Improving the Accuracy of Economic Measurement with Multiple Data Sources: The Case of Payroll Employment Data

Finance and Economics Discussion Series Divisions of Research & Statistics and Monetary Affairs Federal Reserve Board, Washington, D.C. Improving the Accuracy of Economic Measurement with Multiple Data Sources: The Case of Payroll Employment Data Tomaz Cajner, Leland D. Crane, Ryan A. Decker, Adrian Hamins-Puertolas, and Christopher Kurz 2019-065 Please cite this paper as: Cajner, Tomaz, Leland D. Crane, Ryan A. Decker, Adrian Hamins-Puertolas, and Christopher Kurz (2019). “Improving the Accuracy of Economic Measurement with Multiple Data Sources: The Case of Payroll Employment Data,” Finance and Economics Discussion Series 2019-065. Washington: Board of Governors of the Federal Reserve System, https://doi.org/10.17016/FEDS.2019.065. 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.

Improving the Accuracy of Economic Measurement with Multiple Data Sources: The Case of Payroll Employment Data TomazCajner LelandD.Crane RyanA.Decker ∗ AdrianHamins-Puertolas ChristopherKurz August30,2019 Abstract ThispapercombinesinformationfromtwosourcesofU.S.privatepayrollemploymenttoincrease theaccuracyofreal-timemeasurementofthelabormarket.ThesourcesaretheCurrentEmployment Statistics(CES)fromBLSandmicrodatafromthepayrollprocessingfirmADP.Webrieflydescribe theADP-deriveddataseries, compareittotheBLSdata, anddescribeanexercisethatbenchmarks thedataseriestoanemploymentcensus. TheCESandtheADPemploymentdataareeachderived fromroughlyequal-sizedsamples. WearguethatcombiningCESandADPdataseriesreducesthe measurementerrorinherentinbothdatasources. Inparticular,weinfer“true”unobservedpayroll employmentgrowthusingastate-spacemodelandfindthattheoptimalpredictoroftheunobserved stateputsapproximatelyequalweightontheCESandADP-derivedseries. Moreover,theestimated statecontainsinformationaboutfuturereadingsofpayrollemployment. Keywords:labormarket,economicmeasurement,bigdata,state-spacemodels. JELClassification:J2,J11,C53,C55,C81. ∗All authors are at the Federal Reserve Board of Governors. We thank ADP for access to and help with the payroll microdata that underlie the work described by this paper. In particular, this work would not have been possiblewithoutthesupportofJanSiegmund,AhuYildirmaz,andSinemBuber. Wearegratefulfordiscussions withKatharineAbraham, Borag˘anAruoba, SimonFreyaldenhoven, ErikHurst, GrayKimbrough, AlanKrueger, NormanMorin,MatthewShapiro,JohnStevens,DavidWilcox,MarkZandi,andseminarparticipantsattheFederal Reserve Board, the Federal Reserve Bank of Cleveland, ESCoE Conference on Economic Measurement, the BLS, NBERCRIWmeetings,theBankofEngland,andthe2018ASSAmeetings. Theanalysisandconclusionssetforth herearethoseoftheauthorsanddonotindicateconcurrencebyothermembersoftheresearchstaffortheBoardof Governors.

1 Introduction Economistsandstatisticiansareincreasinglyconfrontedwithnewdatasources,oftenproduced byprivatecompaniesaspartoftheirbusinessoperations,thatmaybeusefulforeconomicresearchandmeasurement. Thesenewdataholdpromiseforadvancingeconomicmeasurement andunderstanding,buttheiruseraisesmanyquestions. Howarenew,alternativedatadifferentfromtraditionalsurveysandcensuses? Howarewetoassesstheirreliability? Howshould multipledisparatedatasourcesbesynthesizedtoproducethebestpossibleestimates? We seek to answer these questions in the context of measuring payroll employment. In particular,weusedatafromaprivatepayrollprovider—ADP—tobuildanindexofU.S.private payrollemployment,similarinspirittotheCurrentEmploymentStatistics(CES)survey. While theCESsurveyiscarefullyconductedandusesanextremelylargesample,itstillsuffersfrom significantsamplingerrorandnonresponseissues. TheADP-derivedemploymentindexesare basedonasamplethatisroughlythesamesizeastheCESsample,soitisplausiblethatpooling the information from ADP with that from CES would reduce sampling error and increase our understandingofthestateofthelabormarketatagiventime. PreviousworkbyCajneretal.(2018)describestheconstructionofweeklyandmonthlyaggregate employment series based on ADP’s weekly payroll microdata. Their aggregate series (referred to as ADP-FRB) are designed to be an independent signal about labor market conditions rather than solely an attempt to forecast monthly BLS employment figures. However, Cajneretal.(2018)doindeedfindthatthetimelinessandfrequencyoftheADPpayrollmicrodataimprovesforecastaccuracyforbothcurrent-monthemploymentandrevisionstotheBLS CESdata. InthispaperwefurthercomparetheADP-FRBindextoexisting,high-qualitygovernment estimatesandfindencouragingresults. TheADP-FRBindex,andstate-spaceestimatesderived from it, provide information about future CES estimates in real time, including at the start of the Great Recession. In addition, we integrate benchmark employment data and compare the ADP-FRB benchmark revisions with the CES benchmark revisions. While the CES and ADP- FRB series are both prone to significant sampling and non-sampling error, the BLS Quarterly CensusofEmploymentandWages(QCEW)isgenerallyconsideredthe“finalword”forannual 1

employment growth because of its comprehensive administrative source data. Consequently, we benchmark the ADP-based series to the QCEW on an annual basis. The benchmarking procedureissimilartoCESbenchmarkingandensuresthatyear-to-yearchangesinADP-FRB are governed by the QCEW, while higher-frequency changes, and the period after the most recentbenchmark,aremostlyafunctionoftheADPdata.1 Existing work on using nontraditional data sources for economic measurement typically takes official government data as the source of truth, at all frequencies. For example, the monthly National Employment Report (ADP-NER) series published by ADP are constructed with the goal of predicting the fully revised CES data.2 In this paper we take a different approachbyrecognizingthatbothCESandADP-FRBemploymentaresubjecttonon-negligible measurement error and by using the Kalman filter to extract estimates of unobserved “true” employmentgrowthfromobservationsofbothseries. OurbaselinemodelassumesthattrueU.S.employmentgrowthfollowsapersistent,latent processandthatboththeCESandADP-FRBestimatesarenoisysignalsofthisunderlyingprocess. Standardstate-spacetoolsallowustoestimatethelatentprocessandtheobservationerror associated with each series. We find that the optimal predictor of the unobserved state, using only contemporaneous information, puts approximately equal weight on the CES and ADP- FRB series. This finding is not necessarily surprising, as the ADP sample covers roughly the samefractionofprivatenonfarmU.S.employmentastheCESsample(about20percent),sothe sampling errors ought to be of roughly similar magnitudes. We also show that the smoothed stateestimate,asconstructedinrealtime,helpsforecastfuturevaluesofCES.Throughout,we focus on the role of these privately generated data as a complement to existing official statistics. Whilethereisnosubstituteforofficialstatisticsintermsofconsistency,transparency,and scientificcollectionmethods,officialnumbersdohavelimitationsthatalternativedatasources canaddress. Thepaperproceedsasfollows. Section2reviewstherelatedliterature. Section3describes theprocessofcreatingADP-basedemploymentindexesandlaysoutthestrengthsandthein- 1Benchmarkingillustratesanessentialrolethatgovernmentstatisticsplayevenwhenthereissignificantvalue innontraditionaldatasources. 2Mastercard’sSpendingPulse,whichattemptstoforecastU.S.retailsales,isanotherexample. 2

herent limitations of measuring nationwide payroll employment with ADP data. In section 4 we compare the annual ADP-FRB employment estimates to the official benchmarks, discuss the role of the birth-death model in the official estimates, present a case study of the usefulness of alternative employment data during the Great Recession, and show the efficacy of the ADP-FRB estimates in predicting fully revised CES payroll employment numbers. Section 5 introduces the state-space model that combines the information from both the ADP-FRB and CES-basedestimatesandprovidesevidencethatthecombinedstateimprovesourunderstandingofcurrentandfuturepayrollgains. Section6concludes. 2 Related Literature OursisnotthefirstpapertomakeuseofADPpayrolldata. SeveralpapersstudytheNational Employment Report (NER), ADP’s publicly available monthly estimate of U.S. payroll gains constructed jointly with Moody’s Analytics. Importantly, NER estimates are derived from a modelincludingnotonlyADPmicrodatabutalsoothercontemporaneousandlaggedindicators of U.S. economic activity. The existing literature finds that the NER moves closely with CES (Phillips and Slijk, 2015) and has some ability to forecast CES, though it does not appear toimproveforecastsbasedonotheravailableinformation,suchasexistingconsensusforecasts (GregoryandZhu,2014;Hatziusetal.,2016). As noted above, we do not use the NER but instead focus on the ADP microdata. A number of recent papers explore these data. Cajner et al. (2018) analyze the representativeness of ADPmicrodata(relativetoCESandQCEW)andconstructanADPpayrollindexthatcanimprove forecasts of CES; we employ that index in the present paper. Ozimek, DeAntonio and Zandi (2017) use ADP’s linked employer-employee microdata to study the negative effect of workforceagingonaggregateproductivitygrowth. Grigsby,HurstandYildirmaz(2019)study wage rigidity in the same data, finding that the high-frequency microdata can be useful for shedding light on a key business cycle question. Cho (2018) uses ADP microdata to study the employmentandwageeffectsofthe2009AmericanRecoveryandReinvestmentAct. Ourapproachinthepresentpaperisdifferentfromthoseaboveinthatweexplicitlyinves- 3

tigate the usefulness of ADP as a supplement to CES data for tracking the underlying state of thelabormarket. Inthisrespect,ourworkisinspiredbyAruobaetal.(2016)whonotedifficulties in assessing the growth of aggregate output in real time given limitations on the comprehensiveness and timeliness of GDP measures. Two independent measures of GDP exist—the commonlyreportedexpenditure-sideapproachandtheincome-basedapproach—andbothare prone to measurement errors arising from various sources. Aruoba et al. (2016) combine the twomeasuresusingastate-spaceframework,recoveringanunderlyingstateofoutputgrowth which they label “gross domestic output”. We follow this general approach with a focus on employmentratherthanoutput. 3 Data Thispaperprimarilyusesthreedatasources: ADPmicrodata,theCurrentEmploymentStatistics(CES)survey,andtheQuarterlyCensusofEmploymentandWages(QCEW).BeforeturningtotheADPmicrodatainSection3.1,itisusefultobrieflylayouttherelevantfeaturesofthe CESandtheQCEW. TheCESisthemainsourceofmonthlyemploymentinformationintheUnitedStates. Itis publishedbytheBLSafewdaysaftereachreferencemonthandisbasedonastratified-sample surveyofabout500,000privateestablishmentscovering23percentofallU.S.privateemployees.3 The CES asks each respondent for the count of employees who worked for pay in the payperiodincludingthe12thofthereferencemonth. AggregateCESemploymentgrowthisa (weighted) average of the growth reported by units that respond for two or more consecutive months,plusaresidualadjustmentforestablishmentbirthanddeath. While the CES is a very large survey, it is still based on a sample and subject to sampling andnon-samplingerror(asdiscussedfurtherbelow). Incontrast, theQCEW,alsomaintained bytheBLS,isanear-censusofemploymentcoveredbyunemploymentinsuranceandservesas thesamplingframeformuchoftheCESaswellasthetargetfortheannualbenchmarkofthe CES. The main drawback of the QCEW is that the data are collected quarterly and published 3SeeBLS(2019).NotethattheCEScontainsdatafortotalnonfarmpayrollemployment,butherewefocusonly onprivatepayrollemployment,excludinggovernmentemploymenttobeconsistentwiththereliablescopeofADP. 4

withalagoftwoquarters. Thus,whiletheQCEWhasnegligiblesamplingerror,itisoflimited use to real-time decision makers. In addition, the QCEW is subject to various sources of nonsampling error.4 Nevertheless, we follow CES in using the QCEW for reweighting the ADP microdataandasabenchmarktarget. 3.1 StructureoftheADPMicrodata ADPprovideshumancapitalmanagementservicestofirms,includingpayrollprocessing. Processing payroll for a client firm involves many tasks, including maintaining worker records, calculating taxes, and issuing paychecks. The structure of the microdata is determined by the business needs of ADP. ADP maintains records at the level of payroll account controls (PAC), which often correspond to business establishments (but may sometimes correspond to firms) as defined by the Census Bureau and the BLS. Each PAC updates their records at the end of eachpayperiod. Therecordsconsistofthedatepayrollwasprocessed,employmentinformation for the pay period, and many time-invariant PAC characteristics (such as an anonymized PAC identifier, NAICS industry code, zip code, etc.). PAC records include both the number of individuals employed (“active employees”) and the number of individuals issued a paycheckinagivenpayperiod(“paidemployees”). Activeemployeesincludewageearnerswith no hours in the pay period, workers on unpaid leave, and the like. Paid employees include any wage or salary workers issued regular paychecks during the pay period as well as those issued bonus checks and payroll corrections. In this paper we focus exclusively on active employment, having found that it is substantially less volatile, more closely resembles officially published aggregates, and performs better in forecasting exercises, though we plan to further investigatetheactive/paiddistinctioninthefuture.5 The data begin in July 1999.6 In terms of frequency, the files we use are weekly snapshots of individual PAC records, taken every Saturday since July 2009 (snapshots were taken semi- 4ForadetailedanalysisofmeasurementchallengesinCESandQCEW,seeGroen(2012). 5Onetopicforfurtherinvestigationisexactlywhyactiveemploymentperformsbetterthanpaidemployment. Itispossiblethatdoublecountingduetotheinclusionofpayrollcorrections,reimbursements,andbonusesadds noisetopaidemploymentasmeasuredintheADPdata.SeeCajneretal.(2018)forfurtherdiscussion. 6Whenaccessingthemicrodata,wefollowanumberofprocedurestoensureconfidentiality.Businessnamesare notpresentinthedataweaccess. 5

monthly between May 2006 and June 2009 and monthly before May 2006). Each snapshot containsthemostrecentpaydateforeachPAC,therelevantemploymentcounts,andtheother informationdescribedabove. Asfewfirmsregularlyprocesspayrollmorethanonceperweek, theweeklysnapshotsprovideacomprehensivehistoryofPAC-levelemploymentdynamics. We can compare ADP payroll microdata to the QCEW and CES data in terms of pay frequency, region, establishment size, and industry composition. Most notably, ADP has significantly more employment in mid-sized units than does CES, with a distribution that looks reasonablysimilartoQCEW.7 3.2 SeriesConstruction The process of transforming the raw data to usable aggregate series is complex. Here we provide a brief, simplified explanation of the process. The interested reader may refer to Cajner etal.(2018)fordetails. Each week, we calculate the weighted average growth of employment at PACs appearing in the data for two consecutive weeks. The restriction to “continuers” allows us to abstract fromchangesinthesizeofADP’sclientbase: aslongasclientturnoverisrandom,thegrowth rate of continuers will be a valid estimate of aggregate growth (of continuers). Growth rates are weighted by PAC employment and further weighted for representativeness by size and industry. We use QCEW employment counts by establishment size and two-digit NAICS as the target population. Formally, let w be the ratio of QCEW employment in a size-industry j,t cell j to ADP employment in cell j in week t, let C(j) be the set of ADP businesses in cell j, let e be the employment of the i’th business, and let g = ei,t −ei,t−1 be the weekly growth rate of i,t i,t ei,t−1 businessi.8 Aggregategrowthisestimatedas: ∑J w ∑ e g j=1 j,t−1 i∈C(j) i,t−1 i,t g = . (1) t ∑J w ∑ e j=1 j,t−1 i∈C(j) i,t−1 7Formoredetail,seeCajneretal.(2018). 8Forweighting,weuseMarchQCEWemploymentvaluesforeachyear.ForyearswheretheMarchQCEWhas notbeenreleased,weusethelastavailableMarchQCEW.WhilewecouldallowQCEWvaluestovaryquarterlyor monthly,thesharesareslowmovingandthusthischangewouldnotsignificantlyaltertheresults. 6

Cumulating the weekly growth rates across time yields a weekly index level for employment. Our focus in this paper is on monthly estimates. We calculate the monthly index as the average of the weekly index for each month, weighting by days to account for partial weeks in each month.9 Monthly averaging smooths through the weekly volatility, and the results in Cajner et al. (2018) suggest that averaging improves performance relative to point-in-time methods more similar to the CES. The monthly index is seasonally adjusted using the X-12 algorithm. Figure 1 displays the seasonally adjusted ADP-FRB series (black thick line) along with the indexed CES estimate (gray thin line). Importantly, the growth rate of the (weighted) ADP- FRB series is very similar to the CES, and the business-cycle frequency fluctuations are very closelyaligned. Moreover,thisADP-FRBseriesdoesnotincorporateanyofthebenchmarking discussed below, so nothing forces it to resemble CES. It is also evident that the ADP-FRB series is volatile, and much of the month-to-month variation does not appear to be related to the monthly swings in the CES data. We interpret this finding as evidence that both series arecontaminatedwithmeasurementerror,whichcanplausiblybeattenuatedbymodelingthe series jointly. For reference, Figure 1 also shows the ADP-FRB unweighted series, which does not correctthe ADPsize-industrydistribution. Clearly, theunweighted series has amarkedly differenttrendgrowthrate,thoughitsharesthequalitativebusiness-cyclefrequencybehavior oftheothers.10 3.3 StrengthsandWeaknessesofDifferentTypesofPayrollEmploymentData Perhaps the most important issue when analyzing the quality of a dataset is its representativeness. Obviously,theQCEWdatahaveaclearadvantageherebecausethesedatarepresent populationcounts.11 Incontrast,CESandADPestimatesaresamplebased. AswithCES,our 9Forexample,ifacalendarweekhasfourdaysinJanuaryandthreedaysinFebruary,ourweightingbydays procedureproportionallyattributestheweeklyemploymenttobothmonths. 10WhilewedonotdirectlyusetheweeklyADP-FRBseriesinthispaper,weviewthesehigh-frequencymeasurementsasapromisingtopicforfutureresearchon,forexample,naturaldisasters. Theweeklyseriesarediscussed inmoredetailinCajneretal.(2018). 11Note,though,thatthereisasmallscopediscrepancybetweenQCEWontheonehandandCES/ADPonthe otherhand: about3percentofjobsthatarewithinscopeforCES/ADPestimatesareexemptfromUItaxlaw. For moredetail,seehttps://www.bls.gov/news.release/cewqtr.tn.htm. 7

Monthly Growth Rates 1 0.5 0 -0.5 -1 Jan2000 Jan2005 Jan2010 Jan2015 Jan2020 egnahC tnecreP CES Private Employment ADP-FRB ADP-FRB Unweighted Indexed Levels 140 130 120 110 100 CES Private Employment ADP-FRB 90 ADP-FRB Unweighted 80 Jan2000 Jan2005 Jan2010 Jan2015 Jan2020 Note:Monthlydata(currentvintage),normalizedto100in2010. Source:ADP,CES,authors’calculations.CESseriesisbenchmarked;ADP-FRBisnot. Figure1: MonthlyGrowthRatesandIndexedLevels ADPsamplesareadjustedwithweightsthataremeanttomaketheestimatesrepresentativeof theUnitedStates,buttheweightingdoesnotsolveallissues. InthecaseofADP,animportant sample selection issue exists because only the firms that hire ADP to manage their payrolls show up in the ADP data. In the case of CES, the data are based on a probability sample of establishments, but as the response rates are only about 60 percent (Kratzke, 2013), this can introduceapotentialsampleselectionissueaswell. BoththeADPandtheCESdataaresubjecttodynamicselectionissuesrelatedtoestablishmententryandexit. IntheUnitedStates, youngfirmsaccountforadisproportionateshareof employment growth (Haltiwanger, Jarmin and Miranda, 2013); indeed, mean and median net employment growth rates of firms above age five tend to be around zero (Decker et al., 2014). AcriticallimitationoftheCESsampleisitslackofcoverageofnewfirmsandestablishments.12 12TheCESsampleisredrawnonlyonceayear(BLS,2019). 8

Inaddition,theCESdoesnotdirectlymeasureestablishmentdeaths. TheBLSattemptstocorrect for these shortcomings using a two-step CES birth-death methodology. In the first step, employment losses from known business deaths are excluded from the sample to offset the missing employment gains from new business births. Thus, dead establishments (i.e., those reportingzeroemployment)andnonrespondents(suspecteddeadestablishments)areimplicitly given the same growth rate as the continuing establishments in the CES survey. In the secondstep,anARIMAmodelbasedonhistoricalQCEWdataestimatesthebirth/deathresidual: employment at newly formed establishments less employment at exiting establishments. ThisestimateisaddedtotheestimatesfromtheCESestablishmentsampletogeneratethefinal CESestimate. Inmanymonths,themodel’scontributiontoheadlineemploymentestimatesis sizable.13 ActualnewfirmsdonotaffectCESestimatesuntilthesampleisrotated.14 Even after a benchmark revision, the monthly CES data never truly account for the birth anddeathofestablishments. Whenabenchmarkrevisionoccurs,withtheJanuaryCESrelease each year, the previous year’s March level of the CES data is set to the March level of QCEW employment. The monthly sample-based estimates for the 11 months preceding the March benchmark are revised with a “wedge-back” procedure, where a linear fraction of the benchmarkrevisionisaddedtotheCESleveleachmonth(BLS,2019). Thewedging-backprocedure results in a constant being added to the monthly change in employment each year. So, while theyear-to-yearchangeinthepost-benchmarkCESdatawillcapturethewithin-QCEW-scope dynamicsofentryandexitattheannualfrequency,themonthlynumberswillnot. ADP data are subject to a related limitation in that we do not know the age composition ofADPclients,nordoweobservefirmorestablishmentageintheADPmicrodata. However, new and young firms may enter the ADP data immediately upon engaging ADP for payroll 13Seeadiscussionofthemodelanditsrecentcontributionshere:https://www.bls.gov/web/empsit/cesbd.htm. Forexample,since2009thenetbirth-deathadjustmenthasaddedanontrivialaverageof800,000jobstoaparticular year’semploymentgains,orroughly40percent. 14ThesamplingframeisbasedonQCEWsourcedata(stateunemploymentinsurance(UI)records), whichlag severalmonths. ItmightbewonderediftheUIrecordspickupnewestablishmentsquickly;thisisapparentlythe case. EmployersmustfileUItaxesiftheyhavepaid(cumulatively)$1,500ormoreinpayroll, somostnewemployerswouldappearintheUIrecordsveryquickly;seehttps://oui.doleta.gov/unemploy/pdf/uilawcompar/ 2018/coverage.pdf. However, notethatevenafterabusinessbirthappearsintheUIrecords, thereisalsotime requiredforsampling,contacting,andsolicitingcooperationfromthefirmaswellasverifyingtheinitialdataprovided. Inpractice, CEScannotsampleandbegintocollectdatafromnewfirmsuntiltheyareatleastayearold (BLS,2019). 9

services. While the number of young firms in ADP data is unknown, any number could be a usefulsupplementtotheCESdata,inwhichnewfirmsareentirelyabsent. Asdiscussedabove,theADPdataconsistofweeklysnapshots(sinceJuly2009). Incontrast, theQCEWandCESdatacontaininformationforonlythepayperiodthatincludesthe12thday ofthemonth. Asaresult,theCESandQCEWdatacannotmeasureemploymentactivityover theentiremonth,whichcanbeespeciallyproblematicinthecaseoftemporarydistortingevents during the reference period. For example, an unusually large weather event (e.g., a hurricane orasnowstorm)thatreducedemploymentduringthereferenceperiodbutlefttherestofthe month unaffected would result in a CES employment report that understates the strength of thelabormarketthroughoutthemonth. IntheweeklyADPdatawecan,inprinciple,observe boththeshockandtherecovery. Inanycase,averagingthelevelofemploymentforthemonth attenuatestheimpactofsuchshort-livedevents. Finally,theQCEWandADPdataarebothessentiallyadministrativedataandthusarguably somewhatlesspronetoreportingerrorsandnonresponse,whichareoftensignificantproblems surveydatasuchastheCES. 4 Comparing ADP-FRB to Official Data 4.1 PredictingAnnualBenchmarks In this section we evaluate the ability of ADP-FRB and CES to forecast the QCEW, which can plausibly be treated as “truth”. We restrict attention to annual changes (March-to-March) to avoidcomplicationsrelatedtoseasonalityandseameffectsintheQCEW. We follow the CES in benchmarking the level of our ADP-FRB indexes to the QCEW each year. Our procedure closely follows that of the CES: we iteratively force each March value of ADP-FRBtomatchthecorrespondingQCEWvalue,andwelinearlywedgebackthepre/post benchmark revision. The wedge reaches zero at the previous (already benchmarked) March. ThedataarecurrentlybenchmarkedthroughMarch2017. Throughout the paper, we use our monthly ADP-FRB index starting in 2007. For the purpose of annual benchmarking, this means we begin annual benchmark comparisons with the 10

2008benchmarkyear,whichmeasuresthechangeinprivatenonfarmemploymentfromApril 2007 through March 2008. In the 10 years starting from 2008, the pre-benchmark ADP-FRB estimates were closer to the eventually published population counts in four years, while the pre-benchmark CES estimates were more accurate in six years (see Table 1). Overall, the rootmean-squared benchmark revision is 0.49 percent for the ADP-FRB data and 0.36 percent for theCESdatafrom2008onward. Interestingly,theADP-FRBestimatesmarkedlyoutperformed the CES estimates during the Great Recession (2008-2010). Specifically, from 2008 to 2010 the ADP-FRB absolute revisions averaged 200,000 per year, whereas the BLS-CES absolute revisionsaveraged490,000peryear. Incontrast,overthepastfiveyearsthepre-benchmarkADP- FRBestimatesconsistentlyoverpredictedemploymentgrowth. An evaluation of the CES benchmark misses should also take the net birth-death model into account, as the net birth-death adjustment adds roughly 40 percent to a particular year’s employmentchange. Asaresult,acomparisonofthebenchmarkmissesofADP-FRBseriesto theCESdataisnotexactlydirect,astheADP-FRBdatawouldlikelyonlycaptureaportionof the contribution of the employment contribution of births. The third row in Table 1 presents the benchmark miss of the CES data without the inclusion of the net birth-death adjustment. Thatis, the“CESnoBD”rowreflects thegrowthtothelevelofemploymentsolelyduetothe sampleofbusinessesforwhichtheCESdataiscollected. As can be seen in the table, the benchmark misses for CES excluding the net birth-death adjustment are substantially larger (with a root-mean-squared revision of 0.65 percent on average since 2008). Since 2008, the misses have also been almost always positive, reflecting a positive effect of establishments’ births on the level of employment. The negative revisions in 2009 and 2010 point toward the autoregressive nature of the birth-death adjustment carrying inertiaforwardfrompreviousyears’employmentchanges. Thatis,becausenewbusinessformationfallsinrecessionaryyears,theneteffectofthebirth-deathframeworkoverpredictsthe actualbirth-deathcontributiontoemploymentgrowth,andthusCESbenchmarkmisseswere largerthanbenchmarkmissesofCESdatawithnobirth-deathadjustment. We more formally test the performance of ADP-FRB and CES in predicting annual benchmarkedemploymentgrowthbyrunningthefollowingregressions. Thedependentvariableis 11

2008 2009 2010 2011 2012 2013 2014 2015 2016 2017 ADP-FRB -173 -451 12 709 283 -230 -1030 -853 -322 -623 CES -137 -933 -391 229 481 340 105 -259 -151 136 CESNoBD 645 -216 -55 561 972 975 874 638 737 1066 Notes:Units:Thousandsofjobs.CESrevisionsarethepost-benchmark(QCEW-based)Marchestimatelessthepre-benchmarkestimate.ADP-FRBrevisionsarecalculatedanalogously.CESnoBD aretheCESbenchmarkrevisionsthatwouldhaveoccurredexcludingnetbirth-deathadjustment. Source:https://www.bls.gov/web/empsit/cesbmart.pdf,authors’calculations. Table1: LevelDifferencesbetweenPrivateEmploymentBenchmarksandEstimates theannualchangeinemploymentfromMarchofyeart−1toMarchofyeartasknownupon thereleaseoftheCESbenchmarkrevisioninFebruaryofyeart+1. Weconsiderthreedifferent independentvariables,witheachannualobservationspecifiedastheeconometricianobserved them at the time of the CES jobs report for March of year t: (1) annual employment change from March of t−1 to March of t as estimated by monthly CES non-seasonally-adjusted figures;(2)estimatedannualemploymentchangefromMarchof t−1toMarchof t asestimated bymonthlyCESnon-seasonally-adjustedfiguresinwhichthecontributionsofthebirth-death modelhavebeenremoved;and(3)annualemploymentchangefromMarchoft−1toMarchof tasobservedintheADP-FRBnon-seasonally-adjusted(“active”)employmentindex. Thepurposeoftheexerciseistoevaluatetheabilityofananalysttoestimate“true”(i.e.,benchmarked) employmentgainsforthepastyear,observedatthetimeoftheCESMarchemploymentreport (inearlyApril). Atthattime,theanalysthasinhandCESdataforthefirstreleaseofMarchof yeart(whichincludesthesecondreleaseofFebruaryofyeartandthethirdreleaseofJanuary ofyear tandallpriormonths). Theanalystalsohasinhandthepastyear’sADP-FRBdataup throughthethirdweekofMarchofyeart. Thatis,weestimatethefollowing: ∆EMPB = α+β ∆EMPMarch+ε , t t t where ∆EMP isthechangeinprivatenonfarmemploymentfromMarchofyeart−1toMarch t of t, the B superscript indicates the benchmark revision vintage of the series, the March superscript indicates the vintage of the series that is released with the March jobs report in year t (where we construct the annual estimate by summing all non-seasonally-adjusted monthly estimates through the year), and ∆EMPMarch can be the March vintage of CES, CES without t 12

(1) (2) (3) (4) (5) CES 1.126*** 1.104*** (0.0316) (0.142) CESexcludingBirth-Death 1.154*** 0.927*** (0.0235) (0.0847) ADP-FRB 0.976*** 0.0197 0.199** (0.0543) (0.121) (0.0818) Constant -163.7* 604.5*** -135.1 -163.6* 452.5*** (76.93) (75.29) (172.8) (82.61) (79.37) RMSE 299.2 243.3 535.9 319.7 224.2 Notes:Dependentvariableisbenchmarkedannualchangeinprivatenonfarmemployment, MarchtoMarch. Years2008-2017. *,**,and***indicatestatisticalsignificanceatthe10%, 5%,and1%levels,respectively.Robuststandarderrorsinparentheses. Table2: ForecastingAnnualEmploymentChanges birth-deathmodelcontributions,orADP-FRB(“active”)employment. Table2reportsresultsfromthisannualforecastingexercise. Whilewebelievethereisvalue in reporting this formal test, given the extremely small sample size the results are suggestive atbestandshouldbetreatedwithcaution. Thatsaid,wefindthatthebestpredictorofbenchmarked employment growth, according to both adjusted R2 and RMSE, is the CES series that excludes birth-death model contributions (column 2). That is, the birth-death model does not appear to improve estimates of annual employment growth beyond the inclusion of a simple regressionconstant(comparecolumns1and2). TheADP-FRBseries(column3)haspredictive content but is outperformed by both CES series. However, we do find that adding the ADP- FRB series to the CES series that excludes birth-death contributions does improve forecasts (column5).15 WhiletheregressionresultsinTable2areinteresting,itisdifficulttodrawconclusionsfrom such small-sample exercises. Moreover, ADP-FRB data are most valuable to policymakers if they increase our ability to understand recessions in real time; the predictive power of ADP- FRB during periods of steady, modest job growth is much less useful. We illustrate the point withasimplecasestudyfromtheonlyrecessioninourADPsample.16 ConsiderthebeginningoftheGreatRecession. TheNBERbusinesscycledatingcommittee identifiedDecember2007asthebusinesscyclepeak,butthroughout2008,economicdatasent 15Inunreportedexercises,wefindthattheresultsarehighlysensitivetothespecifictimeperiodincluded. 16ADPbegantakingsnapshotsonasemimonthlybasisstartinginMay2006. 13

116200 116000 115800 115600 115400 115200 115000 114800 114600 Jul2007 Oct2007 Jan2008 Apr2008 Jul2008 Oct2008 sboJ fo sdnasuohT ,leveL ADP-FRB, real time CES, real time CES, final Note:Monthlydata.NBERrecessionisshadedingray.Real-timelinesshoweachsuccessivevintageasaconnected line,withtheendpointatthefirst-printvalueforthatmonth.Allserieshavebeennormalizedtomatchthecurrent vintageCESestimateinAugust2007. Source:ADP,CES,authors’calculations. Figure2: Real-Timevs. CurrentVintageEstimates somewhatmixedsignalsaboutthedeteriorationoflabormarketconditions. CESdatareleases fromthroughout2008wererevisedsubstantiallywiththe2009QCEWbenchmark. Figure2reportsthreepayrollrealtimeADP-FRBandCESestimatesofthelevelofemployment, alongwiththefinal(currentvintage)CESestimate. ThethickblacklineisthefinalCES estimate, which shows employment losses of about 1.4 million jobs by August 2008. The dotted gray lines show each real-time vintage CES estimate for 2008: each end point represents a first-printestimate,andthethickercentrallinerepresentstheestimateafterafewmonthlyrevisions(butbeforethebenchmarkrevision). Thatis,followingthelinebackfromanendpoint inmontht,thelinereflectsthepathofemploymentasitwouldhavebeenknowntoobservers in month t (including revisions up to that date). The thin black lines show the same set of 14

real-timeestimatesfortheADP-FRBindex.17 AsisapparentfromFigure2, inrealtimetheADP-FRBserieswastypicallymoreaccurate in tracking the true pace of labor market deterioration during the first year of the recession. ByAugust, real-timeCESestimatesshowedjoblossestotalingabout750,000, whileADP-FRB wasatapproximately1.0million(bothnumbersshouldbecomparedwiththecurrentvintage estimateof1.4millionjobslost). Betterknowledgeofthisdeteriorationwouldhavebeenuseful topolicymakersasthecriticalfourthquarterof2008approached. Infuturecyclicaldownturns, ADPdatamayagainproveusefulinpreviewingtheeventualrevisionstoCESdata. 4.2 PredictingMonthlyEmployment While annual forecasts of the benchmark revisions are important, the CES is a monthly measure of employment that revises over several releases as both more data and benchmarks becomeavailable. InthissectionweevaluatetheabilityoftheADP-FRBemploymentindexesto improve forecasts of CES data in real time and in conjunction with other real-time indicators. Table3reportsforecastingmodelsdescribedinCajneretal.(2018)usingreal-timeADPindexes andothervariablestopredictthefinalprintofCES(i.e.,afteralloftherevisions). Inparticular, weestimatedthefollowingregressionmodel: ∆EMP CES,final = α+β ∆EMPADP-FRB,RT5+β ∆EMPCES,RT +βX +ω (2) t 1 t 2 t−1 t t Theexplanatoryvariablesincludecurrent-monthreal-time(fiveweeksafterthestartofthe month, which corresponds to the week before or the week of the Employment Situation release) ADP-FRB data, previous-month real-time (first print) CES private employment, as well as initial unemployment insurance claims, Michigan Survey unemployment expectations, the lagged(previous-month)unemploymentratechange,andBloombergmarketCESpayrollemploymentexpectations. Inaddition,ω t = ε t +ρε t−1 isanMA(1)errorterm.18 17Allofthereal-timeserieshavebeennormalizedtoequaltheCEScurrentvintageestimatesinAugust2008to removealevelshiftduetobenchmarkrevisions. 18The MA error term corrects for serial correlation in the errors when estimating equations of the change in employment. The results for a similar specification using OLS are qualitatively similar, despite the existence of serialcorrelation. 15

Cajneretal.(2018)discusssimilarresultsinmoredetail;herewesimplynotethattheADP- FRB indexes for active employment make statistically significant contributions to the model andgeneratemodestimprovementstoforecastingaccuracy. Column(1)ofTable3reportsthe baselineforecastingmodelwithouttheADP-FRBdataormarketexpectations. Addingmarket expectations in column (2) improves the forecast notably, as can be seen from the 15,000-job reduction in RMSE. In column (3) we add the ADP-FRB index and find that RMSE declines and the ADP-FRB coefficient is statistically significant; that is, the inclusion of the ADP-FRB index provides further marginal forecasting improvement beyond the inclusion of market expectations,incontrasttotheGregoryandZhu(2014)resultsusingADP-NER.Incolumn(4)we reportamodelincludingADP-FRBbutomittingmarketexpectations,whichreducesRMSEby 7,000jobsrelativetothebaseline. Finally,column(5)indicatesthatevenwhenthefirstprintof CESdataisavailable,thereal-timeADP-FRBdataprovideadditionalsignalaboutthefinalor “true”BLSmeasureofemploymentchange. The forecasting success of the ADP-FRB indexes should not be overstated. Cajner et al. (2018)showthattheimprovementsinforecastingduetoADPdataarestatisticallysignificant, though they are not particularly dramatic in magnitude. However, we should not expect dramatic improvement because the sampling variance of the CES estimate is large relative to the RMSE of our forecasts. For example, from 2013 until 2017 (which omits the Great Recession period of large forecast errors), the out-of-sample RMSE for predicting monthly payroll employment using the ADP-FRB data (along with other predictors) is 70,700 jobs, whereas the (sampling) standard error of the CES estimate is 65,000 (BLS, 2019). To the extent that samplingerrorisi.i.d.,thesamplingerrorprovidesalowerboundontheforecastingerrorforCES estimates. Practically, it should be nearly impossible to reduce the RSME of a forecast below 65,000,andanyforecastthatachievedbetterperformancewouldbeforecastingsamplingerror, notactualchangesinemployment. The fact that forecasting errors are already close to the 65,000 lower bound, even without ADP-FRB,suggeststhatthemainvalueoftheADPdataisnotinforecastingCES.Instead,the ADPdatacanbeusedtoobtainestimatesthataretimelier,moregranular,andhigherfrequency. Inaddition,theADPdatamaybecombinedwiththeCEStoreducemeasurementerror. 16

(1) (2) (3) (4) (5) ADP-FRBactiveemployment 0.29** 0.39*** 0.16** (0.11) (0.11) (0.07) LaggedprivateCESemployment 0.82*** -0.13 -0.21 0.51*** (0.07) (0.15) (0.14) (0.12) LaggedURchange -156.73** -45.66 -43.05 -123.09** (61.56) (52.17) (46.84) (58.02) Unemploymentexpectations 39.17*** 30.95*** 14.08 16.55 15.21 (11.82) (11.01) (12.29) (12.74) (10.88) InitialUIclaims -3.10*** -0.91 -0.79 -2.52*** -0.56 (0.74) (0.71) (0.72) (0.83) (0.52) CESemploymentexpectations 1.15*** 0.98*** (0.16) (0.15) PrivateCESemployment 0.97*** (0.07) URchange 33.12 (36.03) Constant 4.87 -17.77* -24.39** -7.48 -17.85** (9.36) (10.40) (11.58) (10.77) (8.98) RMSE 99 84 80 92 58 Notes: DependentvariableisfinalprintofCESprivateemployment. ADP-FRBseriesarereal-time vintage,asof5weeksafterthestartofthemonth(i.e.,theweekbeforeorweekoftheEmployment Situationrelease). UnemploymentexpectationsarefromtheMichigansurvey. CESemploymentexpectationsareeve-of-releasemedianmarketsexpectations. LaggedprivateCESemploymentrefers topre-EmploymentSituationrelease. Robuststandarderrorsinparentheses. RSMEsarecalculated in-sample.*p<0.10,**p<0.05,***p<0.01.Estimationperiod:2007m1-2018m9. Table3: ForecastingMonthlyEmploymentChanges On net, the ADP-FRB index adds to our understanding of annual and monthly employment changes and has some predictive power for benchmark revisions. Importantly, we find that during the Great Recession the ADP-FRB index provided a more accurate measure of the employment declines. With these findings in mind, we now turn to a methodology that combinestheinformationfromboththeCESandtheADP-FRBseries. 5 State-Space Model of Employment Payrollemploymentgrowthisoneofthemostreliablebusinesscycleindicators. Eachpostwar recessionintheUnitedStateshasbeencharacterizedbyayear-on-yeardropinpayrollemploymentasmeasuredbyCES,and,outsideoftheserecessionarydeclines,theyear-on-yearpayroll employmentgrowthhasalwaysbeenpositive. Thus,ifoneknewthe“true”underlyingpayroll employmentgrowth,thiswouldhelpenormouslyinassessingthestateoftheeconomyinreal 17

time. Inthissection,wepresentresultsfromastate-spacemodeltoinferthe“true”underlying payrollemploymentgrowth.19 Let ∆EMPU denotetheunobserved“true”changeinprivatepayrollemployment(inthout sandsofjobs),whichisassumedtofollowanAR(1)process: ∆EMPU = α+ρ ∆EMPU +(cid:101)U. t t−1 t ∆EMPU is a latent variable for which we have two observable noisy measures, that is CES t ( ∆EMPCES) and ADP-FRB ( ∆EMPADP-FRB). Both are monthly changes in thousands of jobs. t t TheobservedvaluesofCESandADP-FRBemploymentgainsareafunctionoftheunderlying stateaccordingtothefollowingmeasurementequations:       ∆EMPADP-FRB β (cid:101)ADP-FRB  t  =  ADP-FRB  ∆EMPU + t . t ∆EMPCES β (cid:101)CES t CES t Without loss of generality, we can assume that β = 1. This assumption only normal- CES izes the unobserved state variable to move one-for-one (on average) with CES. We make the assumptioninourbaselinespecificationbutleave β unrestricted.20 ADP-FRB WeassumethatallshocksareGaussianandthat(cid:101)U isorthogonaltotheobservationerrors t ((cid:101)ADP-FRB, (cid:101)CES). However,wedoallowtheobservationerrors((cid:101)ADP-FRB, (cid:101)CES)tobecontemt t t t Σ poraneouslycorrelated,withvariance-covariancematrix :   σ2 σ2 Σ =  ADP-FRB ADP-FRB,CES . σ2 σ2 ADP-FRB,CES CES Both the CES and ADP-FRB estimates can be regarded approximately as sample means, with the samples drawn from the same population. As such, both CES and ADP-FRB are (approximately) truth plus mean-zero sampling error. This sampling error is captured by the 19Aruobaetal.(2016)useasimilarapproachtoprovideabettermeasureofoutput. 20The approach is in contrast to Aruoba et al. (2013), who assume that both the observation variables in their paper (GDP and GDI) have unit loadings on the unobserved state variable. While those authors’ assumption is justifiablegiventheiruseofthetwowell-understood(andconceptuallyequivalent)measuresofoutput,giventhe relativelyuntestednatureoftheADP-FRBdatawefeelitisbettertoletthemodelchoosetheloading. 18

Kalmanfilterintheobservationnoiseterms.21 5.1 CharacterizationoftheState TheestimatesforthemodelabovearecollectedinthefirstcolumnofTable4. Interestingly,the estimateofβ ispreciselyestimatedandnotstatisticallydifferentfromunity. Somewhat ADP-FRB surprisingly, thecovarianceoftheobservationerrors σ2 isnegative, thoughitisnot ADP-FRB,CES statisticallydifferentfromzero. Specification2furthergeneralizesthemodel,allowingforthe ADP-FRB observation equation to have its own intercept α . This modification makes ADP-FRB littledifference,andthepointestimatesareessentiallyunchangedfromthebaseline. Specifica- Σ tion 3 imposes a unit factor loading in the ADP-FRB equation and a diagonal . Again, these alterations do not significantly change the point estimates, though the variances of the observationerrorsareinflatedsomewhat. Finally,Specification4assumesthattheunobservedstate follows a random walk. All of the qualitative features of Specification 1 carry through to this modelaswell. As discussed above, the BLS produces estimates of the sampling error of CES. These estimates are based on the observed cross-sectional variation in employment growth and knowledgeofthestratifiedsamplingscheme. Theestimatedstandarderrorforthechangeinprivate CES employment is about 65,000 jobs, which is remarkably close to our estimates of σ ; the CES squarerootofσ2 reportedinTable4rangesbetween61,000and69,000jobs. Inourstatespace CES model,σ capturesallsamplingandnon-samplingerrorintheCESseries,soitisreassuring CES thatourerrorestimatesalignsocloselywiththoseoftheBLS. Given that both the CES and the ADP-FRB series have been benchmarked to the QCEW, it may not be surprising that the model tends to treat them symmetrically. It is possible that mostoftheidentificationiscomingfromyear-over-yearvariation,whichwouldbedominated bytheQCEW.WeaddressthisconcerninSpecification5,whichusesanunbenchmarkedADP- 21A critical assumption for our setup is that this noise is i.i.d. over time, which would be exactly true if CES andADP-FRBredrewtheirsampleseverymonth,butthereis,infact,muchoverlapintheunitsfromonemonth tothenext. Thus,anypersistenceinidiosyncraticestablishment-levelgrowthcanpropagatetopersistenceinthe samplingerror. Fortunately,theavailableevidencesuggeststhatthereisverylow,orevennegative,persistencein short-runestablishmentgrowth(Cooper,HaltiwangerandWillis,2015),whichinturnimpliesnearlyi.i.d.sampling errorandjustifiestheKalmanfilter. 19

Parameter (1) (2) (3) (4) (5) ρ 0.96*** 0.96*** 0.96*** 1.00 0.96*** (0.02) (0.02) (0.02) (0.02) α 4.39 4.31 4.21 0.88 4.31 (4.84) (4.84) (4.69) (5.03) (4.58) β 1.00 1.00 1.00 1.00 1.00 CES β 1.03*** 1.03*** 1.00 1.03*** 1.06*** ADP (0.03) (0.03) (0.03) (0.04) σ2 3765.41*** 3786.13*** 3609.16*** 3698.76*** 3290.51*** U (827.64) (832.95) (678.03) (805.89) (733.10) σ2 3796.51*** 3779.60*** 3984.78*** 3860.32*** 4727.96*** CES (721.96) (721.17) (642.11) (713.98) (853.74) σ2 −393.91 −388.67 −315.56 −869.32 CES,ADP (573.61) (573.63) (563.56) (560.55) σ2 3758.90*** 3773.01*** 4171.35*** 3852.70*** 3517.13*** ADP (792.63) (793.08) (680.98) (782.16) (761.84) α 4.10 ADP (8.15) Notes: Maximum likelihood parameter estimates. Measurement series are the monthly change in thenumberofjobsaccordingtoCESandADP-FRB,inthousandsofjobs. *,**,and***indicatestatisticalsignificanceatthe10%,5%,and1%levels,respectively. Standarderrorsareinparentheses. Specification2allowsforanon-zerointerceptintheADP-FRBobservationequation. Specification 3restrictsbothobservationequationloadingstounity,andassumesthattheobservationerrorsare uncorrelated. Specification4imposesarandomwalkontheunobservedstate. Specification5uses anunbenchmarkedversionoftheADP-FRBseries.Estimationperiod:2006m5-2018m8. Table4: KalmanFilterParameterEstimates FRB series. The results are remarkably similar to the other specifications, indicating that the QCEWbenchmarkisnot,infact,dominatingourestimates. Takentogether,theresultsinTable4suggestthatisitreasonabletothinkofADP-FRBand CES as two symmetric measurement series, each with approximately the same relation to the unobserved state (i.e., the same loading and intercept) and with approximately equal degrees ofuncorrelatedmeasurementerror. With these estimates in hand, we can extract estimates of the unobserved state process. Figure3showsthesmoothed(two-sided)estimateofthestate(theheavyblackline),alongwith 90percentconfidenceintervals(thegrayshadedarea). Naturally,thestateestimateappearsless volatile than either observation series. The smoothed state estimates use data for all available sampleperiodstoestimatethestate. A simpler exercise is also instructive. Following Mankiw, Runkle and Shapiro (1984) and 20

500 250 0 -250 -500 ADP-FRB -750 CES Smoothed State 90 Percent Confidence Interval -1000 Jan2005 Jul2007 Jan2010 Jul2012 Jan2015 Jul2017 Jan2020 Note: Monthlydata,changeofemploymentinthousands. BothCESandADP-FRBarecurrentvintageandbenchmarkedtoQCEW.SmoothedstateestimateiscalculatedfromSpecification1. Source:ADP,CES,authors’calculations. Figure3: SmoothedStateEstimate Aruoba et al. (2013), we seek to approximate the state estimate using only contemporaneous observationsofCESandADP-FRB.Inparticular,lettheestimatorbe: ∆EMPC = λ ∆EMPADP-FRB+(1−λ)∆EMPCES t t t where λ istheweightingparametertobechosen. Weminimizethedistancebetweenthestate estimateandtheweightedaverage: (cid:40) (cid:41) min ∑ T (cid:16) ∆E(cid:100)MPU −∆EMPC (cid:17)2 t t λ t=1 where ∆E(cid:100)MPU is the state estimate from the Kalman smoother. This exercise is particularly t simpleundertheassumptionsofSpecification3,wherebothseriesarejusttruthplusuncorrelatednoise. Inthatcase,wecanplugintheestimatedparametersandsolveforλas: σ(cid:100)2 λ ∗ = CES . σ2 (cid:100) +σ(cid:100)2 ADP-FRB CES 21

whereσ(cid:100)2 istheestimatedvarianceoftheobservationerrorinCES,andsimilarlyforσ2 (cid:100) . CES ADP-FRB Using the values from Specification 3 yields λ∗ = 0.49, so the optimal contemporaneous estimator puts nearly equal weight on the two series.22 Relatedly, the Kalman gains for the two series(notshown)arealsoverysimilar. Placing roughly equal weight on CES and ADP-FRB employment gains might seem counterintuitive. However, both data sets cover roughly a similar share of private U.S. payroll employment(23percentforCES,20percentforADP)andthusthesamplingerrorcouldplausiblybeofsimilarmagnitude. Additionally,whiletheBLSeventuallybenchmarksCESpayroll employment to the QCEW as discussed earlier, the month-to-month changes are largely unaffected by benchmarking due to the linear wedging-back procedure. Thus, if in a particular month the CES sample estimate of payroll employment gain is distorted because of the sampling error, it is likely that the error will survive even the subsequent revisions. As the ADP data rely on a (mostly) different sample, it should be unsurprising that taking a Kalman filter estimateofunderlyinggainsbasedonbothobservedmeasuresshouldgiveamorepreciseestimateofthecurrentpaceofemploymentgrowth,withweightsbeingroughlysimilarbecause ofthesimilarsamplesize.23 5.2 EvaluatingtheEstimatedState’sPredictiveContent The fact that the CES and ADP-FRB series receive roughly equal weight when extracting the commonsignalsupportstheideathatcombiningthesignalfrombothseriescancontributeto ourunderstandingof“true”employmentgrowth. Inthissectionwetentativelytreatthefully revised CES as “truth” and employ the state-space estimates to predict the future readings of finalCESemploymentgains. Fortheforecastingexercises,weemployaframeworksimilartothatfoundinequation(2), withouttheadditionalcontrols. ThedependentvariableisthecurrentvintageoftheCESesti- 22NotethatthelinearcombinationoftheADP-FRBandCESseriesisnearlyidenticaltothesmoothedtwo-sided stateestimatefromtheKalmanfilter. 23Inanotherexercise,wereplacetheADP-FRBserieswiththechangeinemploymentcalculatedfromtheCurrent PopulationSurvey(CPS),adjustedtotheCESscopeofprivateemployment. Wefindthattheoptimalweighting onlyputs4percentoftheweightontheCPSseries,showingthatnear-equalweightingschemeforCESandADP- FRBserieswasnotaninevitableresult. 22

(1) (2) (3) CESEmp. CESEmp. 3-monthav. CESEmp. ADP-CESEmp. State 1.43*** 1.50*** 1.69*** (0.49) (0.55) (0.44) ADP-FRBEmp. -0.18 -0.19 -0.30** (0.15) (0.16) (0.15) CESEmp. -0.18 -0.11 -0.41 (0.34) (0.55) (0.31) CESEmp. State -0.12 -0.04 (0.68) (0.42) Constant -28.14 -28.52 -17.05 (19.43) (18.78) (20.35) Notes:Thedependentvariableincolumns1and2isthefullyrevisedchangeinCES privateemploymentattimet+1;incolumn3thedependentvariableistheaverageofthefullyrevisedchangeinCESprivateemploymentfort+1,t+2andt+3. ADP-FRB series are real-time vintage, as of 5 weeks after the start of the month. CESseriesappearingasindependentvariableorinstate-spaceestimatesarerealtimevintage.Robuststandarderrorsinparentheses.*p<0.10,**p<0.05,***p<0.01. Estimationperiod:2007m1-2018m9. Table5: ForecastingMonthlyEmploymentChangesusingStateSpaceEstimates mate. AsindependentvariablesweincludevariouscombinationsoftheADP-FRBemployment estimate,theCESemploymentestimate,thesmoothedstateasestimatedusingbothADP-FRB and CES, and the smoothed state as estimated by CES only. This final variable is included to distinguishthetime-averagingeffectofthestate-spacemodelfromtheadditionalinformation included in ADP-FRB. If the ADP-FRB series has no information, then CES and the smoothed state based on CES only ought to be the only relevant predictors. Importantly, all of the independent variables are real-time estimates, which means that the state-space estimates include nofutureinformation. TheresultsofthisexercisecanbefoundinTable5. Thefirsttwocolumnsincludethe t+1 currentvintageCESemploymentvalueasitsdependentvariable. Thesecondcolumnaddsthe CES state as an additional explanatory variable. The third column contains the average employmentgrowthovert+1,t+2,t+3—i.e.,theaveragegrowthrateofthenextthreemonths of employment. Estimated together, the only variable that is statistically significant across all threespecificationsistheADP-CESstate.24 Thehorseraceresultsindicatethatwhencomparing 24In unreported results, we find that estimating each equation using only one of the explanatory variables indicatesthateachvariableisindependentlysignificant. Inaddition, thehorseraceresultsarequalitativelysimilar whenusingfirst-printCESvaluesasthedependentvariable. 23

employment-basedindicatorsoffutureCESreadingsofemploymentgains,thecombinationof the ADP-FRB series and the past CES gains provides the most information about future employment. 6 Conclusion Inthispaperweaskedwhetheradditionalinformationonpayrollemploymentcouldimprove theaccuracyofemploymentestimates. Webelievetheanswerisaqualifiedyes. Atthemonthly frequency,thisquestionistricky,asthereisno“true”measureofmonthlyemploymentgains.25 That said, the ADP-FRB estimates and the resulting state-space measures that combine both the ADP-FRB and CES information provide insight into the current state and future values of employment. Moreover, we find that the monthly ADP-FRB estimates outperformed CES in tracking the rapid employment decline during the Great Recession and can help predict eventual revisions to the first prints of the CES data. At the annual frequency the official CES data best predict benchmark revisions, though the sample is small. That said, the ADP-FRB datawereclosertotheQCEWlevelsinfouroutofthepast10years. Could the BLS make use of data from payroll processors to supplement the CES? Our understanding is that payroll processors almost never report any client firm employment numberstoBLS.TheonlyexceptionsareisolatedcaseswheretheclientfirmexplicitlydirectspayrollprocessorstosubmittheirinformationfortheCESsurvey. Importantly,webelievetheCES sample and the ADP sample are collected largely independently. To be sure, an environment in which the BLS works directly with payroll processors to process real-time labor aggregates islikelyawaysoff. AfirststepinthisdirectionwouldbetolinkasubsetoftheADPmicrodatatoBLSdatabases on secure Census or BLS computer systems. If such an undertaking were possible, the project would allow for much better weighting and evaluation of the ADP sample, improving the quality of any estimates. In particular, it would be possible to evaluate what types of sample 25Asdiscussedabove,theQCEWismorecomprehensivethaneitherCESorADP-FRB,andservesastheannual benchmarkforCES.However,theQCEWhasmeasurementerrorandisnotusedasatimeseriesbytheBLS.See Groen(2012),KruegerandFortson(2003),andHiles(2016). 24

selection bias are present in the ADP sample by comparing ADP businesses to control groups or comparing businesses before and after enrollment with ADP. In addition, we could better evaluatethedifferencesbetweenpaidemploymentandactiveemploymentifwehadBLSemploymentmeasuresavailable. Finally, linkingwouldalsoprovideacheckonBLSdata, which can be subject to misreporting and other issues. Crosschecking employment counts, industry codes,andmulti-unitstatuswouldbeinformativeforallparties. Theresultsinthispaperlaythefoundationforfutureworkemployingprivatepayrollmicrodata. We plan on testing the estimated state-space results against other measures of employment, including state- and national-level measures of employment from the QCEW. We alsoplanonfurtherexploringthegeographicandindustrydetailtoimproveemploymentestimates. Importantly,thereisadditionalinformationinthemeasureofADPpaidemployment andattheweeklyfrequencythatwehavenotfullyleveragedinourcurrentresearch. References Aruoba,S.Borag˘an,FrancisX.Diebold,JeremyNalewaik,FrankSchorfheide,andDongho Song. 2013. “Improving U.S. GDP Measurement: A Forecast Combination Perspective.” In RecentAdvancesandFutureDirectionsinCausality,Prediction,andSpecificationAnalysis: Essays inHonorofHalbertL.WhiteJr.,ed.XiaohongChenandNormanR.Swanson,1–25.Springer, NewYork. Aruoba,S.Borag˘an,FrancisX.Diebold,JeremyNalewaik,FrankSchorfheide,andDongho Song. 2016. “Improving GDP Measurement: A Measurement-Error Perspective.” Journal of Econometrics,191(2):384–397. BLS. 2019. “Technical Notes for the Current Employment Statistics Survey.” Bureau of Labor Statistics,https://www.bls.gov/web/empsit/cestn.htm. Cajner,Tomaz,LelandCrane,RyanA.Decker,AdrianHamins-Puertolas,ChristopherKurz, and Tyler Radler. 2018. “Using Payroll Processor Microdata to Measure Aggregate Labor 25

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