower(only 0.41)ifthepre-1999revisionsareexcluded. Finally, we also examined whether our results are affected by using a shorter period to compute the summary statistics for the gap revisions. Our set of real-time estimates ends with the October 2006 Greenbook, while our “final” gap estimate is taken from the December 2006 Greenbook. To the extent that potential GDP growth is relatively slowmoving,itseemsplausibletoexpectlittlescopeforrevisionstotheoutputgapinperiods neartheendofoursample. Wethereforecomputeasecondsetofsummarystatisticsthat onlyusedatathroughtheDecember2004Greenbook;usingthisdateensuresthatatleast twoNIPAannualrevisionsseparatethereal-timegapestimatesinthelatterportionofthe sample from the final gap estimates. These statistics are shown in Table 1 in line 2 (for the real-time gaps) and line 4 (for the final gap estimates); as can be seen, the change in the mean and variability of the gap revisions that results from shortening the sample in thismannerisextremely small.9 9In addition, the results obtained by using the univariate detrending procedures considered by Orphanides and van Norden (2002) are also little changed when at least two years separate the real-time andfinalgapestimates—comparetheupperandlowerpanelsofTable2. 6

IV UsingReal-TimeGap EstimatesforInflationForecasting Wenowconsiderwhethertheuncertaintyassociatedwithcurrentandfuturevaluesofthe Greenbookoutputgapaffectsitsusefulnessasapredictorofinflation. Specifically,wefit Phillips curve models that relate core PCE price inflation (expressed at an annual rate) to six of its own lags (with the lag coefficients constrained to sum to one, but not otherwise restricted) and to the contemporaneous and once-lagged value of share-weighted relative coreimportpriceinflation.10 IncontrasttomanycommonlyusedempiricalPhillipscurve specifications, we do not include the relative rates of food and energy price inflation in ourmodel.11 The starting date for the estimation is 1975:Q1 (this is dictated by the availability of historical data on the real-time output gap). For a real-time gap estimate from a Greenbookforecastinquarter(t+1),weestimatethemodelthroughquartertandthencompute dynamicout-of-samplesimulationsatvarioushorizonsusingtheprojectedpathofthegap from that vintage of the Greenbook. Note, however, that we use the most recent vintages of core PCE and import prices in the regression; implicitly, we seek to assess how well theFederalReserve’soutputgapestimatespredicttheeconomy’s“true”rateofcoreinflation,whereweassumethatthetrueinflationrateiscapturedbythemostrecentvintageof NIPA data. We present results for three forecast horizons: two quarters ahead, four quarters ahead, and six quarters ahead; in addition, we use the simulated values to compute 10OurchoiceoflaglengthisinformedbyapplyingtheSchwarzinformationcriteriontothefull-sample model that uses the final estimate of the output gap. The relative import price term is defined as the annualizedpercentchangeintime-tcorenonfuelimportpriceslessthetime-(t−1)rateofcorePCEprice inflation,weightedbythetwo-quartermovingaverageoftheshareofnominalcoreimportsinnominalcore PCE.Inaddition,weadd0.75percentagepointtocorePCEinflationin2001:Q3(anddeductacorrespondingamountin2001:Q4)tocontrolfortheswingininflationthatwasinducedbytheBureauofEconomic Analysis’streatmentofinsurancepaymentsrelatedottheSeptember11thterroristattacks. 11Weomittheseotherrelativepricetermsbecauseourestimationperiodexcludesthefirstenergy-and food-priceshocksof1973and1974. Inaddition,asHooker(2002)documents,energyprices(specifically, oilprices)playessentiallynoroleinPhillipscurvemodelsofcoreinflationafter1981. 7

theaverageinflationrateoverthenextfour quarters. The forecasts from our baseline Phillips curve model (using a real-time output gap) arethencomparedtocorrespondingout-of-sample projections fromfourothermodels: • An identical Phillips curve specification that uses the “final” estimate of the GDP gap (that is, the GDP gap from the December 2006 Greenbook) and that therefore assumes that the future path of the gap is available for constructing the model forecastsofinflation; • A specification that omits the GDP gap but is otherwise identical to the baseline model(with six lagsof inflationwhosecoefficientsareconstrained tosumtounity andthecurrentandonce-laggedvalueoftherelativecoreimport term); • AunivariateAR(6)specificationinwhichcorePCEpriceinflationisrelatedtosix of its lags, with the sum of the coefficients on lagged inflation constrained to equal one;and, • A univariate AR(6) specification in which the sum of the inflation lags is unrestricted.12 Note that the last three specifications use no real-time data (again, the most current vintages of core PCE and import prices are employed); however, in every quarter two (identical) forecasts are generated for each equation in order to mimic the output from the modelsthatusereal-timeestimatesofthegap. Table4givestheRMSEforeachmodeloverthevariousprojectionhorizons. Comparingthetoptworowsofeachpanelrevealsthatusingthereal-timeestimatesandforecasts 12For the unrestricted AR(6) model, the sum of the coefficients on lagged inflation is relatively stable andclosetoone,rangingfrom0.91to0.93overtheperiodweconsider. 8

of the GDP gap in lieu of the final estimate has almost no effect on forecast accuracy. That said, models that condition on a measure of the GDP gap improve only slightly on theunconstrainedunivariatemodelofinflation(notethateventhefinalestimateofthegap only contributes about a percentage point to the equation’s R2 value in the full sample). We would emphasize that we attribute no significance to the fact that the Phillips curve modelsdoslightlybetterthantheunrestrictedautoregressivemodel: Becausewetreatthe path of import prices as known over the forecast period, we are providing these models with an important informational advantage. Rather, the result that we would highlight here is that there is essentially no reduction in forecasting performance from using the real-timegapmeasureinthePhillipscurvemodelasopposedtothefinalgapestimate,as canbeseenfromacomparisonoflinesoneandtwoofTable4. (Bycontrast,Orphanides and van Norden, 2005, find that real-time estimates of the statistical gap measures that they consider do significantly less well in predicting inflation than do the corresponding finalor“expost”gapestimates.) Theseresultsalsorevealaninterestingrelationshipamongthevariablesinthemodel. As can be seen from Table 4, merely omitting the gap yields a noticeable deterioration in forecast performance. Likewise, omitting import prices but keeping either the final or real-time gap (not shown) results in a large increase in the forecast RMSE. In addition, imposing that the sum of the coefficients on lagged inflation equals one in the univariate model also acts to reduce its forecast accuracy. The sensitivity of the model’s forecasting performance to these modifications is somewhat surprising given that jointly these three elements of the specification—imposition of a unit coefficient sum and inclusion of an output gap together with an import price term—appear to contribute very little to the overall model’s forecasting performance (the RMSEs from the full model using the 9

finalestimateoftheoutputgaparequiteclosetothosefromtheunconstrainedunivariate AR(6)model). V Conclusions TheresultspresentedinSectionIIIsuggestthattheconclusionsfoundinOrphanides(1998) and Orphanides and van Norden (2002) regarding the reliability of output gap measures in real time are too pessimistic along at least one dimension. Over a nearly decadelong period, staff at the Federal Reserve Board produced estimates of the output gap whose revision properties were considerably better than those found by Orphanides and van Norden for the statistical gap measures that they considered, as well as being considerably better than the earlier Federal Reserve output gap estimates that Orphanides examined. Importantly, these more-recent estimates were constructed during a period in which the Federal Reserve staff were attempting to identify and incorporate the effects of a perceived shift in trend productivity growth; in addition, the improvement that we observe for the Greenbook output gap estimates is not shared by gap measures obtained under alternative, purely statistical detrending methods. Hence, our finding provides circumstantial evidence of an improvement in the procedures used by the Fed to estimate potentialoutput andtheGDPgap. Our results regarding the usefulness of gap estimates for inflation forecasting are in closer agreement with Orphanides and van Norden (2005), in that we find that it is not really possible to improve on the forecasting performance of a simple univariate model with a gap-based model. However, in contrast to these authors’ findings, our result does notappeartostemfromdifficultiesassociatedwithmeasuringtheoutputgapinrealtime: Phillips curve models based on real-time gap measures perform about as well as models 10

basedonafull-samplegap. Instead,weviewourresultasreflectingthegeneraldeclinein the forecastability of inflation in recent decades (particularly by gap-based models) that hasbeendocumentedbyStockandWatson(2007, 2009). On balance, our results suggest that the output gap can serve as a useful input to the policy process. Although the gap measures we consider cannot be used to improve inflation forecasts, real-time estimates of the gap appear to provide a reasonable characterization of the current state of real activity in the economy. Such a gauge is necessary for a central bank like the Federal Reserve, whose statutory mandate requires it to aim for maximum sustainable output growth and employment as well as stable prices; similarly,somesortofoutputgapmeasureisalsonecessaryforanycentralbankthatseeksto implement aTaylor-typemonetarypolicyrule. Of course, it remains to be seen whether the improvement in output gap estimation thatwedocumentwillprovetobeadurablephenomenon. TheU.S.economyhasrecently undergone a once-in-a-generation upheaval that caught many analysts by surprise and whose longer-term effects—if any—are still unknown. As additional real-time estimates oftheFederalReserveBoard’soutputgapbecomepubliclyavailable,itwillbeinteresting toseewhetherthereliability ofthesegapestimateswillbemaintained. VI References Clark,PeterK.,“TheCyclicalComponentofU.S.EconomicActivity,”QuarterlyJournal ofEconomics102(1987), 797-814. Harvey, A. C., “Trends and Cycles in Macroeconomic Time Series,” Journal of Business andEconomicStatistics3(1985), 216-227. Hooker, Mark A., “Are Oil Shocks Inflationary? Asymmetric and Nonlinear Specifi- 11

cations versus Changes in Regime,” Journal of Money, Credit, and Banking 34 (2002), 540-561. Meyer, Laurence H., A Term at the Fed: An Insider’s View (New York: Harper Business, 2004). Mishkin, Frederic S., “Estimating Potential Output,” presentation at the Conference on PriceMeasurementforMonetaryPolicy(May24,2007);availableat http://www.federalreserve.gov/newsevents/speech/mishkin20070524a.htm. Orphanides, Athanasios, “Monetary Policy Evaluation with Noisy Information,” Federal ReserveBoardFinanceandEconomicsDiscussionSeriesno.1998-50(1998). Orphanides, Athanasios and Simon van Norden, “The Unreliability of Output-Gap EstimatesinRealTime,”ReviewofEconomicsandStatistics 84(2002), 569-583. Orphanides, Athanasios and Simon van Norden, “The Reliability of Inflation Forecasts BasedonOutputGapEstimatesinRealTime,”JournalofMoney,Credit,andBanking37 (2005), 583-601. Solow,RobertM.,“WhereHaveAlltheFlowersGone? EconomicGrowthinthe1960s” in Joseph A. Pechman and N. J. Simler (Eds.), Economics in the Public Service: Papers inHonorofWalterW.Heller (NewYork: W.W.Norton,1982). Stock,JamesH.,andMarkW.Watson,“WhyHasU.S.InflationBecomeHardertoForecast?,”JournalofMoney,Credit,andBanking39(S1)(2007), 3-33. Stock,JamesH.,andMarkW.Watson,“PhillipsCurveInflationForecasts”inJeffFuhrer, Yolanda K. Kodrzycki, Jane Sneddon Little, and Giovanni P. Olivei (Eds.), Understanding Inflation and the Implications for Monetary Policy: A Phillips Curve Retrospective (Cambridge, MA:MITPress,2009) Tulip, Peter, “Has Output Become More Predictable? Changes in Greenbook Forecast Accuracy,” Federal Reserve Board Finance and Economics Discussion Series no. 2005- 31(2005). Watson, Mark W., “Univariate Detrending Methods with Stochastic Trends,” Journal of MonetaryEconomics18(1986), 49-75. 12

Table1: StatisticsonGreenbookOutputGapRevisionsand“Final”Estimates Noise-signalratios Mean Std.dev. RMSE Std.dev. RMSE Greenbookoutputgaprevisions 1. Fullsample,1996-2006 −0.04 0.71 0.71 0.47 0.47 2. ThroughDec.2004GB −0.15 0.73 0.74 0.45 0.45 Memo: “Final”gapestimates 3. Fullsample,1996-2006 0.25 1.50 4. ThroughDec.2004GB 0.29 1.64 Note: “Final” estimates replicate observations in individual quarters for comparability withreal-timeestimates(seetextfordetails). Fullsamplecontains84observations;samplethrough December2004Greenbookcontains69observations. 13

Table2: Noise-to-Signal Ratiosfrom StatisticalDetrendingProcedures Hodrick- Broken Quadratic Linear Harvey- Prescott Trend Trend Trend Watson Clark I.Usinglastvintageofdatafor“final”gapestimate A.Basedonstandarddeviationofrevisions 1. 1980-1992 1.10 0.62 0.40 0.72 0.77 0.78 2. 1996-2006 1.03 1.11 0.61 1.17 0.59 0.71 B.BasedonRMSEofrevisions 3. 1980-1992 1.10 1.13 0.47 1.15 1.26 0.77 4. 1996-2006 1.03 1.45 1.58 1.43 0.77 0.70 II.Usingdatavintagefromtwoyearsaftersample’sendfor“final”gapestimate A.Basedonstandarddeviationofrevisions 1. 1980-1992 1.08 0.52 0.47 0.67 0.75 0.76 2. 1996-2006 1.01 1.04 0.43 1.13 0.52 0.70 B.BasedonRMSEofrevisions 3. 1980-1992 1.08 1.53 0.60 1.49 1.25 0.75 4. 1996-2006 1.00 1.57 1.60 1.56 0.79 0.69 14

Table3: Autocorrelation ofGapRevisions,StatisticalDetrendingProcedures Hodrick- Broken Quadratic Linear Harvey- Prescott Trend Trend Trend Watson Clark 1. 1980-1992 0.92 0.95 0.83 0.93 0.93 0.87 2. 1996-2006 0.92 0.94 0.93 0.94 0.93 0.88 3. 1999-2006 0.93 0.68 0.89 0.63 0.89 0.90 Table4: RootMeanSquareForecastErrorsfrom CorePCEModels 2Qahead 4Qahead 4Qave. 6Qahead Modelwithfinalgap 0.47 0.47 0.30 0.49 Modelwithreal-timegap 0.48 0.48 0.32 0.49 Modelexcludinggap 0.60 0.67 0.50 0.78 AR(6)model(coeff. sum=1) 0.59 0.68 0.48 0.81 UnconstrainedAR(6)model 0.53 0.53 0.37 0.57 Memo: Numberofobservations 81 77 77 73 15