The Accuracy of Forecasts Prepared for the Federal Open Market Committee

Finance and Economics Discussion Series Divisions of Research & Statistics and Monetary Affairs Federal Reserve Board, Washington, D.C. The Accuracy of Forecasts Prepared for the Federal Open Market Committee Andrew C. Chang and Tyler J. Hanson 2015-062 Please cite this paper as: Chang, Andrew C. and Tyler J. Hanson (2015). “The Accuracy of Forecasts Prepared for the Federal Open Market Committee,” Finance and Economics Discussion Series 2015-062. Washington: Board of Governors of the Federal Reserve System, http://dx.doi.org/10.17016/FEDS.2015.062. NOTE: Staff working papers in the Finance and Economics Discussion Series (FEDS) are preliminary materials circulated to stimulate discussion and critical comment. The analysis and conclusions set forth are those of the authors and do not indicate concurrence by other members of the research staff or the Board of Governors. References in publications to the Finance and Economics Discussion Series (other than acknowledgement) should be cleared with the author(s) to protect the tentative character of these papers.

The Accuracy of Forecasts Prepared for the Federal Open Market Committee Andrew C. Chang∗and Tyler J. Hanson† July 9, 2015 Abstract We analyze forecasts of consumption, nonresidential investment, residential investment, governmentspending,exports,imports,inventories,grossdomesticproduct,inflation,andunemploymentpreparedbythestaffoftheBoardofGovernorsoftheFederalReserveSystemfor meetings of the Federal Open Market Committee from 1997 to 2008, called the Greenbooks. Wecomparetherootmeansquarederror,meanabsoluteerror,andtheproportionofdirectional errorsofGreenbookforecastsofthesemacroeconomicindicatorstotheerrorsfromthreeforecastingbenchmarks: arandomwalk,afirst-orderautoregressivemodel,andaBayesianmodel averaged forecast froma suiteof univariatetime-series modelscommonly taughtto first-year economicsgraduatestudents. Weestimateourforecastingbenchmarksbothonend-of-sample vintage and real-time vintage data. We find find that Greenbook forecasts significantly outperform our benchmark forecasts for horizons less than one quarter ahead. However, by the one-year forecast horizon, typically at least one of our forecasting benchmarks performs as well as Greenbook forecasts. Greenbook forecasts of the personal consumption expenditures and unemployment tend to do relatively well, while Greenbook forecasts of inventory investment,governmentexpenditures,andinflationtendtodopoorly. JELCodes: C53;E17;E27;E37;F17 Keywords: BayesianModelAveraging;FederalOpenMarketCommittee;ForecastAccuracy;Greenbook;NationalIncomeandProductAccounts;NIPA;Real-TimeData ∗Chang: Board of Governors of the Federal Reserve System. 20th St. NW and Constitution Ave., Washington DC 20551 USA. +1 (657) 464-3286. a.christopher.chang@gmail.com. https://sites.google.com/site/andrewchristopherchang/. †Hanson: Hopper. 275 Third Street, Cambridge, MA 02142 USA. thanson2691@gmail.com. The views and opinionsexpressedherearethoseoftheauthorsandarenotnecessarilythoseoftheBoardofGovernorsoftheFederal Reserve System or Hopper. We thank Stephanie Aaronson, David Lebow, Paul Lengermann, Phillip Li, Priyanka Shahane, and Missaka Warusawitharana for helpful comments. We thank Kim T. Mai for research assistance. Any errorsareours. 1

1 Introduction Accurateassessmentsofthereal-timestateofeconomicactivityandaccurateforecastsofthefuture path of activity are important inputs for monetary policy decisions. Central banks invest considerable resources in forecasting economic activity to guide policy decisions. For example, prior to meetingsoftheFederalOpenMarketCommittee(FOMC),theFederalReserveBoardstaffprepare a detailed projection of US economic activity for the FOMC, known as the Greenbook.1 Production of the Greenbook employs around a hundred economists and research assistants in addition to other editorial, legal, and administrative staff.2 Despite the considerable effort that goes into GreenbookproductionbecauseoftheGreenbook’scontributiontomonetarypolicydecisions,significantuncertaintysurroundsGreenbookforecasts(ReifschneiderandTulip,2007;Tulip,2009). Our primary contribution is analyzing the accuracy of Greenbook forecasts of 10 key aggregatesoftheUSeconomyinaunifiedframework,asopposedtoonlygrossdomesticproduct(GDP) or inflation (Romer and Romer, 2000; Faust and Wright, 2009; Wright, 2009; Tulip, 2009; Arai, 2014). In addition to these two key macroeconomic indicators, we analyze the unemployment rate and the major components of GDP from the National Income and Product Accounts (NIPA): consumption, nonresidential investment, residential investment, government spending, exports, imports,andbusinessinventories. Weconsiderforecastsfrom1997to2008. WecomparetheaccuracyofGreenbookforecaststotheaccuracyofforecastsfromthreebenchmark reduced-form univariate methods: a random walk, a first-order autoregressive (AR) model, and a Bayesian model averaged forecast from a pool of univariate time-series models taught in first-year economics graduate courses. We choose these benchmarks because of their parsimony, ease ofimplementation, and independencefrom auxiliary data. Weassess whether theGreenbook forecasts, which require substantially more resources to prepare than any of these methods, empirically outperform these simple forecasts. Our dependence only on simple univariate methods also allows us to use only models that were available to forecasters at the time the forecasts were 1Since2010thisprojectioniscalledtheTealbook. 2As of this writing, there are approximately forty economists and research assistants are formally assigned to Greenbookpreparation,butmanymoreparticipantsareinformallyinvolved. 2

generated, which reduces potential hindsight bias in model selection (Tulip, 2009). We measure accuracy as root mean squared error (RMSE), mean absolute error (MAE), and the proportion of forecasts where the predicted sign of the acceleration is incorrect, which we call mean directional error(MDE). To avoid the pitfalls of conducting pseudo out-of-sample forecasting exercises on currentvintage data, we estimate our three benchmarks using two classes of data available to Greenbook forecastersatthetimetheforecastsweregenerated.3 Forthefirstclassofdata,weestimatemodels using the “conventional” data that professional forecasters employ, or what Koenig, Dolmas, and Piger(2003)refertoasend-of-samplevintage(EOS)data. Thesedataarethefullyrevisedversion ofaseriesatagivenpointintime. Forexample,toforecastGDPgrowthfor2000Q1,weestimate modelsusingthelatest-reviseddataavailableasof1999Q4. ToforecastGDPgrowthfor2000Q2, we estimate models using the latest-revised data available as of 2000 Q1, and so on. Because of the practice of US statistical agencies of continually revising previously published estimates, the olderdatapointsinEOSdatahaveundergonemorerevisionsthanmorerecentdatapoints. For the second class of data, we estimate models on real-time vintage (RTV) data, a time series of datapoints where each datapoint has undergone the same number of data revisions. For example,toestimatethethird-release(twice-revised)estimateofGDPgrowthfor2000Q1usinga univariatemodelinGDPwithRTVdata,theright-handsideobservationsconsistofonlyprevious third-release (twice-revised) estimates of GDP growth. In contrast with EOS data, older RTV datapointshaveundergonetheidenticalnumberofdatarevisionsasthenewerdatapoints.4 WefindthatGreenbookforecastssignificantlyoutperformourbenchmarkforecastsinthevery near term, typically for forecast horizons within one quarter. This performance carries through whether we measure performance by RMSE, MAE, or MDE. However, by the one-year forecast horizon, typically at least one of our forecasting benchmarks performs as well as Greenbook fore- 3Estimatingmodelsusingcurrent-vintagedata,thefullyrevisedversionsofdatathatareavailabletoday,canskew theforecastingperformanceofmodelswithinformationnotavailabletoforecastersatthetimeforecastswereactually generated (Koenig, Dolmas, and Piger, 2003; Reifschneider and Tulip, 2007; Tulip, 2009; Clements and Galvão, 2013). 4Thethird-release(twice-revised)estimateisalsocalledthe“final”estimate. 3

casts. There is some sector heterogeneity of forecast performance. The Greenbook forecasts of the unemployment rate and personal consumption expenditures (PCE) tend to outperform our benchmarksforlongerforecasthorizons. TheGreenbookforecastsofthechangeinbusinessinventories, core PCE inflation, and government spending tend to perform similarly to or are outperformed by ourbenchmarksatshorterforecasthorizons. 2 Data and Sample Frame We obtain historical unemployment rates and NIPA data from the St. Louis Federal Reserve’s archival database (ALFRED). In addition to analyzing total GDP, we also consider PCE, nonresidential private fixed investment (NRPFI), residential private fixed investment (RES), government expenditures (GOV), change in business inventories (CBI), exports, imports, and core PCE inflation. Most NIPA series are quarterly and the Greenbook contains forecasts on a quarterly basis. For core PCE inflation and unemployment, where data are available monthly, we convert monthly variablestoquarterlyvariablesbyaveragingmonthlyvalues. WeuseGreenbookforecastsfrom1997to2008(1997istheearliestfullyearinwhichallseries are available, and 2008 is the latest year of Greenbook forecasts that have been made public as of this writing). Greenbook forecasts are available from the publicly available Domestic Economic DevelopmentsandOutlooktextsontheFederalReserveBoard’swebsite(FederalReserveBoard, 2014). Because Greenbooks are published at irregular intervals that do not correspond directly to calendar months or quarters, we use the final Greenbook released in each quarter. We estimate our benchmark forecasts using the vintage data series as of the Greenbook’s day of release, giving equal information sets to both our benchmark forecasts and the Greenbook releases. Our estimation sample period begins in the first quarter of 1986, a year that succeeds most estimates for the beginning of the “great moderation” and falls just after a NIPA benchmark revision at the end of 4

1985. We use real seasonally adjusted annual percent changes for all series except for business inventories,whereweuseannualizedrealseasonallyadjustedfirst-differences,andtheunemploymentrate,whereweuselevels. WechoosetheseunitstomatchGreenbookforecasts. To compute loss functions, for GDP and its components we take then Bureau of Economic Analysis’s(BEA)third-release(twice-revised)estimateastheforecastingtarget. Forthelossfunctions for core PCE inflation and the unemployment rate, we use the quarterly average computed whenthelastmonthofdataforthequarterisfirstavailable.5 Theresultsarelargelyrobusttousing the December 2014 vintage of data as the forecasting target. Table 1 shows summary statistics of ourdata. 3 Comparison Models To establish a relevant comparison between Greenbook forecasts and univariate forecasts, we first estimatethreenaïvebenchmarkforecasts: thehistoricalmean,arandomwalk,andaAR(1)model. Letybeourvariableofinterestandyˆbeaforecastofyfromaparticularmodel. Therandomwalk isspecifiedas: y =y +ε (1) t t−1 t such that the forecast for each horizon is equal to the last observed value, which we take as the observed value two quarters prior to the Greenbook publication quarter.6 We specify the AR(1) modelwithaconstant: y =α+βy +ε (2) t t−1 t For our final benchmark, we construct a Bayesian model averaged (BMA) forecast. We use 5MonthlyestimatesofcorePCEinflationandtheunemploymentrateareavailableinthesubsequentmonth.Therefore, this procedure yields quarterly averages computed with the core PCE inflation and unemployment releases in January,April,July,andOctober. 6TwoquarterspriortopublicationisthefirstquarterwheretheBEAhaspublisheditsthird-release(twice-revised) estimateforthequarterforeveryGreenbookinthesample. 5

Bayesian weights over 43 univariate forecasting models, using the Schwarz Bayesian Information Criterion(SBIC)approximationforthelogmarginallikelihoodproposedbyRaftery(1995). TheBMAforecasty¯isrepresentedas: N y¯ = ∑yˆ Pr(M |y) (3) t i,t i i=1 wherePr(M |y)representstheprobabilitythatmodeliistruegiventhedata. Thisprobabilitycan i beapproximatedusingtheSBICsuchthat: eSBIC iPr(M) i Pr(M |y)= (4) i ∑ N i=1 eSBIC iPr(M i ) where Pr(M) represents the prior model probability for model i. For our weighted forecast, we i assign equal prior probability to all 43 model specifications, so Pr(M) = 1/43 ∀i = 1...43. Foli lowing Morley and Piger (2012), we compute the SBIC using the specification in Davidson and MacKinnon(2004): N N i k SBIC =− i log(∑(y −yˆ )2)− i log(N) (5) i t i,t i 2 2 t=1 where N is the number of observations and k is the number of parameters. For our BMA forecast, weconsiderARmodelsofordersonethroughtwelve: p y =α+∑ρy +ε , p=1..12 (6) t i t−i t i=1 Wealsoweightoverforecastsfrommoving-average(MA)modelsofordersonethroughtwelve: q y =α+ ∑θ ε +ε , q=1..12 (7) t j t−j t j=1 Wealsoweightoverautoregressivemoving-average(ARMA)models,againwithordersonethrough twelve,wherethenumberofARcomponentsequalsthenumberofMAcomponents: 6

p q y =α+∑ρy + ∑θ ε +ε , p=1..12, q=1..12, p=q (8) t i t−i j t−j t i=1 j=1 Together, equations (6) through (8) encompass a variety of specifications of basic AR, MA, and ARMAmodelsthatmightcharacterizeaforecastedseries. Beyondthesethreetypesofmodels,we consider two simple specifications of an unobserved components model, as described by Harvey (1989). Both specifications assume a first-order cyclical component and exclude a trend component. While the Bureau of Economic Analysis (BEA) seasonally adjusts quarterly NIPA series, some residual seasonal variation may remain, so we try versions with and without a quarterly seasonalcomponent. Thespecificationwithaseasonalcomponentis: s−1 y = ∑γ +ψ +ε , s=4 (9) t t−j t t j=1 We consider several specifications of autoregressive conditional heteroskedasticity (ARCH) and generalized autoregressive conditional heteroskedasticity (GARCH) models, with different lags,autoregressiveterms,andin-meanARCHterms: p q y =α+∑ρy + ∑φ σ2 +ε (10) t i t−i j t−j t i=1 j=0 wheretheerrortermofequation(10)containsARCHandGARCHterms: r s Var(ε )=γ + ∑α ε2 + ∑ α σ2 (11) t 0 1,k t−k 2,m t−m k=1 m=1 We specify three variants of equations (10) and (11): p = 4, q = 2, r = 2, s = 2; p = 0, q = 2, r = 2,s=1;andp=1,q=1,r=1,s=1. Thefinalsetofmodelscontainssingle-anddouble-exponentialsmoothedforecasts(Chatfield, 2001). Thesingle-exponentialforecastestimatesamodelwithasinglesmoothingparameter: yˆ =αy +(1−α)yˆ (12) t t−1 t−1 7

The double-exponential version applies the smoothing process of equation (12)’s once-smoothed series. Weestimateallmodelswithmaximumlikelihood. WeexcludemodelforecastsfromtheBMA forecast that give an implied annual growth rate outside of [-400%, 400%] to avoid skewing the BMAforecasttowardsanyonespecificmodel. 4 Results 4.1 RMSEs and MAEs Using End-of-Sample Vintage Data, Fixed Sample Figures 1 and 2 plot RMSEs of Greenbook forecasts and our forecasting benchmarks estimated on EOS vintage data, with the sample starting in 1986 Q1. We normalize the forecasting RMSEs relativetotherandom-walkRMSEsfollowingHyndmanandKoehler(2006),soanumbergreater than one indicates a RMSE worse than the random walk. The horizontal axis denotes the forecast horizon relative to the quarter the forecast is made, so t = 0 indicates a forecast of the current quarter. The Greenbook forecasts tend to significantly outperform all four of our benchmark forecasts for t = −1 and t = 0. This result is consistent with earlier evidence that Federal Reserve Board forecasters take considerable lengths to replicate the procedures of national statistical agencies’ upcomingdatareleases(FaustandWright,2009;Baghestani,2011). However, even by the one-quarter ahead forecast horizon (t =1), the relative forecast performanceoftheGreenbookdecreasessubstantially. TheGreenbookforecastsofgovernmentspending are comparable with the AR(1), historical mean, and BMA forecasting benchmarks att =1 while Greenbook forecasts of PCE perform comparably with the BMA forecasting benchmark at t =1 but outperform the AR(1), random walk, and historical mean. The Greenbook forecast accuracy ofGDPiscomparabletoourbenchmarksbyt =2. By the one-year forecast horizon (t =4), the RMSEs of the Greenbook forecasts are comparable with at least one of our benchmarks for all sectors except the unemployment rate, where 8

the Greenbook forecasts tend to do quite well against our benchmarks for the entire eight quarter forecast horizon. Greenbook forecasts of core PCE inflation are outperformed by the AR(1) and BMAforforecasthorizonsgreaterthanoneyear. Figures 3 and 4 display MAEs of Greenbook forecasts and our forecasting benchmarks, again estimatedwithEOSdatawiththesamplestartingin1986Q1. Theresultsarelargelysimilartothe RMSE results in Figures 1 and 2. The Greenbook outperforms the benchmarks in the short term across all sectors, but by the one-year forecast horizon the performance is comparable between the Greenbook and our benchmarks. For horizons longer than one year the Greenbook core PCE inflationforecastsareoutperformedbyourbenchmarks.7 4.2 RMSEs Using Real-Time Vintage Data, Fixed Sample Figures 5 and 6 show the results with our forecasting benchmarks estimated with RTV data, as opposed to EOS data. For GDP and its components, we use a time-series of BEA third-release (twice-revised) estimates as our RTV data whenever possible.8 The RTV results are similar when we use a time-series of BEA first-release (never revised) or second-release (once-revised) data. ForcorePCEinflationandtheunemploymentrate,ourRTVseriesisquarterlyaveragescomputed whenthelastmonthofdataforthequarterisfirstavailable. The results from Figures 5 and 6 are largely similar to the results estimated on EOS data. For GDP and its components, the use of RTV data tends to worsen the RMSE of the BMA forecast relativetotherandomwalk. However,forcorePCEinflationRTVdataimprovestheBMAforecast relative to the random walk. The RMSEs of Greenbook forecasts are still comparable with at least one of our benchmarks by the one-year horizon except the unemployment rate, which still outperformsourbenchmarksfortheentireeightquarterforecasthorizon. 7MAEresultsarealwayssimilartotheRMSEresults,soweomitMAEresultsfortheremainderofthispaper. 8Fortheseseries,whenweforecastahorizonthatusesNIPAdatafromt =−1whenathirdreleaseestimatefor t=−1isunavailable,weusethelatestavailableNIPAreleasefort=−1. 9

4.3 RMSEs Using End-of-Sample Vintage Data, Rolling Sample The results so far all use a fixed sample start date of the first quarter of 1986. Figures 7 and 8 reestimate our benchmarks using a 40-quarter rolling sample, as opposed to the fixed sample start date. For example, the forecast for 1997 Q1 uses models estimated on data from 1986 Q1 to 1996 Q4. Theforecastfor1997Q2usesmodelsestimatedondatafrom1986Q2to1997Q1,andsoon. The results in Figures 7 and 8 are largely similar to Figures 1 and 2, although the BMA forecasts tendstoperformmorepoorlyatlongerhorizonsusingthe40-quarterrollingsample. 4.4 MDE Using End-of-Sample Vintage Data, Fixed Sample As a final method of evaluation, we check to see whether Greenbooks accurately forecast differences in growth rates, following Baghestani (2011). For each forecast horizon, we compute the differenceingrowthratesrelativetot =−2,whichisboththefirstquarterwherewehaveathirdreleaseNIPAseriesineveryGreenbookandthemostrecentquarterforwhichtheFederalReserve staff does not prepare a Greenbook forecast. We define mean directional error (MDE) as the proportion of forecasts where the sign of the predicted difference in growth rates was incorrect, so highervaluesofMDEindicateworseforecastperformance.9 Figures9and10showourresultsfromtheMDEmeasureofaccuracy. WenormalizetheMDE relative to the MDE for the historical mean and omit the random walk, because the random walk forecastalwaysimpliesnoaccelerationordeceleration.10 Figures 9 and 10 confirm that the Greenbook MDE outperforms our forecasting benchmarks for very short horizons. Much like the results for the RMSEs and MAEs, by approximately the one-year horizon, typically Greenbook MDEs are comparable with at least one of our forecasting benchmarks. The Greenbook MDEs for core PCE inflation, exports, change in business inventories, government spending, and residential investment are worse than at least one benchmark by 9The unemployment rate is still in levels and change in business inventories is still in first-differences, so we computefirst-differencesandsecond-differences,respectively,forthesetwocategories. 10For forecasts in growth rates, the random walk predicts constant growth (no acceleration or deceleration of the growthrate),sotheimpliedeffectonthelevelisanacceleration. 10

the two-quarter forecast horizon. Notably, the Greenbook MDEs for nonresidential investment, PCE,andimportscomparequitefavorablytoourbenchmarks. 5 Conclusion This paper compares Greenbook forecasts of the unemployment rate, core PCE inflation, GDP, and the major components of GDP to forecasts from several simple univariate benchmarks. The primarycontributionofthispaperistoanalyzeawiderrangeofGreenbookprojectionsinaunified frameworkthanpreviousstudies. We find that Greenbook forecasts generally outperform our simple benchmarks in the very short forecasting horizon. However, typically by the one-year forecast horizon, the accuracy of Greenbook forecasts is comparable with or worse than at least one of our benchmarks. These results hold whether we measure forecast accuracy as RMSE, MAE, or MDE. These results are consistent with earlier evidence that Greenbook forecasts carefully attempt to replicate the data release procedures of US statistical agencies, such as taking into account leading indicators that the BEA uses in constructing GDP, which gives Greenbook forecasts high short-term accuracy (FaustandWright,2009). One caveat to our analysis is that we treat Greenbook forecasts as unconditional forecasts, comparing the forecasts to the unconditional forecasts generated from our benchmark models. However, in practice the Greenbook forecasts are conditioned on an exogenous path for policy. Explicitly taking into account the conditional nature of Greenbook forecasts may either improve ordiminishtheirmeasuredaccuracy. References 11

Arai, Natsuki, “Using Forecast Evaluation to Improve the Accuracy of the Greenbook Forecast,” InternationalJournalofForecasting30:1(2014),12-19. Baghestani, Hamid, “Federal Reserve and Private Forecasts of Growth in Investment,” Journal of EconomicsandBusiness63:4(2011),290-305. Chatfield,Chris,Time-SeriesForecasting,London: Chapman&Hall/CRC(2001). Clements, Michael P., and Ana Beatriz Galvão, “Real-Time Forecasting of Inflation and Output Growth With Autoregressive Models in the Presence of Data Revisions,” Journal of Applied Econometrics28:3(2013),458-477. Davidson, Russell, and James G. MacKinnon, Econometric Theory and Methods, New York: OxfordUniversityPress(2004). Faust, Jon, and Jonathan H. Wright, “Comparing Greenbook and Reduced Form Forecasts Using aLargeRealtimeDataset,”JournalofBusiness&EconomicStatistics27:4(2009),468-479. FederalReserveBankofSt.Louis.ALFRED.alfred.stlouisfed.org.VariousAccessDates. Federal Reserve Board. Federal Open Market Committee. Transcripts and Other Historical Materials.www.federalreserve.gov/monetarypolicy/fomc_historical.htm.VariousAccessDates. Harvey,AndrewC.,Forecasting,StructuralTimeSeriesModelsandtheKalmanFilter.Cambridge: CambridgeUniversityPress(1989). Hyndman,RobJ.,andAnneB.Koehler,“AnotherLookatMeasuresofForecastAccuracy,”InternationalJournalofForecasting22:4(2006),679-688. Koenig, Evan F., Sheila Dolmas, and Jeremy Piger, “The Use and Abuse of Real-Time Data in EconomicForecasting,”ReviewofEconomicsandStatistics85:3(2003),618-628. Morley, James, and Jeremy Piger, “The Asymmetric Business Cycle,” Review of Economics and Statistics94:1(2012),208-221. 12

Raftery,AdrianE.,“BayesianModelSelectioninSocialResearch,”SociologicalMethodology25 (1995),111-163. Reifschneider, David, and Peter Tulip, “Gauging the Uncertainty of the Economic Outlook From HistoricalForecastingErrors,”FEDSWorkingPaper2007-60(2007). Romer, Christina D., and David H. Romer, “Federal Reserve Information and the Behavior of InterestRates,”AmericanEconomicReview90:3(2000),429-457. Tulip, Peter, “Has the Economy Become More Predictable? Changes in Greenbook Forecast Accuracy”,JournalofMoney,CreditandBanking41:6(2009),1217-1231. Wright, Jonathan H., “Forecasting US Inflation by Bayesian Model Averaging,” Journal of Forecasting28:2(2009),131-144. 13

Figure1: RMSEsUsingEnd-of-SampleVintages,FixedSample GDP Nonresidential investment RMSE RMSE 1.4 1.2 1.2 1.0 1.0 0.8 0.8 0.6 0.6 0.4 Staff forecast 0.4 AR(1) forecast Model-averaged forecast 0.2 0.2 Historical mean 0.0 0.0 -1 0 120152 3 4 520166 7 8 -1 0 120152 3 4 520166 7 8 Forecast horizon Forecast horizon Residential investment PCE RMSE RMSE 2.0 1.4 1.2 1.5 1.0 0.8 1.0 0.6 0.4 0.5 0.2 0.0 0.0 -1 0 120152 3 4 520166 7 8 -1 0 120152 3 4 520166 7 8 Forecast horizon Forecast horizon Government spending Imports RMSE RMSE 1.4 1.2 1.2 1.0 1.0 0.8 0.8 0.6 0.6 0.4 0.4 0.2 0.2 0.0 0.0 -1 0 120152 3 4 520166 7 8 -1 0 120152 3 4 520166 7 8 Forecast horizon Forecast horizon Root mean squared errors (RMSEs) normalized relative to the RMSE for the random walk for each forecast horizon-sector (Hyndman and Koehler, 2006). The horizontal axis denotes the horizon relative to when the forecast is made. Shaded area indicates the RMSEs of the Greenbook forecast calculated with the 68th percentile of Greenbook forecast errors, centered on the Greenbookforecast. 14

Figure2: RMSEsUsingEnd-of-SampleVintages,FixedSample(Continued) Exports Change in private inventories RMSE RMSE 1.4 1.4 1.2 1.2 1.0 1.0 0.8 0.8 0.6 0.6 Staff forecast 0.4 0.4 AR(1) forecast Model-averaged forecast 0.2 0.2 Historical mean 0.0 0.0 -1 0 120152 3 4 520166 7 8 -1 0 120152 3 4 520166 7 8 Forecast horizon Forecast horizon Unemployment rate Core PCE inflation RMSE RMSE 5 1.6 1.4 4 1.2 3 1.0 0.8 2 0.6 1 0.4 0 0.2 -1 0 120152 3 4 520166 7 8 -1 0 120152 3 4 520166 7 8 Forecast horizon Forecast horizon Root mean squared errors (RMSEs) normalized relative to the RMSE for the random walk for each forecast horizon-sector (Hyndman and Koehler, 2006). The horizontal axis denotes the horizon relative to when the forecast is made. Shaded area indicates the RMSEs of the Greenbook forecast calculated with the 68th percentile of Greenbook forecast errors, centered on the Greenbookforecast. 15

Figure3: MAEsUsingEnd-of-SampleVintages,FixedSample GDP Nonresidential investment MAE MAE 1.6 1.4 1.4 1.2 1.2 1.0 1.0 0.8 0.8 0.6 0.6 Staff forecast 0.4 0.4 AR(1) forecast Model-averaged forecast 0.2 0.2 Historical mean 0.0 0.0 -1 0 120152 3 4 520166 7 8 -1 0 120152 3 4 520166 7 8 Forecast horizon Forecast horizon Residential investment PCE MAE MAE 2.5 1.5 2.0 1.0 1.5 1.0 0.5 0.5 0.0 0.0 -1 0 120152 3 4 520166 7 8 -1 0 120152 3 4 520166 7 8 Forecast horizon Forecast horizon Government spending Imports MAE MAE 1.5 1.4 1.2 1.0 1.0 0.8 0.6 0.5 0.4 0.2 0.0 0.0 -1 0 120152 3 4 520166 7 8 -1 0 120152 3 4 520166 7 8 Forecast horizon Forecast horizon Mean absolute errors (MAEs) normalized relative to the MAE for the random walk for each forecasthorizon-sector(HyndmanandKoehler,2006). Thehorizontalaxisdenotesthehorizonrelative to when the forecast is made. Shaded area indicates the MAEs of the Greenbook forecast calculatedwiththe68thpercentileofGreenbookforecasterrors,centeredontheGreenbookforecast. 16

Figure4: MAEsUsingEnd-of-SampleVintages,FixedSample(Continued) Exports Change in private inventories MAE MAE 1.4 1.5 1.2 1.0 1.0 0.8 0.6 0.5 Staff forecast 0.4 AR(1) forecast Model-averaged forecast 0.2 Historical mean 0.0 0.0 -1 0 120152 3 4 520166 7 8 -1 0 120152 3 4 520166 7 8 Forecast horizon Forecast horizon Unemployment rate Core PCE inflation MAE MAE 6 1.6 5 1.4 1.2 4 1.0 3 0.8 2 0.6 1 0.4 0 0.2 -1 0 120152 3 4 520166 7 8 -1 0 120152 3 4 520166 7 8 Forecast horizon Forecast horizon Mean absolute errors (MAEs) normalized relative to the MAE for the random walk for each forecasthorizon-sector(HyndmanandKoehler,2006). Thehorizontalaxisdenotesthehorizonrelative to when the forecast is made. Shaded area indicates the MAEs of the Greenbook forecast calculatedwiththe68thpercentileofGreenbookforecasterrors,centeredontheGreenbookforecast. 17

Figure5: RMSEsUsingReal-TimeVintages,FixedSample GDP Nonresidential investment RMSE RMSE 1.4 1.2 1.2 1.0 1.0 0.8 0.8 0.6 0.6 0.4 Staff forecast 0.4 AR(1) forecast Model-averaged forecast 0.2 0.2 Historical mean 0.0 0.0 -1 0 120152 3 4 520166 7 8 -1 0 120152 3 4 520166 7 8 Forecast horizon Forecast horizon Residential investment PCE RMSE RMSE 2.0 1.4 1.2 1.5 1.0 0.8 1.0 0.6 0.4 0.5 0.2 0.0 0.0 -1 0 120152 3 4 520166 7 8 -1 0 120152 3 4 520166 7 8 Forecast horizon Forecast horizon Government spending Imports RMSE RMSE 1.4 1.2 1.2 1.0 1.0 0.8 0.8 0.6 0.6 0.4 0.4 0.2 0.2 0.0 0.0 -1 0 120152 3 4 520166 7 8 -1 0 120152 3 4 520166 7 8 Forecast horizon Forecast horizon Root mean squared errors (RMSEs) normalized relative to the RMSE for the random walk for each forecast horizon-sector (Hyndman and Koehler, 2006). The horizontal axis denotes the horizon relative to when the forecast is made. Shaded area indicates the RMSEs of the Greenbook forecast calculated with the 68th percentile of Greenbook forecast errors, centered on the Greenbookforecast. 18

Figure6: RMSEsUsingReal-TimeVintages,FixedSample(Continued) Exports Change in private inventories RMSE RMSE 1.4 1.4 1.2 1.2 1.0 1.0 0.8 0.8 0.6 0.6 Staff forecast 0.4 0.4 AR(1) forecast Model-averaged forecast 0.2 0.2 Historical mean 0.0 0.0 -1 0 120152 3 4 520166 7 8 -1 0 120152 3 4 520166 7 8 Forecast horizon Forecast horizon Unemployment rate Core PCE inflation RMSE RMSE 5 1.6 1.4 4 1.2 3 1.0 0.8 2 0.6 1 0.4 0 0.2 -1 0 120152 3 4 520166 7 8 -1 0 120152 3 4 520166 7 8 Forecast horizon Forecast horizon Root mean squared errors (RMSEs) normalized relative to the RMSE for the random walk for each forecast horizon-sector (Hyndman and Koehler, 2006). The horizontal axis denotes the horizon relative to when the forecast is made. Shaded area indicates the RMSEs of the Greenbook forecast calculated with the 68th percentile of Greenbook forecast errors, centered on the Greenbookforecast. 19

Figure7: RMSEsUsingEnd-of-SampleVintages,40-QuarterRollingSample GDP Nonresidential investment RMSE RMSE 1.4 1.2 1.2 1.0 1.0 0.8 0.8 0.6 0.6 0.4 Staff forecast 0.4 AR(1) forecast Model-averaged forecast 0.2 0.2 Historical mean 0.0 0.0 -1 0 120152 3 4 520166 7 8 -1 0 120152 3 4 520166 7 8 Forecast horizon Forecast horizon Residential investment PCE RMSE RMSE 2.0 1.4 1.2 1.5 1.0 0.8 1.0 0.6 0.4 0.5 0.2 0.0 0.0 -1 0 120152 3 4 520166 7 8 -1 0 120152 3 4 520166 7 8 Forecast horizon Forecast horizon Government spending Imports RMSE RMSE 1.4 1.2 1.2 1.0 1.0 0.8 0.8 0.6 0.6 0.4 0.4 0.2 0.2 0.0 0.0 -1 0 120152 3 4 520166 7 8 -1 0 120152 3 4 520166 7 8 Forecast horizon Forecast horizon Root mean squared errors (RMSEs) normalized relative to the RMSE for the random walk for each forecast horizon-sector (Hyndman and Koehler, 2006). The horizontal axis denotes the horizon relative to when the forecast is made. Shaded area indicates the RMSEs of the Greenbook forecast calculated with the 68th percentile of Greenbook forecast errors, centered on the Greenbookforecast. 20

Figure8: RMSEsUsingEnd-of-SampleVintages,40-QuarterRollingSample(Continued) Exports Change in private inventories RMSE RMSE 1.4 1.4 1.2 1.2 1.0 1.0 0.8 0.8 0.6 0.6 Staff forecast 0.4 0.4 AR(1) forecast Model-averaged forecast 0.2 0.2 Historical mean 0.0 0.0 -1 0 120152 3 4 520166 7 8 -1 0 120152 3 4 520166 7 8 Forecast horizon Forecast horizon Unemployment rate Core PCE inflation RMSE RMSE 5 1.6 1.4 4 1.2 3 1.0 0.8 2 0.6 1 0.4 0 0.2 -1 0 120152 3 4 520166 7 8 -1 0 120152 3 4 520166 7 8 Forecast horizon Forecast horizon Root mean squared errors (RMSEs) normalized relative to the RMSE for the random walk for each forecast horizon-sector (Hyndman and Koehler, 2006). The horizontal axis denotes the horizon relative to when the forecast is made. Shaded area indicates the RMSEs of the Greenbook forecast calculated with the 68th percentile of Greenbook forecast errors, centered on the Greenbookforecast. 21

Figure9: MDEsUsingEnd-of-SampleVintages,FixedSample GDP Nonresidential investment MDE MDE 3.0 3.0 Staff forecast AR(1) forecast 2.5 2.5 Model-averaged forecast Historical mean 2.0 2.0 1.5 1.5 1.0 1.0 0.5 0.5 0.0 0.0 -1 0 120152 3 4 520166 7 8 -1 0 120152 3 4 520166 7 8 Forecast horizon Forecast horizon Residential investment PCE MDE MDE 2.5 3.5 3.0 2.0 2.5 1.5 2.0 1.5 1.0 1.0 0.5 0.5 0.0 0.0 -1 0 120152 3 4 520166 7 8 -1 0 120152 3 4 520166 7 8 Forecast horizon Forecast horizon Government spending Imports MDE MDE 2.5 3.0 2.5 2.0 2.0 1.5 1.5 1.0 1.0 0.5 0.5 0.0 0.0 -1 0 120152 3 4 520166 7 8 -1 0 120152 3 4 520166 7 8 Forecast horizon Forecast horizon Mean directional errors (MDEs) normalized relative to the MDE for the historical mean for each forecast horizon-sector. The horizontal axis denotes the horizon relative to when the forecast is made. 22

Figure10: MDEsUsingEnd-of-SampleVintages,FixedSample(Continued) Exports Change in private inventories MDE MDE 3.0 2.0 Staff forecast AR(1) forecast 2.5 Model-averaged forecast 1.5 Historical mean 2.0 1.5 1.0 1.0 0.5 0.5 0.0 0.0 -1 0 120152 3 4 520166 7 8 -1 0 120152 3 4 520166 7 8 Forecast horizon Forecast horizon Unemployment rate Core PCE inflation MDE MDE 1.4 1.2 1.2 1.1 1.0 1.0 0.8 0.9 0.6 0.8 0.4 0.7 0.2 0.6 0.0 0.5 -1 0 120152 3 4 520166 7 8 -1 0 120152 3 4 520166 7 8 Forecast horizon Forecast horizon Mean directional errors (MDEs) normalized relative to the MDE for the historical mean for each forecast horizon-sector. The horizontal axis denotes the horizon relative to when the forecast is made. 23

Table1: SummaryStatistics VintageofData Variable Mean Standard Minimum Maximum Deviation End-of-sample, GDP 2.89 2.06 -2.98 7.48 December2008 Consumption 3.12 1.99 -3.74 7.12 Greenbook NonresidentialInvestment 4.55 7.95 -13.57 22.10 ResidentialInvestment 1.31 11.55 -27.01 24.15 GovernmentSpending 2.01 3.20 -4.48 9.43 Exports 7.31 7.91 -18.18 27.36 Imports 6.45 7.37 -12.62 18.04 BusinessInventories -0.71 29.74 -76.60 76.50 UnemploymentRate 5.53 0.94 3.90 7.63 CorePCEInflation 2.53 1.08 0.84 5.37 Real-time GDP 2.99 2.09 -2.79 8.20 Consumption 3.17 1.99 -3.39 7.74 NonresidentialInvestment 5.99 8.74 -16.30 26.74 ResidentialInvestment 1.77 11.77 -25.33 31.66 GovernmentSpending 1.74 3.91 -8.31 16.68 Exports 7.33 8.94 -18.76 30.79 Imports 7.21 8.10 -12.99 22.31 BusinessInventories -1.33 27.02 -74.90 91.60 UnemploymentRate 5.53 0.94 3.90 7.63 CorePCEInflation 2.59 1.10 1.05 5.36 Unemployment rate is in levels. Inventories is in real first-differenced billions of dollars seasonally adjusted at an annual rate. All other variables are in real seasonally adjusted annual percent changes. Real-timedataforgrossdomesticproduct(GDP)anditscomponentsaretheBEA’sthirdreleasetwice-revised(“final”)releaseasoftheDecember2008Greenbook. Real-timedataforthe unemployment rate and core personal consumption expenditures (PCE) inflation are quarterly averagescomputedwhenthelastmonthofdataforthequarterisfirstavailable. 24