Assessing the Change in Labor Market Conditions

Finance and Economics Discussion Series Divisions of Research & Statistics and Monetary Affairs Federal Reserve Board, Washington, D.C. Assessing the Change in Labor Market Conditions Hess T. Chung, Bruce Fallick, Christopher J. Nekarda, and David D. Ratner 2014-109 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.

Assessing the Change in Labor Market Conditions Hess T. Chung Bruce Fallick FederalReserveBoardofGovernors FederalReserveBankofCleveland Christopher J. Nekarda David D. Ratner FederalReserveBoardofGovernors FederalReserveBoardofGovernors December 17, 2014 Abstract This paper describes a dynamic factor model of 19 U.S. labor market indicators, covering the broad categories of unemployment and underemployment, employment, workweeks, wages, vacancies, hiring, layoffs, quits, andsurveysof consumers’andbusinesses’perceptions. Theresultinglabormarketconditionsindex(LMCI)isausefultoolforgaugingthe changeinlabormarketconditions. Inaddition,themodelprovidesawaytoorganizediscussions of the signal value of different labor market indicators in situations when they mightbesendingdiversesignals. Themodeltakesthegreatestsignalfromprivatepayroll employment and the unemployment rate. Other influential indicators include the insured unemployment rate, consumers’ perceptions of job availability, and help-wanted advertising. ThroughthelensoftheLMCI,labormarketconditionshaveimprovedatamoderate pace of over the past several years, albeit with some notable variation along the way. In addition, from the perspective of the model, the unemployment rate declined a bit faster overthepasttwoyearsthanwasconsistentwiththeotherindicators. JELcodes: E24,E66,J20,J6 Keywords: LMCI, U.S. labor market, dynamic factor model, unemployment rate, employment WethankStephanieAaronson,CharlesFleischman,CraigHakkio,DavidLebow,andJonathanWillisfortheirvaluable comments and suggestions. We are grateful to Gary Burtless for helping us account for changes in the unemploymentinsurancesystem. DennisMawhirterandErikLarssonprovidedoutstandingresearchassistance. The viewsexpressedinthispaperdonotnecessarilyreflecttheviewsoftheBoardofGovernorsoftheFederalReserve System,theFederalReserveBankofCleveland,orothermembersoftheirstaffs.

1 Introduction TheU.S. labormarket islargeand multifaceted. Often-citedindicators, suchasthe unemployment rate or payroll employment, each measure a specific dimension of labor market activity, and it is not uncommon for different indicators to send conflicting signals about labor market conditions,especiallyatmonthlyfrequencies. Eventhemostprominentindicatorscandisagree. To cite one instance, the Bureau of Labor Statistics (BLS)’s employment report for December 2013 indicated that the unemployment rate had fallen 0.3 percentage point while payroll employmentroseonly74,000. Thus,theunemploymentratewassignallingastrongimprovement inthelabormarketandpayrollemploymentatepid(atbest)improvement. In such situations, analysts naturally look at additional indicators to try to infer the true rateofchangeinlabormarketconditions. Butthedesiretousemoreinformationisnotlimited to occasional situations. In recent years, for example, some observers have emphasized labor force participation and involuntary part-term employment as additional dimensions that merit particular attention, suggesting that these measures point to a more slowly improving labor market than does the more prominent unemployment rate. However, it is often difficult to knowhowtoweighthesignalsfromvariousindicators,especiallywhenthoseindicatorsareas diverseas,say,wageratesandconsumersentiment. Astatisticalmodel,whilenosubstitutefor judicious consideration, can be useful because it provides one relatively non-judgemental way tosummarizeinformationfromnumerousindicators. Therehavebeenseveraleffortsalongtheselinesinrecentyears. Forexample,Barnesetal. (2007),HakkioandWillis(2013)andZmitrowiczandKhan(2014)developedprincipalcomponentmodelsof12,24,and8labormarketindicators,respectively. Principalcomponentmodels attempttosummarizethecommonmovementinanumberofdataseries. Forthebroadereconomy, the Chicago Fed National Activity Index is derived from a principal component analysis of 85 monthly indicators (including 24 indicators from the labor market).1 In a related vein, numerousresearchershavedevelopedfactormodelsfornow-castingandforecastingaggregate outputfromalargenumberofmacroeconomicindicators(forexample,StockandWatson,2002; Giannone,ReichlinandSmall,2008;StockandWatson,2011). Thispaperdescribesadynamicfactormodelofnineteenlabormarketindicatorsandtheresultinglabormarketconditionsindex(LMCI).Section2describestheindicatorsthatweinclude inthemodel. Section3describesthefactormodelinsomedetail,includingourdetrendingprocedure, and how each indicator relates to the estimated LMCI. In section 4, we explain why we believe the LMCI is best viewed as an indicator of changes in labor market conditions and that its level is not a measure of the magnitude of labor market slack. Section 5 describes the behavioroftheLMCIbroadlyoverhistoryandhighlightsmovementsintheLMCIsincethebe- 1. http://www.chicagofed.org/publications/cfnai/index 1

ginning of the Great Recession. In section 6, we use the model to argue that the decline in the unemployment rate has somewhat overstated the improvement in labor market conditions in recentyears. Section7providesconcludingremarks. 2 Labor Market Indicators Information about the state of the labor market is available monthly from a variety of sources, including official government statistics, privately gathered data, and surveys of businesses and households. We include in our model a large, but certainly not exhaustive, set of the available data—19indicatorsinall. Because a modelof this type emphasizesthe common movementsamong indicators, it can besensitivetothebalanceacrossdifferenttypesofindicatorsincluded. Itisthereforedesirable toavoidweightingthescaletooheavilywithindicatorsthatreflectcloselyrelatedaspectsofthe labor market. That is to say, more indicators is not always better. On the one hand, including twomeasuresofasimilarobjectlikelyenhancesthemodel’sabilitytoidentifysignal(common movement) from noise (idiosyncratic variation). On the other hand, including too many measuresofthesamethingmaydistortthepictureintheirfavor. Forexample,if,inadditiontothe officialunemployment rate(designated“U-3” bythe BLS),wealso includedtheU-1, U-2, U-4, andU-5underutilizationrates—whicharehighlycorrelatedwithU-3—wewouldbiastheLMCI tolookmoreliketheunemploymentrate. Withthisconsiderationinmind,wechoseindicatorscoveringthebroadcategoriesofunemployment and underemployment, employment, workweeks, wages, vacancies, hiring, layoffs, quits, and surveys of consumers’ and businesses’ perceptions. Table 1 lists the indicators and provides some information about the form, source, and availability of each measure; they are discussed in more detail below. In order to enhance the real-time usefulness of our index, all data are measured at a monthly frequency and seasonally adjusted. Accordingly, the resulting LMCIdoesnotexhibitseasonalvariation. WebeginourestimationsamplewithJuly1976becausethatiswhenmostpublishedseries calculatedfromtheCPSbegin. However,asnotedinTable1,someindicatorsarenotavailable asfarbackas1976. Perhapsmoreimportantly,themostrecentmonthavailableforafewofthe indicatorsroutinelylagstheothersbyoneortwomonths. Inparticular,themost-recentobservationsforthehiringandquitratesfromtheJobOpeningsandLaborTurnoverSurvey(JOLTS) always lag the Current Population Survey (CPS) or Current Employment Statistics (CES) data by at least one month—and often two months. The indicators from the National Federation of Independent Businesses (NFIB)’s Small Business Employment Trends, net hiring plans and unfilledjobopenings,areoccasionallymissingforthemost-recentmonth,particularlywhenthe EmploymentSituationisreleasedearlyinthemonth. Ineithercase,dynamicfactormodelsare 2

Table 1. Labor Market Indicators Included in the LMCI Indicator Units Source Begins Unemploymentandunderemployment Unemploymentrate Percentoflaborforce CPS 1976m7 Laborforceparticipationrate Percentofpopulation CPS 1976m7 Involuntarypart-timeemployment Percentofemployment CPS 1976m7 Employment Privateemployment Percentofpopulation CES 1976m7 Governmentemployment Percentofpopulation CES 1976m7 Temporaryhelpservicesemployment Percentofpopulation CES 1982m1 Workweeks Averageweeklyhoursofproduction Hoursperweek CES 1976m7 workers Averageweeklyhoursofpersonsat Hoursperweek CPS 1976m7 work Wages Averagehourlyearningsof Dollarsperhour,percentchange CES 1976m7 productionworkers frompreviousyear Vacancies Compositehelp-wantedindex Index CB 1976m7 Hiring Hiringrate† Percentofnonfarmemployment JOLTS 1990m4 Transitionratefromunemployment Percentofunemployedinprevious CPS 1976m7 toemployment month Layoffs Insuredunemploymentrate Percentofcoveredemployment ETA 1976m7 Joblosersunemployedlessthanfive Percentofemployedinprevious CPS 1976m7 weeks month Quits Quitrate† Percentofnonfarmemployment JOLTS 1990m4 Jobleaversunemployedlessthan Percentofemployedinprevious CPS 1976m7 fiveweeks month Surveysofconsumers’andbusinesses’perceptions Jobavailability Percentofrespondentsanswering CB 1978m1 thatjobsareplentifulminuspercent answeringthatjobsarehardtoget ∗ Nethiringplans Percentoffirmsplanningtoexpand NFIB 1986m1 employmentinthenext3months minuspercentoffirmsplanningto cutjobs ∗ Unfilledjobsopenings Percentoffirmswithajobopening NFIB 1986m1 theycouldnotfill Notes: CB = Conference Board and Barnichon (2010); CES = Bureau of Labor Statistics, Current Employment Statistics;CPS=BureauofLaborStatistics,CurrentPopulationSurvey;ETA=DepartmentofLabor,Employment and Training Administration; JOLTS = Bureau of Labor Statistics, Job Openings and Labor Turnover Survey; NFIB=NationalFederationofIndependentBusiness. Seetheappendixforadditionaldetails. Availabilitylags (†)ormaylag(∗)thatoftheCES/CPSdata. 3

well-suitedtodealwithunbalancedpanelslikethisone. Theremainderofthissectionbrieflydescribestheindicatorsincludedinthemodel. Details abouttheirconstructionandabouttheunderlyingsourcedatacanbefoundintheappendix. 2.1 Unemployment and Underemployment The unemployment rate, plotted in Figure 1a, is one of the most closely watched labor market indicators. It measures the number of persons who do not currently have a job and that are available for work and have been actively searching for a job within the prior 4 weeks, and is thus arguably the most direct measure of the underutilization of labor resources. Movements inunemploymenttendtobecloselyrelatedtomovementsinaggregateeconomicactivity. (The redlineinthisandsubsequentfiguresistheestimatedtrend,whichisexplainedinsection3.) The labor force participation rate (LFPR), the number of persons either working or looking forworkasapercentageofthepopulation,alsoprovidesameasureoflabormarketutilization. It is plotted in Figure 1b. Although the unemployment rate provides the most direct measure of underutilization, the LFPR does respond to labor market conditions. For example, in tight labormarkets,personspreviouslynotinthelaborforcemayenterbecausejobopportunitiesare plentiful; incontrast,inslacklabormarkets,individualsmayleaveornotenterthelaborforce becausejobprospectsaredim. As many observers have noted, there are prominent trends in the labor force participation rate reflecting structural influences such as the aging of the baby boom generation, increasing longevity,andhigherlevelsofeducation.2 Thus,distinguishingcyclicalmovementsintheLFPR fromtrendisparticularlyimportant. AthirdmeasureofunderutilizationweincludeintheLMCIisinvoluntarypart-timeemployment (Figure 1c), specifically the number of persons working part-time for economic reasons. Although these persons have jobs, they are working fewer than 35 hours per week for reasons suchasslackwork,unfavorablebusinessconditions,inabilitytofindfull-timework,orseasonal declines in demand. Including this indicator captures a degree of underutilization that would notbemeasuredbytheunemploymentrateortheLFPR.3 2.2 Employment Thenumberofpersonsemployedisanotherobviouslyimportantindicatoroflabormarketconditions. We use nonfarm payroll employment from the CES, rather than employment from the 2. SeeAaronsonetal.(2014)foradiscussionofrecentdevelopmentsandfutureprospects. 3. Wewouldhavelikedtoincludeameasureofpersonsmarginallyattachedtothelaborforce(fromtheCPS). Insomerespects,wethinkthisindicatorcouldbesuperiortotheLFPRasameasureofunderutilization,because suchpersonsseemmostlikelytojoinorremainoutofthelaborforceinresponsetolabormarketconditions. Alas, becausetheseriesisavailableonlystartingin1994,itproveddifficulttodetrendanddifficultforthefactormodel toinferitscyclicaldynamics. 4

Figure 1. Underemployment Indicators (a)UnemploymentRate Percent of labor force 12 Trend 10 8 6 Nov. 4 2 1980 1985 1990 1995 2000 2005 2010 2015 Source: CurrentPopulationSurvey. Note: GrayshadedbandsindicateaperiodofbusinessrecessionasdefinedbytheNBER. (b)LaborForceParticipationRate Percent of population 68 Trend 67 66 65 64 Nov. 63 62 61 1980 1985 1990 1995 2000 2005 2010 2015 Source: CurrentPopulationSurvey. Note: Adjusted to account for changes in population weights. Gray shaded bands indicate a period of business recessionasdefinedbytheNBER. (c)InvoluntaryPart-TimeEmployment Percent of CPS employment 7 Trend 6 5 Nov. 4 3 2 1980 1985 1990 1995 2000 2005 2010 2015 Source: CurrentPopulationSurvey. Note: Levelupto1994adjustedbystafftoaccountforsurveyredesign. Grayshadedbandsindicateaperiodof businessrecessionasdefinedbytheNBER. 5

CPS,tomeasureemployment,becauseitisdrawnfromalargersurveythantheCPSandisless noisyatmonthlyfrequency. Wedividetotalnonfarmemploymentintoprivateemploymentand governmentemployment(Figures2aand2b). Torendertheseseriesstationary,wedividebythe civiliannoninstitutionalpopulation. We also include temporary help services employment (Figure 2c). Temporary help employmentmayleadoverallemployment,asfirmsconsideringraisingpayrollsmayfirsthireworkers on a temporary basis through a staffing agency. The use of temporary help employment increasednoticeablythroughthemid-1990s,whenitreachedarelativelystablelevelaboutwhich ithasfluctuatedsince. 2.3 Workweeks In addition to the number of persons at work, which represents the extensive margin of labor utilization, we included average weekly hours of persons at work to represent an intensive margin. We include two measures of workweeks, taken from different surveys and capturing slightlydifferentconcepts. Averageweeklyhoursofproductionandnonsupervisoryworkerscomes from the CES, and measures paid hours per job. We also include a measure of average weekly hours of persons at work from respondents in the CPS. As shown in Figures 3a and 3b, both measuresincreaseduringexpansionsanddeclineduringrecessions. TheCESmeasureofhours perjobappearstohaveaseculardownwardtrend,whereastheCPSmeasureofhoursperperson hasfluctuatedaround39hoursformostofthesampleperiod. 2.4 Wage Growth Accordingtomosttheories,wageinflationisanimportantindicatoroflabormarketconditions. Aggregate wages are thought to increase faster when conditions in labor markets are tight, because firms must raise wages to attract and retain workers. We include the twelve-month changein(nominal)averagehourlyearningsofproductionandnonsupervisoryworkersfromthe CES(Figure4). Thisseriesisthelongestmonthlytime-seriesonwagesavailable. Althoughthe BLS’s measure of average hourly earnings of all employees is more comprehensive, that series beganonlyin2005andsoistooshorttobeusefullyincludedinthemodel. 2.5 Vacancies The number of vacant positions at U.S. firms is another important indicator of labor market conditions. Businesseswishingtoexpandemploymenttypicallyidentifyvacantpositions,hence the stock of vacancies may proxy for unmet labor demand. For this reason, vacancies play a majorroleinthelargeliteratureonlabor-marketsearchandmatching. 6

Figure 2. Employment Indicators (a)PrivatePayrollEmployment Percent of population 54 Trend 52 50 48 Nov. 46 44 42 40 1980 1985 1990 1995 2000 2005 2010 2015 Source: CurrentEmploymentStatisticsandCurrentPopulationSurvey. Note: GrayshadedbandsindicateaperiodofbusinessrecessionasdefinedbytheNBER. (b)GovernmentPayrollEmployment Percent of population 10.0 Trend 9.8 9.6 9.4 9.2 9.0 8.8 Nov. 8.6 1980 1985 1990 1995 2000 2005 2010 2015 Source: CurrentEmploymentStatisticsandCurrentPopulationSurvey. Note: GrayshadedbandsindicateaperiodofbusinessrecessionasdefinedbytheNBER. (c)TemporaryHelpEmployment Percent of population 1.4 Trend Nov. 1.2 1.0 0.8 0.6 0.4 0.2 1980 1985 1990 1995 2000 2005 2010 2015 Source: CurrentEmploymentStatisticsandCurrentPopulationSurvey. Note: GrayshadedbandsindicateaperiodofbusinessrecessionasdefinedbytheNBER. 7

Figure 3. Workweek Indicators (a)AverageWeeklyHoursofProductionWorkers Hours 37 Trend 36 35 34 Nov. 33 32 1980 1985 1990 1995 2000 2005 2010 2015 Source: CurrentEmploymentStatistics. Note: GrayshadedbandsindicateaperiodofbusinessrecessionasdefinedbytheNBER. (b)AverageWeeklyHoursofPersonsatWork Hours 40.5 Trend 40.0 39.5 39.0 38.5 Nov. 38.0 37.5 1980 1985 1990 1995 2000 2005 2010 2015 Source: CurrentPopulationSurvey. Note: GrayshadedbandsindicateaperiodofbusinessrecessionasdefinedbytheNBER. TheJOLTSprovidesadirectmeasureofvacanciesatfirmsinthescopeoftheCES.However, this series begins only in December 2000. Moreover, the interaction of the short history of this series and the lag with which the data are published (resulting in a missing contemporaneous value) produced unstable results when we attempted to enter it into the model. For practical reasons, then, we have not included the JOLTS vacancy rate. Instead, we rely on a measure derived from data on help-wanted advertising from the Conference Board as a proxy for vacancies. In particular, we calculate a composite help-wanted index following Barnichon (2010) (Figure5). 8

Figure 4. Average Hourly Earnings of Production and Nonsupervisory Workers Dollars per hour, percent change from previous year 10 Trend 8 6 4 2 Nov. 0 1980 1985 1990 1995 2000 2005 2010 2015 Source: CurrentEmploymentStatistics. Note: GrayshadedbandsindicateaperiodofbusinessrecessionasdefinedbytheNBER. Figure 5. Composite Help-Wanted Index Index 120 Trend 100 Nov. 80 60 40 1980 1985 1990 1995 2000 2005 2010 2015 Source: ConferenceBoardandauthors’calculationsbasedonBarnichon(2010). Note: GrayshadedbandsindicateaperiodofbusinessrecessionasdefinedbytheNBER. 2.6 Hiring The change in employment can be divided into its component flows of hiring and types of separations. Becausethesecomponentshavedifferentcyclicalproperties,andcanbemeasured in various ways from various sources, we include measures of the most important (for this purpose)oftheminthemodel. We include two measures of hiring. The first is the total hiring rate from the JOLTS. Although, as noted above, the JOLTS data begin only in December 2000, Davis, Faberman and Haltiwanger(2012)usedgrossjobcreationanddestructionratesandtheircross-sectionalrelationship with gross hiring to construct a historical series of hiring rates beginning in 1990:Q2; weusetheirhistoricalseriesasdata.4 4. Seetheappendixforadditionaldetails. 9

Figure 6. Hiring Indicators (a)HiringRate Percent of payroll employment 4.5 Trend 4.0 Oct. 3.5 3.0 2.5 1980 1985 1990 1995 2000 2005 2010 2015 Source: JobOpeningsandLaborTurnoverSurvey,CurrentEmploymentStatistics,andauthors’calculations. Note:DatabeforeDecember2000wereprovidedbyDavis,FabermanandHaltiwanger(2012),whouseunpublished microdatatoinferseriesbackto1990:Q2. Grayshadedbandsindicateaperiodofbusinessrecessionasdefined bytheNBER. (b)TransitionRatefromUnemploymenttoEmployment Percent of unmployed in previous month 40 Trend 35 30 25 Nov. 20 15 10 1980 1985 1990 1995 2000 2005 2010 2015 Source: CurrentPopulationSurveyandauthors’calculations. Note: GrayshadedbandsindicateaperiodofbusinessrecessionasdefinedbytheNBER. The second measure of hiring is the transition rate from unemployment to employment calculated from the CPS. Although the latter series measures only a portion of total hiring, it representsaportionthatisparticularlycyclicallysensitive.5 2.7 Layoffs In some respects, unemployment due to layoff may be more reflective of labor demand than is aggregateunemployment,whichalsoincludes,forexample,thatduetolabormarketentry. We includetheinsuredunemploymentratefromtheDepartmentofLabor’sEmploymentandTrain- 5. Elsby,HobijnandS¸ahin(2013)showthattransitionsbetweenunemploymentandemploymentaccountforat least60percentofthevariationintheunemploymentrate. 10

Figure 7. Layoff Indicators (a)InsuredUnemploymentRate Percent of covered employment 6 Trend 5 4 3 2 Nov. 1 1980 1985 1990 1995 2000 2005 2010 2015 Source: EmploymentandTrainingAdministrationandauthors’calculations. Note:Rateupto1978adjustedbystafftoaccountforexpansionofUIcoveragetoincludestateandlocalgovernment andnonprofitjobs. GrayshadedbandsindicateaperiodofbusinessrecessionasdefinedbytheNBER. (b)JobLosersUnemployedLessthanFiveWeeks Percent of employed in previous month 2.5 Trend 2.0 1.5 Nov. 1.0 0.5 1980 1985 1990 1995 2000 2005 2010 2015 Source: CurrentPopulationSurvey,seasonallyadjustedbyauthors. Note: GrayshadedbandsindicateaperiodofbusinessrecessionasdefinedbytheNBER. ingAdministrationasagaugeoftheextentofthestockofunemploymentduetolayoffs,andjob losersunemployedlessthanfiveweeksfromtheCPSasameasureoftheflowintounemployment followinglayoffs. 2.8 Quits Separations due to workers quitting behave differently than do separations due to layoffs or other causes. Notably, workers’ decisions whether to quit appear to be especially sensitive to their prospects for finding another job. We include two measures of quit rates. The first is the quit rate from the JOLTS. As with the hiring rate, we extended this series back to early 1990usingestimatesfromDavis,FabermanandHaltiwanger(2012). Thesecondisjobleavers 11

Figure 8. Quits Indicators (a)QuitRate Percent of payroll employment 3.0 Trend 2.5 2.0 Oct. 1.5 1.0 1980 1985 1990 1995 2000 2005 2010 2015 Source: JobOpeningsandLaborTurnoverSurvey,CurrentEmploymentStatistics,andauthors’calculations. Note:DatabeforeDecember2000wereprovidedbyDavis,FabermanandHaltiwanger(2012),whouseunpublished microdatatoinferseriesbackto1990:Q2. Grayshadedbandsindicateaperiodofbusinessrecessionasdefined bytheNBER. (b)JobLeaversUnemployedLessthanFiveWeeks Percent of employed in previous month 0.40 Trend 0.35 0.30 0.25 0.20 0.15 Nov. 0.10 1980 1985 1990 1995 2000 2005 2010 2015 Source: CurrentPopulationSurvey,seasonallyadjustedbyauthors. Note: GrayshadedbandsindicateaperiodofbusinessrecessionasdefinedbytheNBER. unemployedlessthanfiveweeksfromtheCPS. 2.9 Surveys of Consumers’ and Businesses’ Perceptions We include indicators from two private surveys of households and businesses: the Conference Board’s Consumer Confidence Survey and the NFIB’s Small Business Economic Trends. From the Conference Board, we include a measure of job availability, the percent of respondents answering that jobs are plentiful minus the percent answering that jobs are hard to get. From the NFIB we include a measure of small firms’ net hiring plans, the percent of firms planning to expand employment in the next three months minus percent of firms planning to decrease employment,andoneofunfilledjobopenings,thepercentoffirmswithajobopeningthatthey 12

couldnotfill. 3 A Model of Overall Labor Market Conditions 3.1 The Overall Condition of the Labor Market as a Common Factor Weareinterestedinconstructinganindexrepresentinggenerallabormarketconditions,inthe sense that this index should capture, to as great a degree as possible, common movements in ourpaneloflabormarketindicators. Oneapproachtothisobjectivewouldbetoconstructthe first principal component of the indicators, as in some of the papers noted in the introduction. However,asnotedabove,ourpanelofindicatorsisunbalanced,featuringanumberofindicators with relatively short samples. Moreover, we wish to be able to produce stable index estimates contemporaneouswiththemonthlyEmploymentSituationreport,atwhichtimethefullpanelis notavailableattheendofthesample. Althoughmethodsforestimatingprincipalcomponents with missing data do exist (such as Stock and Watson, 1998), their application to our set of indicators proved unsatisfactory at producing stable estimates of the index; in particular, the resulting estimates revised considerably upon receipt of new observations for the indicators thatweremissingforthelastmonthofthesample. Inthispaper,therefore,weinsteadestimateadynamicfactormodel,alongthelineslaidout byGeweke(1977)andSargentandSims(1977). Inadynamicfactormodel,asintheprincipal components framework, the observable vector, Y , is a linear combination of a small number t of “common” factors, F , and an “idiosyncratic” component, ω : Y = HF +ω . In turn, the t t t t t lawofmotionforthecommonfactorsisassumedfollowavectorautoregression(VAR).Inour case, the persistence implied by the VAR dynamics substantially ameliorates the instability of factor estimates with missing end-of-sample data. As shown by Stock and Watson (1998), as thenumberofindicatorsinthepanelgrowslarge,principalcomponentandfactoranalysisare equivalent. Given our objective of capturing overall labor market conditions, we wish to focus on the commonvariationwhichaccountsforthelargestshareofthevarianceoftheindicators. Accordingly,weconstructtheLMCIasthefirstprincipalcomponentoftheprojectionoftheindicators ontothecommonfactors.6 Specifically,letθ betheeigenvectorofHvar(F)H (cid:48) associatedwith thelargesteigenvalue. Then (1) LMCI =θHF . t t 6. Ofcourse, thecommonfactorsthemselvesareidentifiedonlyuptoaninvertiblelineartransformation; that is,foranyinvertiblematrixP andsetoffactorestimatesF,thereisanobservationallyequivalentmodelthatyields factorestimatesPF. 13

Figure 9. Surveys of Consumers’ and Businesses’ Attitudes (a)JobsAvailability Net percent 60 Trend 40 20 0 Nov. -20 -40 -60 -80 1980 1985 1990 1995 2000 2005 2010 2015 Source: ConferenceBoard Note: Percentofrespondentsansweringthatjobsareplentifulminuspercentansweringthatjobsarehardtoget. GrayshadedbandsindicateaperiodofbusinessrecessionasdefinedbytheNBER. (b)NetHiringPlans Net percent 25 Trend 20 15 10 5 Nov. 0 -5 -10 1980 1985 1990 1995 2000 2005 2010 2015 Source: NationalFederationofIndependentBusinesses,seasonallyadjustedbyauthors. Note: Percentoffirmsplanningtoexpandemploymentinthenextthreemonthsminuspercentoffirmsplanningto decreaseemployment. GrayshadedbandsindicateaperiodofbusinessrecessionasdefinedbytheNBER. (c)UnfilledJobOpenings Percent 40 Trend 35 30 25 20 Nov. 15 10 5 1980 1985 1990 1995 2000 2005 2010 2015 Source: NationalFederationofIndependentBusinesses,seasonallyadjustedbyauthors. Note: Percentoffirmswithatleastonejobopeningthattheycouldnotfill. Grayshadedbandsindicateaperiodof businessrecessionasdefinedbytheNBER. 14

3.2 Detrending Many of the indicators in our panel appear to display trending behavior and explicit modeling of those low-frequency movements would substantially complicate estimation of the dynamic factormodel,whilelikelycontributinglittletoourprimarygoalofassessingthecyclicalbehavior ofthelabormarket. Forthisreason,beforeestimatingthefactormodelwedetrendeachseries, usingalocallyweightedscatterplotsmoother(LOWESS)filterwithabandwidthof16years(96 months on each side of a data point).7 This window is about twice as wide as would typically be used for monthly data; however the trends in many of the indicators appear to be lowerfrequencythanthestandardbandwidth,presumablyreflectingdemographicchangesandother slow-movingphenomena. Additionally,thislongerbandwidthimpliesalessvolatiletrendand, inparticular,onethatisnotheavilyinfluencedbyafewmonthsofadditionaldata. Asdiscussed later in section 4, having slow-moving trends makes it easier for us to interpret the change in theLMCIasasignalaboutaggregatelabormarketconditions. Unfortunately, our method for estimating trends is not immune to the endpoint problems associated with other time-series filters. In particular, at the first observation the window is entirelyforward-looking,andatthelastobservationthewindowisentirelybackward-looking. In order to lessen this problem at the end of the sample, we extend the series forward withsimulateddataforthepurposeofestimatingthetrend. Thesimulateddataaregenerated from an autoregressive moving-average (ARMA) equation for each indicator.8 For most series, beginning-point issues are not a problem, as their history is sufficiently long that the LOWESS trend is fully two-sided by July 1976. However, where the observed history is too short, we simulated 8 years of data backward from the start of the series using its historical relationship with a similar labor market indicator (described in the appendix). These simulated data, both backward and forward, were used only for estimating the level of the trend at the beginning andendofpublishedhistory;theydonotenterthemodeldirectly. Figure10providesanillustrationofthisprocedureusingtheunemploymentrate. Theblack lineplotstheactualdatathroughNovember2014. Themodelparameterswereestimatedusing datafromJuly1976toSeptember2014,denotedbytheunshadedarea;theshadedareasshow 8yearsbeforeandaftertheestimationsample.9 ThedashedredlineisaLOWESStrendbased on data only from the estimation sample. The endpoint issues are clear. The blue line is a simulation of the unemployment rate from an ARMA(3,1) model estimated over April 1987 to 7. Cleveland(1979). Thisfilterfitsapolynomialonaneighborhoodofqobservationsaroundtheestimatedpoint byweightedleastsquares. Wechosethebandwidthforeachindicatorsuchthatq=192months. 8. WechosethenumberofARterms,thenumberofMAterms,andwhethertoincludeatimetrendonacase-bycasebasis. Thesearedescribedintheappendix. 9. Although most indicators were available through November as of this writing, the JOLTS data were only availablethroughOctober. Therefore,themostrecentquarterwithdataforallindicatorswasthethirdquarter,and wechosetoendestimationatthatpoint. 15

Figure 10. Unemployment Rate and Estimated Trends Percent 12 Trend using estimation sample only 11 Trend using projection Data 10 Projection 9 8 7 6 5 4 3 1970 1975 1980 1985 1990 1995 2000 2005 2010 2015 2020 September2014. Thetrendweusedforthefactormodel(thesolidredline)iscomputedfroma hybridseriesthatincludestheadditional8yearsofhistoryplusthe8yearsofsimulatedfuture data. AlthoughtheARMAequationprojectionsmaynotprovetobeparticularlygoodforecasts, thisprocedureclearlyreducestheendpointbias. 3.3 The Stationary Dynamic Factor Model Afterdetrending,observablesarerelatedtothecommonfactorsviatheobservationequation (2) Y =HF +ω , t t t where Y is a 19×1 vector of labor market indicators, H is a 19×3 matrix of coefficients that t mapfromthethreecommonfactorstotheindicators, F isa3×1vectorofthecommonfactors. t Elementsoftheidiosyncraticerrorvectorω areassumedtobeGaussiananduncorrelatedboth t acrossobservablesandovertime. ThefactorsfollowaVAR(2)system: (3) F t =A 1 F t−1 +A 2 F t−2 +ε t , whereε isa3×1vectorofindependentandidenticallydistributedGaussianinnovations. The t system is estimated by maximizing the likelihood function, computed using the Kalman filter. The ending date for estimation of the trends and model parameters is the final month of the most recent quarter for which all series are available (September 2014 for the analysis in this paper). Thisdaterollsforwardeveryquarter. The model’s 3 factors explain roughly 75 percent of the common variation among the 19 16

Figure 11. The LMCI Index points 250 One-sided estimate 200 Two-sided estimate 150 100 Nov. 50 0 -50 -100 -150 -200 -250 -300 1976 1978 1980 1982 1984 1986 1988 1990 1992 1994 1996 1998 2000 2002 2004 2006 2008 2010 2012 2014 Note: GrayshadedbandsindicateaperiodofbusinessrecessionasdefinedbytheNBER. indicators; of this common variation, the LMCI alone accounts for about 85 percent (or 2/ 3 of thetotalvariationoftheindicators). Figure 11 plots the one- and two-sided estimates of the LMCI obtained using the Kalman smoother algorithm. For the remainder of the paper, we use the two-sided estimate because it providesthebestassessmentofthelabormarketconditionsgivenallavailableinformation. In practice, and as is visually evident in Figure 11, the one- and two-sided estimates track each othercloselyoverallhistory. 3.4 Relations between Individual Indicators and the LMCI Table2presentssomestatisticsthatdescribetherelationsbetweenindividualindicatorsandthe LMCI.ThefirstsetofcolumnsreportstheKalmangainoneachindicator,ameasureofhowthe current estimate of the LMCI responds to news about a given observable. Because an upward surpriseinsomeindicatorswouldcausetheLMCItorevisedown(asfortheunemploymentrate forexample)theindicatorsareorderedinthetablebytheabsolutevalueoftheKalmangain.10 Privatepayrollemploymentstandsoutashavingaparticularlylargegain,followedbythetwo unemploymentratesandjobavailabilityfromtheConferenceBoardsurvey. Thesecondsetofcolumnsreportsthein-samplecorrelationofthelevelofthe(detrended) indicatorwiththeLMCI.Variableswithlargegaincoefficientstendalsotobestronglycorrelated 10. Forafewindicators,suchasgovernmentemploymentandlaborforceparticipation,thegainhasacounterintuitivesign. Thegainsfortheseindicatorsaresmallandprobablyreflectaheavierloadingoncommoncomponents orthogonaltotheLMCIthanontheLMCIitself. Suchindicatorswouldessentiallyservetocontrolfortheinfluence ofthoseorthogonalcomponents. 17

Table 2. Relations between Individual Indicators and the LMCI Correlation Correlation Kalmangain withLMCI with∆LMCI Indicator Value Rank Value Rank Value Rank Privateemployment 3.44 1 0.92 7 0.83 1 Unemploymentrate −1.91 2 −0.97 1 −0.64 4 Insuredunemploymentrate −1.88 3 −0.94 3 −0.74 2 Jobavailability 1.40 4 0.94 2 0.53 5 Compositehelp-wantedindex 1.37 5 0.93 4 0.47 6 Joblosersunemployedlessthan5weeks −1.03 6 −0.83 13 −0.28 8 Jobshardtofill 0.96 7 0.93 6 0.20 10 Nethiringplans 0.89 8 0.78 14 0.15 13 Involuntarypart-timeemployment −0.74 9 −0.93 5 −0.39 7 Averageweeklyhoursofproductionworkers 0.71 10 0.68 15 0.20 9 Hiringrate 0.70 11 0.84 12 0.13 15 Quitrate 0.60 12 0.90 8 0.17 12 Temporaryhelpservicesemployment 0.58 13 0.86 10 0.70 3 Averageweeklyhoursofpersonsatwork 0.50 14 0.85 11 0.17 11 Transitionratefromunemploymenttoemployment 0.34 15 0.87 9 0.12 16 Governmentemployment −0.33 16 0.08 19 −0.03 19 Averagehourlyearningsofproductionworkers −0.28 17 0.36 18 0.14 14 Laborforceparticipationrate −0.24 18 0.52 17 0.06 18 Jobleaversunemployedlessthan5weeks 0.11 19 0.63 16 0.06 17 Notes: Indicators are ordered by absolute value of Kalman gain. Kalman gain measures the impact on the currentLMCIestimateofaone-standard-deviationforecasterrorinagivenindicator. Correlationsarecalculatedin sample. with the LMCI, with 7 of the 9 indicators in the top half of the ranking by Kalman gain having correlations in excess of 0.9. By contrast, outside of those 9 indicators, only the quit rate has suchahighcorrelationwiththeLMCI.Thefinaltwocolumnsreportthecorrelationoftheoverthe-month change in each indicator with the change in the LMCI. The ranking by correlation in changes is also similar to the ranking by the gains. Notably, however, whereas in levels the unemployment rate was the most highly correlated with the LMCI, in changes that distinction belongstoprivateemployment. While all of these measures identify broadly the same set of variables as especially influential, the detailed rankings may differ, for two noteworthy reasons. First, the Kalman gain is a multivariateconcept,analogoustoapartialderivative,thattakesintoaccountthecontributions ofotherindicators. Thegainforagivenindicatoristhereforesensitivetotheassumedpresence of the full set of other indicators. Were this information set to change, the gains would also be different. Thecorrelations,incontrast,aremoreanalogoustototalderivatives: Thecorrelation betweenagivenindicatorandtheLMCIcanreflectcontributionstotheindexofotherindicators thatarecorrelatedwiththegivenindicator. 18

Second,theKalmangainreferstotheinfluenceofasinglemonth’snewsaboutanindicator onthecurrentmonth’svalueoftheindex. However,thefullcontributionofanindicatortothe indexisalsoaffectedbythedegreetowhichtheeffectsofthenewsarepropagatedforwardand backward in time, a property essentially controlled by the VAR dynamics in equation 3. These differences explain why, for example, the unemployment rate can have the highest pairwise correlationwiththeLMCIbutamuchlowergainthanprivateemployment. We found two results from this exercise surprising. The first is the strong signal the model takesfromtheindicatorsofconsumers’andbusinesses’perceptionsoflabormarketconditions, mostnotablythatofjobavailability. Ourpriorwasthat“subjective”indicatorslikethesewould havelittleadditionalcontributionafterincludingharddatasuchastheunemploymentrate,hiring,andvacancies. Thesecondistherelativelyweaksignalthemodeltakesfromtheindicators of quits, as we think of quits as strongly related to labor market conditions. It is possible that the relatively low gain on the indicators of quits reflect a combination of monthly noise in the CPSmeasureofjobleaversandtheshorthistoryoftheJOLTSquitrate. 4 Levels versus Changes Figure11showstheleveloftheLMCI.Notsurprisingly,itspeaksandtroughsalignfairlyclosely withbusinesscyclesidentifiedbytheNationalBureauofEconomicResearch(NBER).However, in our view, the level of the index itself, and notably an LMCI equal to zero, has no obvious economically meaningful interpretation. In particular, the level of the index itself is severely limited as a gauge of the labor market slack, or the distance of the labor market from full employment. Thisissoforthreereasons. First,byconstructiontheindexhasanexpectedvalueofzeroovertheperiodofestimation. However, it is far from clear that the economy is at full employment on average over that particularperiod,oroveranylongperiod. WehavenotattemptedtoestimatealevelfortheLMCI thatwouldcorrespondto,forexample,thenaturalrateofunemployment. Second,thetrendsintheindicatorsthatentertheestimationoftheindexwerenotdesigned to be informative about the full-employment levels of each series. This is particularly important if, as is likely, the full-employment levels of those series have evolved over time. For this reason comparisons of the level of the LMCI over long periods are not by themselves reliable. Moreover, as good as a LOWESS procedure is, the estimated trends may be influenced by the businesscycle,and,despitetheARMAaugmentation,maybesubjecttoendpointbiasfromsuch amajorlongperiodofweaknessastheU.S.labormarkethasexperiencedinthepresentcycle. Third,andrelatedtotheabove,theindexcapturescommonmovementsonlyamongthecyclical deviationsoftheindicatorsfromtheirestimatedtrends,neglectinganycommonmovementsin thosetrends. 19

A few examples highlight our concern. As shown in Figure 1a, the unemployment rate has beenbelowtheestimatedtrendsincetheendof2013. WebelievethisisbecausetheLOWESSgeneratedtrendfortheunemploymentratehasbeenpulledupbythedeeprecessionandslow recovery. Inasimilarvein,webelievethetrendsforpart-timeforeconomicreasons(Figure1c) andprivatepayrollemploymenttobeaboveandbelow, respectively, levelsconsistentwithfull employment.11 As suggested by the figures, these biases are probably in play for the estimates of trend even before the recession, with the result that the LMCI reaches its highest level in 2007. Wefinditimplausiblethatthelabormarketwastighterin2007thanitwasin,say,2000. However, becausethecommoncomponentsofthetrendsareslowmovinginourspecification,webelievethatshort-runchangesintheindexareinformativeaboutmovementsinoverall labor market conditions. For that reason in the remainder of the paper we will concentrate on changesin,ratherthanlevelsoftheLMCI,andchangesatareasonablyhighfrequency. 5 Changes in Labor Market Conditions through the Lens of the LMCI Figure12plotstheaveragemonthlychangeintheLMCIsincethesecondhalfof1976. Except for the final bar, which extends only through November 2014, each of the bars represents the averageoverasix-monthperiod. Notsurprisingly,changesintheLMCIalignwellwithbusinesscyclesasdefinedbytheNBER. Thatis,theLMCIgenerallydeclinesduringrecessions(thegreyshadedareas)andtypicallyrises duringexpansions. Andthemagnitudesofthedeclinesaccordwithmostobservers’assessments oftheseverityofthoserecessions. TheaveragemonthlyincreaseintheLMCIsofarduringthe current expansion has been roughly in line with previous expansions, but, of course, follows muchlargeraveragemonthlydeclinesduringtheprecedingrecession. 5.1 Decomposing the LMCI into Contributions of Individual Indicators We can gain more insight into the determinants of the LMCI estimates by explicitly computing the dependence of the estimated LMCI path on the data for each indicator. Specifically, given the linear-Gaussian specification for our dynamic factor model, the paths of the LMCI and the indicatorshaveajointmultivariatenormaldistribution. Asageneralpropertyofsuchdistributions, the expected path of the LMCI, conditional on the data, is linear in the indicators. Thus, we can decompose the estimated LMCI path into contributions from each indicator, holding the remaining indicators constant. As the estimate is two-sided, in principle the entire history 11. Usingtheserieswithoutdetrendingwouldcreateitsownsetofproblems,asitwouldimplicitlyassumethat thetrendineachserieswasconstantatthemeanoftheseries. 20

Figure 12. Average Monthly Change in LMCI Index points 30 20 10 * 0 -10 -20 -30 1976 1978 1980 1982 1984 1986 1988 1990 1992 1994 1996 1998 2000 2002 2004 2006 2008 2010 2012 2014 Note: Each bar is the average monthly change over a six-month period. Gray shaded bands indicate a period of businessrecessionasdefinedbytheNBER.*Thebarfor2014:H2istheaveragemonthlychangeforJulythrough November. of each indicator’s deviation from its trend influences the estimated LMCI at any given date.12 However, in practice, the estimated LMCI for a particular date depends to any significant degree only on observations in a narrow window around that date. In particular, only the last sixmonthsreceiveanysubstantialweightindeterminingtheestimatedLMCIattheendofthe sample. The calculation of these contributions is easily done using the standard Kalman filter and smoothingrecursions. LetuswriteZ t =[F t ;F t−1 ]andW =[A 1 ,A 2 ]. ThenthestandardKalman filterrecursioncanbeexpressedintheform (4) Z t|t =(1−B)WZ t−1|t−1 +BY t t (5) = (cid:88) [(1−B)W]s−t 0BY s s=t 0 whereBistheKalmangainmatrix. Thecorrespondingdecompositionofthetwo-sidedestimates isstraightforward. 12. Thisrepresentsastarkdeviationfromaprincipalcomponentsmodelinwhichthecurrentleveloftheprincipal component is a weighted average of the current indicators only. We believe the richer structure of our model’s decomposition,whilecomplex,isdesirable. 21

Figure 13. Change in LMCI and its Decomposition since 2007 Index points 20 10 Q4* 0 -10 -20 Private payroll employment Job availability -30 Unemployment rate Composite help-wanted index Insured unemployment rate All other indicators -40 2007 2008 2009 2010 2011 2012 2013 2014 Notes: Thesolidblackcircleistheaveragemonthlychangeineachquarter;thestackedbarsarethecontributionof anindicatortotheaveragemonthlychange. Grayshadedbandindicatesaperiodofbusinessrecessionasdefined bytheNBER.*Averagemonthlychangefor2014:Q4istheaverageofOctoberandNovember. 5.2 Changes in Labor Market Conditions since 2007 Figure 13 zooms in on the Great Recession and ongoing recovery. The solid black circles mark the average monthly change in the LMCI in each quarter since 2007. The LMCI began falling in the second quarter of 2007 and deteriorated sharply in late 2008 and early 2009, as the financialcrisisreacheditsheight. TheLMCIstartedimprovinginthesecondhalfof2009. The uneven pace of the ongoing labor market recovery is apparent at this time scale. Indeed, the LMCI captures several periods of sluggish improvement in the early parts of 2010, 2011, and 2012. The particularly marked, but temporary, slowdown in labor market improvement in the secondquarterof2012standsout. The stacked bars decompose the totalchanges into the contributions of the five most influentialindicators,plusthesumofthecontributionsofallotherindicators. Overtherecovery,as is typical, a few indicators have accounted for the bulk of the increase in the LMCI. In the first twoyearsoftherecovery,theinsuredunemploymentrate(thegreenportionofthebars)made alargecontributiontotheimprovementintheLMCI,reflectingasubstantialslowinginlayoffs; thiscontributionhassincediminished. Gainsinprivatepayrollemployment(theblueportionof thebars)anddeclinesintheunemploymentrate(thepinkportionofthebars)havebeenconsistentcontributorstotheimprovement,althoughmoreinsomeyearsthaninothers. In2014, private employment and the unemployment rate have accounted for most of the improvement intheLMCI. 22

6 Has the Unemployment Rate Overstated Recent Improvements in Labor Market Conditions? The unemployment rate has declined by 2 percentage points since the end of 2012. This brisk paceofdecline,setagainstthebackdropofamoremodestimprovementinrealGDPandother indicators,ledsometowonderwhethertheunemploymentratehasoverstatedtheimprovement in labor market conditions. For example, in the press conference after the September 2014 Federal Open Market Committee meeting, Federal Reserve Chair Janet Yellen pointed to two factorssuggestinglessimprovement: thedeclineinlaborforceparticipationandelevatedshare of involuntary part-time employment.13 Our model provides a direct and transparent way to assess this and other questions arising when the model’s indicators appear to send different signals about labor market conditions. This section examines whether the unemployment rate hasbeensendingamorepositivesignalthanhavetheotherindicators. To see how one can use a dynamic factor model to analyze movements in one of the indicators vis-à-vis the other indicators, recall equation 2, which relates the unobserved factors to theindicators. Fromthatrelationship,onecangenerateapredictionfortheindicatorsbygenerating a “fitted” value from the estimated coefficients and estimated factors. The left panel of Figure 14 shows this model prediction for the unemployment rate since 2005. It is no surprise that the predicted unemployment rate tracks the actual unemployment rate quite closely—we showed in section 3.4 that the LMCI and the unemployment rate are highly correlated. Note thatthispredictedvalueineffect“controlsfor”thebehavioroftheotherindicators,notablythe LFPRandinvoluntarypart-timeemployment. Although the LMCI’s prediction for the unemployment rate generally tracks the actual unemploymentrateclosely,thereareperiodswhenthetwodiffer. Lookingoverthepastfewyears, between2011and2012,theunemploymentratewashigherthanthemodel’spredictionbased on its indicators, but over the latter half of 2013 and through 2014 the actual unemployment ratefellbelowthemodel’sprediction. AlthoughtheunemploymentrateinNovemberstoodonly about0.1percentagepointbelowthemodel’sprediction, theunemploymentratehasdeclined byabout1/ 4percentagepointmorethantheLMCI’spredictedvaluesincetheendof2012. Given these discrepancies, the question arises: What would the change in labor market conditions have looked like had the model not seen the decline in the unemployment rate? Again,thestructureoftheLMCIoffersanaturalwaytoconductthisexperiment. Whenmissing values for some of the observables (the elements of Y ), the model generates expectations for t alloftheindicatorsbasedontheassumeddynamicsofthefactorsandtheirrelationshiptothe indicators. To be precise, given an estimate of the factors in month t (F ), the model forms an t 13. http://www.federalreserve.gov/mediacenter/files/FOMCpresconf20140917.pdf,p.11–12. 23

Figure 14. Has the Unemployment Rate Overstated the Improvement in Labor Market Conditions? (a)UnemploymentRateandModelPrediction (b)AverageMonthlyChangeinLMCI PPeercrecennt to of fla labboor rf oforcrece InInddeex xp pooinintsts 1111 88 UUnneemmpploloymymeennt tr aratete BBaaseselinlinee MMooddeel pl prereddicitciotionn WWithith u unneemmpploloymymeennt tr aratete m misissisningg 77 1100 aaftfeter rD Deec.c .2 2001122 66 99 55 88 44 77 33 66 22 NNovo.v. 55 11 44 00 22000066 22000088 22001100 22001122 22001144 22001133 22001144 Note: GrayshadedbandindicatesaperiodofbusinessrecessionasdefinedbytheNBER.Averagemonthlychange for2014:Q4istheaverageofOctoberandNovember. expectationoftheobservablesinmonth T ≥ t viathefollowingequation: (6) E (cid:2) Y |{Y ,s≤ t}, (cid:8) Y˜ ,t <u≤T (cid:9)(cid:3)=HE (cid:2) F |{Y ,s≤ t}, (cid:8) Y˜ ,t <u≤T (cid:9)(cid:3) , T s u T s u where Y˜ contains all available indicators after month t except the unemployment rate. We estimateaversionoftheLMCIthatdeletesobservationsfortheunemploymentratestartingin 2013. The right panel of Figure 14 plots the average monthly change in the LMCI (the blue bars) for each quarter from 2013 forward together with the average monthly change in the LMCI when the unemployment rate was not observed after December 2012 (the orange bars). It is visuallyapparentfromthepanelthatthetheyellowbarsarelowerthanthebluebarsfromthe secondhalfof2013throughtheendof2014. Althoughthemagnitudeismodest—theaverage monthlychangewas0.3pointslowerwhenthemodeldidnotobservetheunemploymentrate than when it did—the constellation of labor market indicators excluding the unemployment ratesuggestsslightlylessimprovementinlabormarketconditions. 24

7 Closing Remarks Overall,theLMCIappearstobeausefultoolforassessingthechangeinlabormarketconditions based on a broad array of labor market indicators. Of course, any purely statistical procedure willbesensitivetothemanychoicesonemustmakeinspecifyingthemodel. Moreover,sucha procedure will not be able to flexibly discount idiosyncratic events nor to account for changes ineconomicstructures. Suchamodelis,therefore,nosubstituteforjudiciousconsiderationof thevariousindicators. Nevertheless,suchamodelprovidesasummarythatcanusefullyinform thosedeliberations. Notsurprisingly,giventhenatureofbusinesscycles,theLMCIishighlycorrelatedwiththe unemployment rate, as it is individually with several other prominent labor market indicators. Of course, we could not be sure this would be the case before developing the LMCI, but that done, one may ask whether the LMCI adds to consideration of the unemployment rate alone. Wethinkthatitdoes. AlthoughtheLMCIandtheunemploymentratemaymoveinreasonably close tandem on average, it is precisely in those times when movements in the unemployment rate seems to be at variance with other indicators that a tool for summarizing a large number ofindicatorsismostvaluable. Thatis,theLMCIisonewaytoorganizediscussionsofthesignal valueofanumberofdifferentlabormarketindicatorsinsituationswhentheymightbesending diversesignals. Examples of such situations are not hard to find, such as recent discussions about whether the unemployment rate has been overstating the degree of improvement in the labor market. Answeringthisquestionrequiresonetocomparetheunemploymentratewithotherlabormarketindicators. TheLMCI,andmultivariatemethodslikeit,arewell-suitedforthattask. Indeed, from the perspective of the LMCI, the unemployment rate has improved slightly faster than is consistentwiththesignalfromtheotherindicatorsoverthepasttwoyears. 25

Appendix Detrending Procedure Inordertomitigateendpointbias,weprojecteachindicatorforwardwithsimulateddata. The simulateddataaregeneratedfromanARMAequationforeachindicator. Thespecificationsare given in Table A1. The estimation period for the projection model is from April 1987 through the last month of the most recent quarter for which all data are available. Starting in 1987 allowsustoomittimetrendsfrommostequations. Inaddition,forsomeseriesforwhichtheobservedhistoryisshort,wealsosimulated8years ofdatabackwardfromthestartoftheseries,asdescribedbelow. Backcasted Series Temporary help services employment was projected backward (as a percent of population) using private employment (as a percent of population) and a linear time trend. The equation was estimated using data from the first observation in January 1982 through December 1992. We used a this period to infer the historical relationship because temporary help employment rose rapidly as a share of employment in the mid-1990s and then stabilized from about 1997 forward. Hiringrateandquitrate. Davis,FabermanandHaltiwanger(2012)usedunpublishedJOLTS microdata to infer quits and hires that extend back to April 1990. We first interpolated the quarterly data from DFH to monthly series covering from April 1990 to November 2000; we appended these to the published data, which begin in Decmeber 2000. We then treat that hybridseriesasdatainthefactormodel. Toestimateatwo-sidedtrend,weprojectedtheseries back 8 years using the transition rates from unemployment to employment (hiring rate) and employment to unemployment (quit rate) computed from the CPS. The backcasting equations wereestimatedusingdatafromtheirfirstobservationinApril1990throughJune2005. Joblosersunemployedlessthanfiveweeks,jobleaversunemployedlessthanfiveweeks, net hiring plans, unfilled job openings, and job availability. These five indicators were projected backward using the unemployment rate. The equations were estimated using data fromtheirfirstobservationthroughJune2005. Data sources UnderlyingsourcedatausedtoconstructtheindicatorslistedinTable1arelistedinTableA2. 26

Table A1. Specification for Projection Equations ARMA(p,q)model usedtoprojectseries Indicator AR MA Other Unemploymentandunderemployment Unemploymentrate 3 1 Laborforceparticipationrate 1 1 t2 Involuntarypart-timeemployment 3 1 Employment Privateemployment 3 1 Governmentemployment 1 0 Temporaryhelpservicesemployment 2 1 Workweeks Averageweeklyhoursofproductionworkers 3 1 t Averageweeklyhoursofpersonsatwork 3 1 Wages Averagehourlyearningsofproductionworkers 1 1 Vacancies Compositehelp-wantedindex 3 1 Hiring Hiringrate 1 1 Transitionratefromunemploymenttoemployment 3 1 Layoffs Insuredunemploymentrate 2 1 Joblosersunemployedlessthanfiveweeks 2 1 Quits Quitrate 1 1 Jobleaversunemployedlessthanfiveweeks 1 1 Consumerandbusinesssurveys Jobavailability 3 1 Nethiringplans 2 1 Unfilledjobsopenings 1 1 27

Table A2. Underlying Source Data Series Source SA/ Units BLSretrievalcode FREDseriesname First Final NSA value value Civiliannoninstitutional CPS NSA Thousands LNU00000000 CNP16OV 1948m1 n.a. population1 Laborforcelevel1 CPS SA Thousands LNS11000000 CLF16OV 1948m1 n.a. Employmentlevel1 CPS SA Thousands LNS12000000 CE16OV 1948m1 n.a. Unemploymentlevel1 CPS SA Thousands LNS13000000 UNRATE 1948m1 n.a. Employmentlevel-Part-time CPS SA Thousands LNS12032194 LNS12032194 1955m5 n.a. foreconomicreasons,all industries2 Employment-Totalnonfarm CES SA Thousands CES0000000001 PAYEMS 1939m1 n.a. Employment-Totalprivate CES SA Thousands CES0500000001 USPRIV 1939m1 n.a. Employment-Government CES SA Thousands CES9000000001 USGOVT 1939m1 n.a. Employment-Temporaryhelp CES SA Thousands CES6056132001 TEMPHELPS 1990m1 n.a. services Employment-Helpsupply CES SA Thousands n.a. n.a. 1982m1 2003m4 services3 Averageweeklyhoursof CES SA Hours CES0500000007 AWHNONAG 1964m1 n.a. productionand nonsupervisoryemployees- Totalprivate Averageweeklyhours-Total CPS NSA Hours LNU02005054 n.a. 1976m6 n.a. atwork,allindustries4 (Continued) 28

Table A2. Underlying Source Data (continued) Series Source SA/ Units BLSretrievalcode FREDseriesname First Final NSA value value Averagehourlyearningsof CES SA Dollarsperhour CES0500000008 AHETPI 1964m1 n.a. productionand nonsupervisoryemployees- Totalprivate Hires-Totalnonfarm5 JOLTS SA Thousands JTS00000000HIL JTSHIL 1990m4 n.a. Quits-Totalnonfarm5 JOLTS SA Thousands JTS00000000QUL JTSQUL 1990m4 n.a. Laborforceflows- CPS SA Thousands LNS17100000 LNS17100000 1967m7 n.a. Unemployedtoemployed6 Laborforceflows-Employed CPS SA Thousands LNS17400000 LNS17400000 1967m7 n.a. tounemployed6 Insuredunemploymentrate7 ETA SA Percentofcovered n.a. IURSA 1971m1 n.a. employemnt Percentoftotaljoblosers CPS NSA PercentofCPS LNU03023633 n.a. 1976m6 n.a. unemployedlessthan5 employment weeks4 Percentoftotaljobleavers CPS NSA PercentofCPS LNU03023717 n.a. 1976m6 n.a. unemployedlessthan5 employment weeks4 Unemploymentlevel-Job CPS SA Thousands LNS13023705 LNS13023705 1967m1 n.a. leavers Help-wantedadvertisingindex CB SA Index n.a. n.a. 1951m1 2010m10 Totalonlinehelp-wantedads CB SA Thousandsofads n.a. n.a. 2005m5 n.a. Employment-Jobsplentiful CB SA Percentofindividuals n.a. n.a. 1978m1 n.a. surveyed (Continued) 29

Table A2. Underlying Source Data (continued) Series Source SA/ Units BLSretrievalcode FREDseriesname First Final NSA value value Employment-Jobshardtoget CB SA Percentofindividuals n.a. n.a. 1978m1 n.a. surveyed Jobopenings4 NFIB NSA Percentoffirmswitha n.a. n.a. 1986m1 n.a. jobopeningtheycould notfill Nethiringplans4 NFIB NSA Percentoffirms n.a. n.a. 1986m1 n.a. planningtoexpand employmentinthenext 3monthsminuspercent offirmsplanningto decreaseemployment Notes: CB=ConferenceBoardandBarnichon(2010);CES=BureauofLaborStatistics,CurrentEmploymentStatistics;CPS=BureauofLaborStatistics,Current PopulationSurvey;ETA=DepartmentofLabor,EmploymentandTrainingAdministration;JOLTS=BureauofLaborStatistics,JobOpeningsandLaborTurnover Survey;NFIB=NationalFederationofIndependentBusiness. 1. Leveladjustedbyauthorstoaccountforchangesinpopulationweights. 2. LeveluptoDecember1993adjustedbyauthorstoaccountfortheCPSredesign. SeePolivkaandMiller(1998). 3. SIC7363. 4. Seasonallyadjustedbyauthors. 5. DatabeforeDecember2000wereprovidedbyDavis,FabermanandHaltiwanger(2012),whouseunpublishedJOLTSmicrodatatoinferseriesbackto1990:Q2. 6. DatabeforeJanuary1994areauthors’calculationsfromCPSmicrodata. 7. Convertedtomonthlyandadjustedbefore1978byauthorstoaccountforexpansionofUIcoveragetoincludestateandlocalgovernmentandnonprofitjobs. 30

References Aaronson, Stephanie, Tomaz Cajner, Bruce Fallick, Felix Galbis-Reig, Christopher Smith, and William Wascher. 2014. “Labor Force Participation: Recent Developments and Future Prospects.”BrookingsPapersonEconomicActivity,2. Barnes, Michelle, Ryan Chahrour, Giovanni Olivei, and Gaoyan Tang. 2007. “A Principal ComponentsApproachtoEstimatingLaborMarketPressureandItsImplicationsforInflation.” FederalReserveBankofBostonPublicPolicyBrief07-2. Barnichon, Regis. 2010. “Building a Composite Help-Wanted Index.” Economics Letters, 109(3):175–78. Cleveland,WilliamS.1979.“RobustLocallyWeightedRegressionandSmoothingScatterplots.” JournaloftheAmericanStatisticalAssociation,74(368):829–36. Davis, Steven J., R. Jason Faberman, and John Haltiwanger. 2012. “Labor Market Flows in theCrossSectionandoverTime.”JournalofMonetaryEconomics,59(1):1–18. Elsby, Michael W. L., Bart Hobijn, and Aysegül S¸ahin. 2013. “On the Importance of the Participation Margin for Market Fluctuations.” Federal Reserve Bank of San Francisco Working Paper2013–05. Geweke, John. 1977. “The Dynamic Factor Analysis of Economic Time Series.” In Latent Variables in Socio-Economic Models. , ed. Dennis J. Aigner and Arthur S. Goldberger, Ch. 19. North-HollandPublishingCo. Giannone, Domenico, Lucrezia Reichlin, and David Small. 2008. “Nowcasting: The Real- Time Informational Content of Macroeconomic Data.” Journal of Monetary Economics, 55(4):665–76. Hakkio, Craig S., and Jonathan L. Willis. 2013. “Assessing Labor Market Conditions: The LevelofActivityandtheSpeedofImprovement.”FederalReserveBankofKansasCityMacro Bulletin(July18). Polivka, Anne E., and Stephen M. Miller. 1998. “The CPS after the Redesign: Refocusing the EconomicLens.”InLaborStatisticsMeasurementIssues.249–89.UniversityofChicagoPress. Sargent, Thomas J., and Christoper A. Sims. 1977. “Business Cycle Modeling without Pretending to Have Too Much A Priori Economic Theory.” In New Methods in Business Cycle Research.,ed.ChristopherSims.FederalReserveBankofMinneapolis. Stock,JamesH.,andMarkW.Watson.1998.“DiffusionIndexes.”NBERWorkingPaper6702. Stock, James H., and Mark W. Watson. 2002. “Macroeconomic Forecasting Using Diffusion Indexes.”JournalofBusiness&EconomicStatistics,20(2):147–62. Stock,JamesH.,andMarkW.Watson.2011.“DynamicFactorModels.”InOxfordHandbookof EconomicForecasting.,ed.MichaelP.ClementsandDavidF.Hendry,35–59.OxfordUniversity Press. 31

Zmitrowicz, Konrad, and Mikael Khan. 2014. “Beyond the Unemployment Rate: Assessing Canadian and U.S. Labor Markets Since the Great Recession.” Band of Canada Review, Spring:42–53. 32