When is the Fiscal Multiplier High? A Comparison of Four Business Cycle Phases

Finance and Economics Discussion Series Divisions of Research & Statistics and Monetary Affairs Federal Reserve Board, Washington, D.C. When is the Fiscal Multiplier High? A Comparison of Four Business Cycle Phases Travis Berge, Maarten De Ridder and Damjan Pfajfar 2020-026 Please cite this paper as: Berge, Travis, Maarten De Ridder and Damjan Pfajfar (2020). “When is the Fiscal Multiplier High? A Comparison of Four Business Cycle Phases,” Finance and Economics Discussion Series 2020-026. Washington: Board of Governors of the Federal Reserve System, https://doi.org/10.17016/FEDS.2020.026. 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.

When is the Fiscal Multiplier High? ∗ A Comparison of Four Business Cycle Phases TravisBerge† MaartenDeRidder‡ DamjanPfajfar§ FederalReserveBoard UniversityofCambridge FederalReserveBoard February24,2020 Abstract Wesynthesizetherecent,attimesconflicting,empiricalliteratureregardingwhetherfiscalpolicyis moreeffectiveduringcertainpointsinthebusinesscycle.Evidenceofstatedependenceinthemultiplierdependscriticallyonhowthebusinesscycleisdefined.Estimatesofthefiscalmultiplierdonot changewhentheunemploymentrateisaboveorbelowitstrend.However,wefindthatthemultiplier ishigherwhentheunemploymentrateisincreasingrelativetowhenitisdecreasing.Thisresultholds usingbothalongtime-seriesattheU.S.nationallevelandforapanelofU.S.states. Keywords:Fiscalmultipliers;countercyclicalpolicy;cross-sectionalanalysis;localprojections JELclassification:E62;C31;C32. ∗ TheviewsexpressedinthispaperarethoseoftheauthorsanddonotnecessarilyreflectthoseoftheFederalReserveBoard. †Address: BoardofGovernorsoftheFederalReserveSystem,20thandConstitutionAveNW,Washington,DC20551,U.S.A. E-mail:travis.j.berge@frb.gov.Web:https://www.federalreserve.gov/econres/travis-j-berge.htm. ‡Address: University of Cambridge, Faculty of Economics, Sidgwick Ave, Cambridge, CB3 9DD, U.K. E-mail: mcd58@cam.ac.uk.Web:http://www.maartenderidder.com/. §Address: BoardofGovernorsoftheFederalReserveSystem,20thandConstitutionAveNW,Washington,DC20551,U.S.A. E-mail:damjan.pfajfar@frb.gov.Web:https://sites.google.com/site/dpfajfar/. 1

1 Introduction TheGreatRecessiontriggeredafocusonthefiscalmultiplier,andespeciallythequestionofwhetherthe multipliervariesovertime. Thequestionisofgreatimportancetofiscalpolicymakers,sinceananswer intheaffirmativeimpliesthatwell-designedandwell-timedfiscalpolicycanspureconomicgrowtheven ifthemultiplierisbelowunityonaverage. Empiricalevidenceonwhetherthemultiplierforfiscalexpenditurevariesoverthebusinesscycleis mixed. Auerbach and Gorodnichenko (2012b) is one prominent study to find that the fiscal multiplier depends on the state of the economy. Using regime-switching models, Auerbach and Gorodnichenko findthatfiscalpolicyisconsiderablymoreefficaciousintheU.S.duringrecessionsthanexpansions. In contrast,whenRameyandZubairy(2018)lookforstate-dependenceinthemultiplierusingalonghistory ofnewsaboutchangestomilitaryspendingintheUnitedStates,theydonotfindevidencethatthefiscal multiplier varies over the business cycle. Further, the Ramey and Zubairy estimate of the multiplier is alsobelowone. Thispapercontributestothisliteraturebyhighlightinghowestimatesofthefiscalmultiplieraresensitive to the manner in which state dependence is defined. To motivate our results, consider figure 1, whichshowsahighlystylizedpathoftheunemploymentrateoverthebusinesscycle.Therearefourdistinctstagesofthebusinesscycle. InstageI,theeconomyis‘runninghot’withtheunemploymentrate below its natural rate, and economic activity is expanding. This phase occurs until the business cycle peak. In stage II, the economy is still operating above trend, but economic activity is slowing and the unemploymentraterising. WehavelabeledstageIIIastheperiodinwhicheconomicactivitycontinues tocontractandtheunemploymentrateisaboveitstrend. Finally, stageIViswhentheunemployment rateisaboveitstrendbuteconomicactivityisexpandingandtheunemploymentratefalling.1 Fromthis figure,welabelfourdistinctstagesofthebusinesscycle.StagesIandIIareaboom,sincetheeconomyis operatingaboveitstrend.Incontrast,stagesIIIandIVareaslump.StagesI/IVandII/IIIarethebusiness cycleexpansionandrecession,respectively. Weshowthatthesimpledistinctionbetweenboom/slumpandexpansion/recessioncanlargelyreconciletheempiricalresultsdescribedabove. Whenwecompareestimatesofthefiscalmultiplierconditionalonwhethertheeconomyisinaboomorslump, wefindsimilarmultipliersinbothstatesthat 1Thestylizedunemploymentrateispurposefullyasymmetricacrossthebusinesscycle,reflectingthefactthatunemploymentrisesmuchmorequicklythanitfalls. Similarly, forsimplicitywehavedrawnthetrendunemploymentrateastimeinvariant,althoughitmaywellvaryovertime. 1

aretypicallynotstatisticallydifferent.However,fiscalmultipliersaresignificantlyhigherwhentheeconomyisinrecessioncomparedtowhenitisinexpansion. Furthermore, multipliersinrecessionsarein almostallspecificationshigherthanone.Thisresultisrobusttoabroadseriesofalternativecontrolsfor thestateoftheeconomy,aswellasdifferentalgorithmsusedtodefinethepeaksandtroughsintheunemploymentrate.Wealsoshowthattheexacttransformationofvariablesusedintheanalysismatter,in particularthetransformationofgovernmentexpenditures.2 Weclaimthatdetrendedgovernmentexpendituresasashareofpotentialoutputareamoreappropriatechoiceduetoaseculartrendingovernment expenditures. Figure1:Stylizedbehaviorofunemploymentrateacrossthebusinesscycle. Notes:Romannumeralsdenotevariousbusinesscyclephases.Seetextfordetails. Estimatingthefiscalmultiplierrequiresidentifyingexogenouschangestogovernmentexpenditures. Therecentliteraturehastakentwoalternativeapproachestoresolvingthisproblem. Thefirstistousea verylongtime-seriesofhistoricaldata,asinRameyandZubairy(2018),andidentifyshocksviaanarrative approach.Thesecondistouseapaneldataset,asinNakamuraandSteinsson(2014),whouseapanelof U.S.statestoestimate‘open-economy’relativefiscalmultipliers.3 Sinceidentifyingexogenouschangestogovernmentexpenditureisdifficult,wewillconductouranalysis using both datasets. To make the results comparable, we use the same definition of the business 2WeuseaGordonandKrenn(2010)transformationforallvariables, butthegovernmentexpenditures. Seefigure4and discussiononpage11foradetails. 3NakamuraandSteinsson(2014)findmixedevidencethatthefiscalmultipliervariesacrossslumpsandbooms,depending onwhethertheslump/boomisdefinedusingoutputorunemployment. 2

cycle,findingbusinesscyclepeaksandtroughsintheunemploymentrateeitheratthenationalorstate level.AsinRameyandZubairy(2018),wedonotfindstate-dependenceconditionalonperiodswhenunemploymentisaboveorbelowitstrendbutdofindevidenceofstatedependencedependingonwhether theunemploymentrateisincreasingversuswhenitisdecreasing. Whenweconducttheanalysisusing defensespendingshocksfromNakamuraandSteinsson(2014),wefindfiscalmultipliersarehigherwhen theU.S.stateisinrecessioncomparedtoperiodswhenitisexpanding. Again,thereisnoevidencethat the fiscal multiplier is different in slumps versus booms. We can also study each stage of the business cycleseparatelyusingstate-leveldata. Weconfirmthatthemultipliersaresignificantlyhigherinstage IIandIIIofthecyclecomparedtotheotherstagesofthebusinesscycle. Insum,wearelargelyableto reconciletheresultsofRameyandZubairy(2018)andNakamuraandSteinsson(2014). Theseempiricalfindingshaveimportantimplicationsfortheoreticalworkthataimstomicro-found fiscal multipliers that vary across the business cycle. Typically, economic models that produce timevariationinfiscalmultipliersrelyonconvexityintheaggregatesupplycurve. Inthissituation,thefiscal multiplierislargerwhentheeconomyisoperatingbelowitspotential. InMichaillat(2014),forexample, thesupplycurveisconvexbecauseitismorecostlytohirelaborwhenlabormarketsaretight. Alternatively,Canzonerietal.(2016)postulatethatfinancialfrictionsaresmallerwhentheoutputgapissmall. While both provide intuitive mechanisms for state-dependence that match some of the empirical evidence, an alternative mechanism is needed to match results in this paper, because these mechanisms implythatthemultipliervariesacrossbooms/slumps,whereaswefindthestrongestevidenceoftimevariation to be based on chronologies that describe recessions and expansions. One possibility is the modelwithloss-aversionutility,asinSantoroetal.(2014),whichhasbeenshowntogeneratestatedependanceformonetarypolicyshocksoverGDPgrowthcyclesthatroughlycorrespondtoincreasesand decreasesintheunemploymentrate. BesidesAuerbachandGorodnichenko(2012a)andRameyandZubairy(2018),severalotherpapers study whether the multiplier is higher during recessions.4 Auerbach and Gorodnichenko (2012b) find evidenceofstate-dependenceusingasampleofOECDcountries. OtherpapersthatuseU.S.dataand find evidence of state-dependence in the fiscal multiplier include: Bachmann and Sims (2012), Baum etal.(2012),Shoag(2013),CandelonandLieb(2013),Fazzarietal.(2015),andDuporandGuerrero(2017). 4ItisworthnotingthatRameyandZubairy(2018)dofindevidencethatthemultiplierishigherwheninterestrateshitthe zerolowerboundstate,inlinewithpredictionsfromDSGEmodels(e.g.,Christianoetal.,2011). 3

Our work is also related to the literature studying regional business cycle differences across U.S. states. CarlinoandDefina(1998)examinethedifferentialimpactofmonetarypolicyacrossU.S.states andregionsandfindthatmanufacturingregionsexperiencelargerreactionstomonetarypolicyshocks thanindustrially-diverseregions. Furthermore,BlanchardandKatz(1992)studythebehaviorofwages and employment over regional cycles, and Driscoll (2004) details the effect of bank lending on output acrossU.S.states.Owyangetal.(2005)andFrancisetal.(2018)alsousestate-leveldatatoevaluatebusinesscyclesandcountercyclicalpolicy. Theremainderofthispaperproceedsasfollows.Section2describesourstrategytoidentifythebusiness cycle phases in figure 1, both for national-level data in the United States as well as for state-level data. Section3describesthedata. Resultsandrobustnesschecksarepresentedinsection4,andfinally section5concludes. 2 Identifyingbusinesscyclephases 2.1 Businesscyclesatthenationallevel Weusetheunemploymentratetodefinethephasesofthebusinesscycle.Wetakethisapproachbecause the unemployment rate is highly cyclical, and because a number of recent papers indicate that labor marketvariablesmeaningfullyidentifybusinesscyclephases.5 Theotheradvantageofusingtheunemploymentrateisthatthereareestimatesatboththenationalandstatelevels,sothatwecanperformour analysisatdifferentgeographicallevelsusingthesamemethodology. TheBryandBoschan(1972)algorithm(BBalgorithm)identifiesourrecessionchronologies.Thealgorithmidentifieslocalpeaksandtroughsinagivenseries,asinfigure1.6 Afterlocalpeaksandtroughsare obtained,threerestrictionsareenforcedontotheresultingchronology.First,peaksandtroughsmustalternate.Inthecasethattwopeaksaresequential,thenthepeakcorrespondingwiththelowerunemploymentrateisused.Theconverseidentifieslocaltroughs.Secondly,theBBalgorithmenforcesaminimum durationofeachbusinesscyclephase,sixmonthsortwoquarters.Finally,forthestate-leveldata,weadd arestrictionthatbusinesscycletroughscorrespondtoacumulativeriseintheunemploymentrateofat least0.5percentagepointfromthepreviouspeak. Thisrestrictionisrequiredforidentifyingstate-level business cycles because it ensures that small movements in the state-level unemployment rate, which 5See,e.g.,HamiltonandOwyang(2012),Francisetal.(2018),andBergeandPfajfar(2019). 6Fordetailsontheimplementationofthealgorithm,seeBryandBoschan(1972). HardingandPagan(2002)andStockand Watson(2014)providerecentapplicationstomacroeconomicdata. 4

maybedueitsrelativelylargesamplingerror,arenoterroneouslyidentifiedasturningpoints(Bureauof LaborStatistics,2017). Asapointofcomparison,wewillperformouranalysisusingtheNBER-defined recessionchronology. Wealsorequireamethodtoidentifyslumpsandbooms. WefollowRameyandZubairy(2018)and impose a time-invariant threshold of 6.5 percent. Slumps are periods when the unemployment rate is above6.5percent,whereasperiodswhentheunemploymentrateisbelow6.5percentisaboom. Figure2andtable1showtheseriesandprovidesummarystatistics.Thethreepanelsoffigure2plot theunemploymentrateandeachbusinesscyclechronology:theBBalgorithmisshowninthetoppanel; thesecondpanelshowsperiodswhentheunemploymentrateisabove6.5percent;andforcomparison, thefinalpanelshowstheNBERrecessiondates. Figure2:VariousbusinesscyclephasesintheUnitedStates. 1890 1900 1910 1920 1930 1940 1950 1960 1970 1980 1990 2000 2010 02 01 0 Unemployment rate and BB recessions % 1890 1900 1910 1920 1930 1940 1950 1960 1970 1980 1990 2000 2010 02 01 0 Unemployment rate and slumps % 1890 1900 1910 1920 1930 1940 1950 1960 1970 1980 1990 2000 2010 02 01 0 Unemployment rate and NBER recessions % Notes:ThebluelineineachpanelistheU.S.unemploymentrate.Greybarsindicatethestateoftheeconomyasidentifiedby theBBalgorithm,the6.5percentthreshold,orbytheNBERbusinesscycledatingcommittee.Seethetextfordetails. The figure and summary statistics highlight importance of the chronology when measuring statedependence. NBER-definedrecessionshavetheshortestduration,astheNBERcommitteelooksacross manydifferentindicatorstoidentifythepeaksandtroughsineconomicactivity. TheBry-BoschanalgorithmproducesbusinesscyclepeaksthatroughlycoincidewiththosefromtheNBER.However,theBB recessions are somewhat longer in duration than those identified by the NBER, especially in the post- 5

Great Moderation period and the so-called ‘jobless recoveries.’ Relative to the NBER dates, the BB algorithmproducesseveralbrieffalsepositivesassociatedwithverysmallupwardmovementsintheunemploymentrate(forexample, 1934, 1967, 1977, and1995), aswellasonefalsenegative(1900). There isalsooneperiodthattheNBERhasidentifiedasadouble-dipthattheBBalgorithmidentifiesasone longrecession,1918–1921.However,onthewhole,thetworecessionchronologiesarequitesimilar.This resultgivesusconfidencethattheBBalgorithmappliedtostate-levelunemploymentrateswillresultin meaningfulrecessionchronologies.7 Incontrast,slumpsareclearlyquitedifferentfromthetworecessionseries,sincetheymeasurethe presenceofeconomicslackandnotsimplywhethertheeconomyisexpandingorcontracting. Thestart ofslumpsroughlycoincidewithbusinesscyclepeaks,buthavemuchlongerduration. Indeed,slumps areonlyweaklycorrelatedwithNBERrecessions,whereasBBrecessionslargelycoincidewithNBERrecessiondates. Table1:SummarystatisticsofU.S.downturns1890–2015. Slump BB NBER recession recession N.obs 13 29 26 Duration(quarters) Mean 13.9 7.5 5.6 Median 10 7 5 Stddev 13.2 3.5 2.5 Min 2 3 3 Max 48 14 15 Notes:Tableshowssummarystatisticsforthreedifferentbusinesscycledownturns:slumps,definedasperiodswhentheunemploymentrateisabove6.5percent;BB-definedrecessions;andNBER-definedrecessiondates. Sampleperiod1890–2015, durationmeasuredinquarters.Seethetextfordetails. Table2summarizesthebehavioroftheunemploymentrate, conditionaloneachphase. Whilethe unemploymentrateisaboutflatoverslumpsandbooms,itclearlyincreasesduringrecessionsandfalls duringexpansions,whetherdefinedbytheBBalgorithmortheNBER.Itisworthnotingthattheminimumunemploymentrateoccurredin1918Q3,aquarterdefinedasabusinesscyclepeakbyboththeBB algorithmandtheNBER. Finally, wealsoprovidetwoalternativeBBchronologiesasarobustnesscheck, showninfigureA.3 andtableA.2. BecausetheBBalgorithmproduceschronologiesthatdifferintheiraveragedurationand 7Further,inourrobustnessexercises,weimposefurtherrestrictionsontheBBalgorithmregardingthedurationofbusiness cycles.TheserestrictionsproducearecessionseriesthatverycloselymirrorstheNBERrecessiondates,seefigureA.3. 6

Table2:SummarystatisticsofU.S.unemploymentratebybusinesscyclephase. Slump Boom BBrec. BBexp. NBERrec. NBERexp. N.phases 13 12 29 28 26 25 Behaviorofunemploymentrate Meanchange 0.1 0.0 0.5 -0.3 0.6 -0.3 Mean 10.3 4.6 6.4 6.8 7.1 6.4 Stddev 4.6 1.2 4.0 4.0 4.5 3.8 Min 6.5 0.6 0.6 0.8 0.6 0.8 Max 24.8 6.4 24.8 24.1 24.8 23.5 Notes: TableshowssummarystatisticsoftheU.S.unemploymentrate,inpercent,conditionaloneachbusinesscyclephase. Sampleperiod1890–2015.Seetextfordetails. producesseveralverybrieffalsepositiverecessionevents,wecomputetwoalternatives. Inthefirst,we imposethatthedurationofthecompletecyclehastobeatleast7quarters.Inthesecond,weimposethat completebusinesscyclehasdurationofatleast16quarters. Wedenotethesetwoalternativesas“prolonged(7)”and“prolonged(16)”cycles.Wealsoprovideanalternativemeasureofslumpsandboomsby identifyingthetrendusinganHPfilter. 2.2 Localbusinesscycles Themethodologydescribedintheprevioussectionisalsoappliedtostate-levelunemploymentratedata todefinestate-levelbusinesscyclechronologies. However,whileweusemonthlydatatodeterminethe U.S. state-level chronologies our regression analysis uses annual data. We define a given state-year as recessionifmorethan6monthsinagivenyearareidentifiedasarecession.8,9Panel(a)offigure3shows Bry-Boschanstate-levelrecessionchronologies. Inpanel(b)weshowourmeasureofslumps. Because wedonotwishtoimposethesamelevelofthenaturalrateacrossstates, wedefineslumpsasperiods whenthestate’sactualunemploymentrateisaboveitsHP-filteredtrend. Again,weidentifyayearasa slumpif7ormoremonthswithinthatyearareslumps. 3 Data In this paper we use both U.S. historical national data and U.S. state level data to calculate fiscal multipliers. RameyandZubairy(2018)collectalongtime-seriesofU.S.quarterlydata, from1889through 8SummarystatisticsareprovidedintableA.3inAppendix. 9Asarobustnesscheck,wehavealsogeneratedrecessionchronologiesusingastate-levelcoincidentindexasourmeasure ofeconomicactivity.Wefindthatourchronologiesarequalitativelyunchanged. 7

Figure3:State-levelrecessionchronologiesfromBry-Boschanalgorithmandstate-levelslumpsusingHP filter. AK AK AL AL AR AR AZ AZ CA CA CO CO CT CT DC DC DE DE FL FL GA GA HI HI IA IA ID ID IL IL IN IN KS KS KY KY LA LA MA MA MD MD ME ME MI MI MN MN MO MO MS MS MT MT NC NC ND ND NE NE NH NH NJ NJ NM NM NV NV NY NY OH OH OK OK OR OR PA PA RI RI SC SC SD SD TN TN TX TX UT UT VA VA VT VT WA WA WI WI WV WV WY WY 1980 1985 1990 1995 2000 2005 2010 2015 1980 1985 1990 1995 2000 2005 2010 2015 (a) Recessions (b) Slumps Notes:EachrowdenotesaU.S.state,bytime.RedshadedareadenotesrecessionasdeterminedbyBry-Boschanalgorithm(left panel)orslumpsasdeterminedbytheHPfilter(rightpanel).Seetextfordetails. 2015. ThedataincludesnominalGDP,theGDPdeflator,governmentpurchases,federalgovernmentreceipts,population,theunemploymentrate,interestrates,BlanchardandPerotti(2002)shocks,andnews aboutdefensespending. Thesenewsshocksrepresentthepresentvalueofchangesinexpecteddefense spendingdividedbytrendnominalGDP.NewsaboutdefensespendingaredetailedinRamey(2011b); theserieshasbeenextendedinRameyandZubairy(2018).ThedataisshowninfiguresA.1andA.2.Detailsontheunderlyingsourcesofthisdata,aswellasthetreatmentappliedtocreateconsistentseriesis providedinRameyandZubairy(2018). Turning to the state-level data, annual state-level real GDP growth is obtained from the Bureau of EconomicAnalysis(BEA),andisavailableoverthepost1976period.Weobtaintwovariablesonmilitary spending from Nakamura and Steinsson (2014) up to 2007, thus our sample for the analysis is 1977– 2007. Thefirstincludesprimemilitaryprocurement,whichconsistsofallcontractsvaluedover$25,000 (‘prime’). Thesecondisabroadermeasureincludingdirectfinancialcompensationtoemployees. The 8

theBureauofLaborStatistics(BLS)alsoprovidesstate-levelunemploymentrates,whichweusetomeasurebusinesscyclephases.10 Wearealsoabletoincludemanycontrolvariablesinourstate-levelregressions. Tocontrolforstate heterogeneityinthelabormarket,weaddcontrolsforlabormarketdynamism,firmsize,unionpower, andminimumwages. Dynamismismeasuredthroughthereallocationrate, definedasthesumofjob destructionandjobcreationrates. Firmsizeismeasuredbytheaveragenumberofemployeesperfirm. Weaccountfordifferencesinstateminimumwageswiththeratioofminimumtomedianwages,which arecompiledusingdatafromtheBLS.Collins(2014)providesdataonunionpower,whichisdefinedby the absence of right-to-work laws in a state. The other control variables relate to the structure of the economy.Theshareofworkersemployedbythegovernmentisincludedsincegovernmentexpenditures arerelativelyinsensitivetoshocks. Theshareofworkersemployedinservicescontrolsforsectoralcomposition: certainindustriesmaybemorevulnerabletodemandfluctuations. Thedataaresummarized intable Table3:Summarystatisticsforstate-leveldataandcontrols. Mean SD Obs. Min. Max. Source BiannualstateGDPgrowth 5.4 5.1 1,478 -12.8 33.5 BEA Militaryspendingshocks Growthinprimemilitaryexp.-state 0.02 0.02 1,478 -5.1 4.0 NS Growthinbroadmilitaryexp.-state 0.03 0.03 1,478 -5.1 4.0 NS Growthinprimemilitaryexp.-national 0.00 0.00 29 -0.4 0.7 NS Growthinbroadmilitaryexp.-national 0.01 0.01 29 -0.5 0.8 NS Statecontrolvariables Labormarketdynamism 0.29 0.05 1,836 0.18 0.69 BDS Firmsize 18.8 3.2 1,836 10.4 29.3 BDS Minimumstatewage/medianstatewage 0.4 0.1 1,683 0.3 0.7 CPS/BLS Unionpower 0.6 0.5 1,938 0 1 Collins Shareservices 0.7 0.1 1,734 0.5 0.8 CPS Sharegovernment 0.1 0.0 1,734 0.0 0.2 CPS Notes:BEAisBureauofEconomicAnalysis;NSstandsforNakamuraandSteinsson(2014);CollinsstandsforCollins(2014); CPSisCurrentPopulationSurvey;BLSisBureauofLaborStatistics;BDSindicatestheBusinessDynamicsStatisticsofthe CensusBureau. 4 Revisitingstate-dependenceofthefiscalmultiplier Section2identifiedthestatesoftheworldwhereinthefiscalmultipliermayvary.Wenowturntoestimatingthefiscalmultiplieritself. Weestimatethemultiplierintwodifferentways. Firstweusethemilitary 10See, https://www.bls.gov/web/laus/laumstrk.htm. We obtain our data from the FRED database, https:// research.stlouisfed.org/pdl/337. 9

newsshocksintroducedbyRamey(2011b)andrecentlyupdatedinRameyandZubairy(2018). Wethen turntothepaneldataapproachofNakamuraandSteinsson(2014). 4.1 Estimatingfiscalmultiplierswithhistoricaltime-series 4.1.1 Empiricalapproach We first identify fiscal shocks using the narrative-based fiscal policy news series of Ramey (2011b) and RameyandZubairy(2018). Withtheidentifiedfiscalpolicyshocksinhand,theresponseofrealgovernmentspendingandrealGDPtothenewsshockismeasuredusingthelocalprojectionsofJordà(2005): y t+h =α y,h +β y,h shock t +γ y,h z t−1 +(cid:178) y,t+h (1) g t+h =α g,h +β g,h shock t +γ g,h z t−1 +(cid:178) g,t+h (2) Here,y t+h isthecumulativechangeinpercapitaGDPbetweent andt+h,g t+h isthecumulativechange in per capita government spending, shock is the identified fiscal spending shock, and z is a vector of t controls. The β coefficients in equations (1)–(2) give the average response of output or government h expendituretoamilitarynewsshockinhorizonh. Toestimatebusinesscyclephase-dependenteffect ofdefensenewsonGDP,forexample, theshocksandcovariatesareinteractedwithadummyvariable indicatingthephaseofthebusinesscycle: y t+h =I t−1 (cid:161)α 1,h +β 1,h shock t +γ 1,h z t−1 (cid:162)+(cid:161) 1−I t−1 ) (cid:161)α 0,h +β 0,h shock t +γ 0,h z t−1 (cid:162)+(cid:178) t+h . (3) The fiscal multiplier can then be calculated as the ratio of the cumulative effect of the news shock to outputrelativetothatonspending.Specifically,thecumulativemultiplierm overanH-quarterhorizon j is: H H (cid:88) (cid:88) m = β / β , (4) j y,j,h g,j,h h=1 h=1 wherethesubscriptjdenotesthefactthatthemultipliermaybeeitheranaverageresponseoraphasedependentresponse. 10

AnequivalentestimationofthemultipliercanbeobtainedfromanIVapproach(RameyandZubairy, 2018).Specifically,weestimateIVregressionsforeachhorizonh: h h h (cid:88) y t+j =I t−1 (cid:161)α 1,h +m 1,h (cid:88) g t+j +γ 1,h z t−1 (cid:162)+(cid:161) 1−I t−1 ) (cid:161)α 0,h +m 0,h (cid:88) g t+j +γ 0,h z t−1 (cid:162)+ω t+h , (5) j=0 j=0 j=0 usingI t−1 ×shock t and(1−I t−1 )×shock t asinstrumentsforcumulatedgovernmentspending. Before turning to the results, we discuss the exact transformations of the variables. The cumulative change in GDP is y t+h =Y t+h /Y t p and the cumulative change in government spending as g t+h = (G t+h −Gp)/Y t p . Yp denotes potential output andGp is the trend in government expenditures. These transformationsdepartfromthoseinGordonandKrenn(2010);ourreasoningisshowninfigure4. Per capitagovernmentspendingasashareofpotentialoutput,thetoppanel,hasaseculartrend. Failingto accountforthistrendintheeconometricspecificationwillbiastheultimateestimateofthefiscalmultiplierdownwards,becausethelocalprojectionswillconfoundexogenousincreasesing withthetrend. Wecircumventthisproblembydetrendingg beforedividingitbypotentialoutput.11 Ourresultingseries isshowninthebottompaneloffigure4. Methodologically,onecouldinterpretthisasthatwearecalculatingthemultipliersofthediscretionarypartofgovernmentspendingandsoitisnotsurprisingthatthe resultscanbesensitivetotheexacttransformation.12 4.1.2 Results Webeginbyexamininginstrumentrelevance.Ourfirst-stageregressionprojectscumulatedrealgovernmentspendingateachhorizonontothenewsshockatperiodt. Weconsidertwoinstrumentsets: the RameyfiscalnewsshocksandtheRameyfiscalnewsshocksalongsidetheBlanchard-Perottishocks. We alsoconditiononfourlagseachofGDP,governmentexpenditure,andcontrols.13 Figure5plotsthedifference between the first-stage effective F-statistics and the thresholds computed in Montiel Olea and Pflueger(2013).ThepurplelinesarethevaluesoftheF-statisticrelativetothethresholdwhenusingonly themilitarynewsshocksastheinstrument,whiletheasteriskedorangelineshowsthevaluewithboth instruments.Thefiguresuggeststhatmilitarynewshashighrelevanceduringslumps,butotherwisethe 11Thiswedobyregressinggontimetrendsuptothefourthpower. 12Alternatively,onecouldcontrolfortrendsinthelocalprojectionanalysis. Wehavefoundthattheresultsareverysimilar betweenthesealternatives, butthatoneshouldbecarefulwhenestimatingstate-dependentmultiplierswithtrends, asthe twoproceduresdescribedabovearenolongerequivalent.Itisalsonotclearwhetherstate-dependenttrendsareconceptually appropriate.Thus,wehaveoptedtoadjustthetransformationofvariablestocontrolfortheseculartrending. 13ThevectorofcontrolvariablesincludestheratioofGDPtopotential,theratioofgovernmentspendingtopotential,lagsof thosetwocontrols,andlaggednewsshocks. 11

Figure4:Realgovernmentexpendituresbeforeandaftercontrollingforitsseculartrend. 1890 1900 1910 1920 1930 1940 1950 1960 1970 1980 1990 2000 2010 06 04 02 0 Real per capita government spending as a share of potential GDP % 1890 1900 1910 1920 1930 1940 1950 1960 1970 1980 1990 2000 2010 04 02 0 Detrended real per capita government spending as a share of potential GDP % Notes:FigureshowstherawandthedetrendedmeasureofrealgovernmentexpenditurespercapitaintheUnitedStates.Vertical dashedlinesdenotestartofvariouswars(Spanish-American, WWI,WWII,Korean, Vietnam, responsetoSovietinvasionof Afghanistan,andSept11,2001).Seetextfordetails. F-statisticremainsbelowtherelevantthresholdsforothercasesconsidered,includingthelinearcase.In general,usingbothshocksappearstobeamorepowerfulinstrumentthanthemilitarynewsshockalone, althoughatlongerhorizonstheF-statisticstendtofallbellowtherelevantthresholds. Table4presentsmultipleestimatesofthecumulativefiscalmultiplier.Column2containsmultipliers fromthelinearmodel.Columns3-4containsresultsforslumpsandbooms,whiletherightmostcolumns presenttheresultscalculatedoverrecessionsandexpansions. Foreachregressionspecificationwecumulatethefiscalmultiplieroveratwoyearandfouryearperiod.Theblocksofthetablepresentdifferent regressionspecifications.ThebaselinespecificationusesthesamecontrolsasRameyandZubairy(2018), butnotethetransformationofgovernmentexpendituresisdifferentinallourestimations.Specification 2adjuststheregressionforaveragetaxratesandinflation. Specifications3and4usebothmilitarynews shocksandBlanchard-PerottishocksasinstrumentsforboththefullsampleandexcludingWWII.14 Thereislittleevidenceofstatedependencewhenwecomparethefiscalmultiplieracrossslumpsand booms when we instrument using only the military spending shock, but there are some signs of state dependancewhenweusebothshocksasinstruments. Duringperiodswhentheunemploymentrateis above6.5percentthecumulativetwo-yearmultiplierinthebaselinespecificationis.76,comparedtoits estimatedvalueof.57periodswhentheunemploymentrateislow.Thenullhypothesisthetwoestimates arethesamecannotberejectedusinganystandardthreshold.RelativetoRameyandZubairy(2018),our 14IntheappendixwereportresultsusingthresholdVARs. FiscalmultipliersestimatedusingTVARssuggestlittledifference acrossthebusinesscyclephasesatthetwoyearintegral,althoughthereissomeevidenceofasymmetryatfouryearhorizon. 12

Figure5:MontielOleaandPfluegertestsofinstrumentrelevance. 0 5 10 15 20 Horizon 03 02 01 0 01− 02− Linear Ramey Ramey + BP 0 5 10 15 20 Horizon 03 02 01 0 01− 02− Slump Ramey Ramey + BP 0 5 10 15 20 Horizon 03 02 01 0 01− 02− Boom Ramey Ramey + BP 0 5 10 15 20 Horizon 03 02 01 0 01− 02− Recession Ramey Ramey + BP 0 5 10 15 20 Horizon 03 02 01 0 01− 02− Expansion Ramey Ramey + BP Notes: Linesshowthedifferencebetweenthefirst-stageF-statisticandthe5percentlevelthresholdfromMontielOleaand Pflueger(2013).PurplelineusesRamey’snewsvariableastheinstrument;asteriskedorangelineusesbothRameynewsvariable andBPshocksasinstruments.RegressionspecifiedasinBaseline(militaryspendingshock)intable4.Seetextfordetails. estimatedmultipliersduringslumpsandthelinearmultipliersareatouchhigher. Thesedifferencesare duetoourslightlydifferenttransformationofgovernmentspending. Whenweaddadditionalcontrols for taxes and inflation, the estimated multiplier increases, especially during slumps, but remains statisticallyindistinguishablefromtheboom-timemultiplier. Finally,theestimatesofthefiscalmultiplier arebelowone;theonlyspecificationwhereslump-specificmultiplierislargerthanoneoccurswhenwe excludeWWII. Resultsthatcomparerecessionsandexpansionsaresomewhatdifferent. Inthebaselinespecification, the two-year cumulative multiplier is 1.6 in recessions, compared to .6 during expansions, a statistically relevant difference at the 5 percent level. The standard errors of the recession multipliers are significantly larger than those from the slump/boom chronologies, reflecting a relative paucity of data points during recessions. The difference between the estimated multiplier in recession versus expansionistypicallynotstatisticallydifferentintheotherspecifications,althoughtheestimatedmultiplieris alwayshigherinrecessionsthanexpansions. 13

Table4:Estimatedfiscalmultipliers. Linear Above/belowtrend Peaktotrough(BBalg) All Slump Boom Recession Expansion 1.Baseline(militaryspendingshock) 2yearintegral 0.72 0.76 0.57 1.60 0.64† (0.09) (0.11) (0.10) (0.42) (0.11) 4yearintegral 0.78 0.76 0.63 1.93 0.74† (0.06) (0.05) (0.10) (0.57) (0.08) 2.Militaryspendingshock,taxesandinflationasadditionalcontrols 2yearintegral 0.74 0.86 0.63 1.28 0.67 (0.09) (0.17) (0.10) (0.33) (0.09) 4yearintegral 0.79 0.82 0.66 1.48 0.78 (0.07) (0.08) (0.12) (0.46) (0.06) 3.Militaryspendingshock+BPshocks 2yearintegral 0.50 0.83 0.42† 0.88 0.54 (0.08) (0.18) (0.08) (0.28) (0.11) 4yearintegral 0.71 0.75 0.56† 1.37 0.69† (0.06) (0.05) (0.08) (0.41) (0.09) 4.Militaryspendingshock+BPshocks,excludingWWII 2yearintegral 0.47 1.94 0.33† 0.57 0.42 (0.16) (0.83) (0.13) (0.37) (0.26) 4yearintegral 0.77 1.67 0.59 1.20 0.59 (0.35) (0.71) (0.31) (0.48) (0.52) Notes: Newey-Weststandarderrorsinparentheses. BPdenotesBlanchardandPerotti(2002). Specification4excludesobservationsfrom1941Q3to1945Q4.Seetextfordetails. †indicatesthatthedifferenceacrossphasesisstatisticallysignificantat10percentlevel. Figure6presentscumulatedmultipliersforthebaselinespecification.Theleftpanelcomparesbooms andslumps, whiletherightpanelshowsrecessionsversusexpansions. Thisfigureshowsaclearstatedependenceinthemultiplierwhencomparingrecessionstoexpansions,whereasthemultiplierisvery similaracrossboomsandslumps.Themultiplierisalwayshigherwhenashockoccursduringrecession, andthisdifferenceissignificantatseveralhorizons. To further clarify these fiscal multipliers, figure 7 show the impulse responses of real government spendingandGDPtoanewsshockequivalentto1percentofGDPandunderthebaselineestimation. The top row shows the estimated response of government expenditure to the news shock, and the response of output is in the bottom panels. The two left panels compare booms and slumps, while the rightpanelsshowtheresultscomparingexpansionsandrecessionsinstead. Thesamelinearmultiplier isaddedtoeachgraphasareference. Thefiguresreveallargedifferencesintheresponseofgovernmentexpendituretoamilitaryspending newsshock.Duringslumps,theresponseofgovernmentexpendituretoanewsshockisdelayed—actual government expenditure peaks four years after the shock. Further, the standard errors in the first two years after the news shock are quite narrow. These results run counter to the case studies in Ramey 14

Figure6:Cumulativefiscalmultipliers. 5 10 15 20 3 2 1 0 1− 2− Cumulative fiscal multipliers Slump Boom 5 10 15 20 3 2 1 0 1− 2− Cumulative fiscal multipliers Recession Expansion Notes: Figuresshowcumulativefiscalmultipliersconditionalonbusinesscyclephase. ResultsarefromtheBaselinespecification of table 4. Blue line represents multipliers in booms/expansions, while red line shows estimated multiplier in slumps/recession.Shadedareasdenote90percentconfidenceintervals.Seetextfordetails. (2011a)andRameyandZubairy(2018),whichpointtosignificantheterogeneityintheresponseofg. In contrast,duringrecessionsthepeakinspendinghappensafterjustthreequarters.WhenRamey(2011a) studiesthetimingofshocksindetail,shearguesthatittakesafewquartersafterthemilitaryspending newsbeforethemilitaryspendingactuallymaterializes,althoughRameyandZubairy(2018)presentcase studieswheretheresponseisfurtherdelayed,betweenoneandtwoyears.Thethreequarterpeakwefind duringrecessionsisconsistentwiththeeventstudyforboththetheKoreanandtheVietnamwars. DuringtheFirstandSecondWorldWars, governmentspendingincreasedimmediately followingthenews shocks, andpeakedsixtoeightquartersafter. Inaddition, duringrecessionsgovernmentspendingremainsattheelevatedlevelforseveralyears.Thisisinlinewiththecasestudiesofseveralwarsmentioned above.Alltold,whilethereissubstantialheterogeneityintheresponseofgovernmentspendingafterthe news,webelievethattheresponseduringrecessionsismoreconsistentwiththeeventstudiesmentioned abovethantheresponseshownforslumps. Puttingtheresponsesofgovernmentexpenditureandoutputtogether,onecanreconcilethemultipliersfromfigure6bymentallyapplyingequation4. Inrecessions,theresponseofgovernmentexpenditureisfront-loadedandpeaksatasmallerlevelthantheresponseduringslumps. Atthesametime, theresponseofoutputiscumulativelylargerinrecessionsthaninexpansions,especiallyinthefirsttwo yearsaftertheshock.(Becausetherearefewnewsshocksduringouridentifiedrecessions,theresponses 15

Figure7:Phase-specificresponseofgovernmentspendingandGDPtoanewsshock. 5 10 15 20 0.1 8.0 6.0 4.0 2.0 0.0 Govt spending response in slump/boom % Slump Boom Linear 5 10 15 20 Quarters 5.1 0.1 5.0 0.0 Govt spending response in recession/expansion % Recession Expansion Linear Quarters 5 10 15 20 0.1 8.0 6.0 4.0 2.0 0.0 GDP response in slump/boom % Slump Boom Linear 5 10 15 20 Quarters 5.1 0.1 5.0 0.0 GDP response in recession/expansion % Recession Expansion Linear Quarters Notes:Panelsshowphase-specificresponseofgovernmentexpenditure(toprow)andGDP(bottomrow)toamilitaryexpenditurenewsshockscaledto1percentofGDP.Regressionspecificationisthebaselinespecificationintable4.Redlinesshowthe responseinslumps(left)orrecessions(right).Bluelineistheresponseinbooms(left)orexpansions(right).Blacklinesarethe responsefromthelinearmodel.Shadedareasdenote90percentconfidenceintervals. of both government expenditure and output are very uncertain.) In contrast, as we can see by the responseofgovernmentexpenditureduringslumps,thebulkofgovernmentexpenditureisquitedelayed fromthenewsshockitself. Giventhattheaveragerecessioninoursamplelastsjustover1.5years,itis unlikely that government expenditure actually occurs during periods of severe economic distress. The responseofoutputitselfisalsoultimatelysmaller. Overall,weviewtheseresultsassupportingtheidea that fiscal multipliers are larger during periods of economic distress, but emphasize that the period of timeinwhichthemultiplierisrelativelylargemaybequiteshort. 16

4.1.3 Robustnesschecks Inthissubsectionwedocumenttherobustnessofourresultstoseveraldifferentbusinesscyclechronologies,showninfigureA.3.Themultipliersassociatedwiththesealternativechronologiesaregivenintable 5.Thefirstalternativechronologywecalculateisanalternativeslumps/boomchronology,wherewedefineslumpsasperiodswhentheunemploymentrateisbeloworaboveitsHP-filterimpliedtrend. The resultsarequalitativelysimilartothoseforslumpsandboomsbasedonafixedthresholdof6.5percent. ForthechronologybasedontheHPfiltertrend,themultiplierisalwaysestimatedtobehigherinslumps thaninbooms,butasbefore,thedifferenceisnotstatisticallymeaningful. Next, we recompute fiscal multipliers under three different definitions of recession. The resulting estimatesofthefiscalmultiplierareintheremainingcolumnsoftable5. Ourresultsareonthewhole robusttothealternativerecession/expansionchronologies. Foreachchronologyandregressionspecification, wefindthatthemultiplierishigherinrecessionthaninexpansion, althoughthedifferenceis notalwaysstatisticallyrelevant. Theestimatedmultiplierinexpansionsistypicallyaround0.5,whilein recession,theestimatedmultiplieroftenexceedsone.SincetheNBERbusinesscyclechronologyisquite similartothechronologybasedontheBry-Boschanalgorithm,itisnotsurprisingthattheresultsusing theNBER’schronologyarebyandlargesimilartothosepresentedintheprevioussection. Theresultsof thetwoprolongedBBchronologiesarealsoquitesimilartotheoriginalresults. 4.2 State-levelanalysisusingmilitaryspendingshocks Wenextshowthatweagainfindevidencethatthefiscalmultipliervariesacrossthebusinesscyclewhen we follow the approach of Nakamura and Steinsson (2014). Nakamura and Steinsson identify exogenousvariationinstate-levelfiscalpolicybyassumingthatthefederalgovernmentdoesnotalternational spendinginresponsetotherelativeperformanceoftheU.S.states.15 Thisapproachhastheadvantage thatitintroducesapanelelementtothedata,whichmayimprovetheprecisionoftheestimatesofthe fiscalmultiplier.Sinceweproducebusinesscyclechronologiesatthestatelevel,weaddtestsofwhether themultiplierdiffersacrossthefourbusinesscyclephases. 15ComparedtotheanalysisinNakamuraandSteinsson(2014),weuseashortersample,withouttheKoreanwar,asadvocated byDuporandGuerrero(2017). 17

.seigolonorhcevitanretla:sreilpitlumlacsfidetamitsE:5elbaT )61degnolorp(BB )7degnolorp(BB ygolonorhcREBN dnertretlfiPHwoleb/evobA raeniL noisnapxE noisseceR noisnapxE noisseceR noisnapxE noisseceR mooB pmulS llA )kcohsgnidnepsyratilim(enilesaB.1 †46.0 56.1 †26.0 88.1 95.0 63.1 06.0 37.0 27.0 largetniraey2 )11.0( )44.0( )21.0( )36.0( )31.0( )65.0( )01.0( )52.0( )90.0( †47.0 00.2 †37.0 03.2 †07.0 89.1 56.0 77.0 87.0 largetniraey4 )80.0( )85.0( )80.0( )07.0( )01.0( )96.0( )61.0( )02.0( )60.0( slortnoclanoitiddasagnidnepsdnasexat,kcohsgnidnepsyratiliM.2 76.0 92.1 76.0 05.1 76.0 02.1 47.0 49.0 47.0 largetniraey2 )90.0( )43.0( )90.0( )94.0( )80.0( )25.0( )21.0( )43.0( )90.0( 87.0 84.1 †67.0 57.1 77.0 46.1 67.0 39.0 97.0 largetniraey4 )60.0( )64.0( )60.0( )75.0( )60.0( )47.0( )71.0( )62.0( )70.0( skcohsPB+kcohsgnidnepsyratiliM.3 45.0 88.0 45.0 20.1 05.0 59.0 24.0 36.0 05.0 largetniraey2 )11.0( )72.0( )11.0( )13.0( )21.0( )44.0( )90.0( )12.0( )80.0( †96.0 83.1 †96.0 05.1 †46.0 06.1 35.0 87.0 17.0 largetniraey4 )90.0( )04.0( )90.0( )04.0( )11.0( )05.0( )31.0( )12.0( )60.0( IIWWgnidulcxe,skcohsPB+kcohsgnidnepsyratiliM.4 14.0 35.0 34.0 05.0 44.0 20.1 53.0 08.0 74.0 largetniraey2 )52.0( )73.0( )03.0( )63.0( )92.0( )07.0( )71.0( )14.0( )61.0( 45.0 31.1 36.0 70.1 75.0 77.1 35.0 71.1 77.0 largetniraey4 )15.0( )84.0( )25.0( )44.0( )25.0( )26.0( )83.0( )15.0( )53.0( noissecerREBN;dnertretlfiPHwoleb/evoba:sadetaluclacseigolonorhcevitanretlA.)2002(ittorePdnadrahcnalBsetonedPB.sesehtnerapnisrorredradnatstseW-yeweN:setoN morfsnoitavresbosedulcxe4noitacfiicepsnoissergeR .sretrauq61foelcycmuminimhtiwmhtiroglaBB;sretrauqnevesfonoitarudmuminimhtiwmhtiroglaBB;ygolonorhc .sliatedroftxeteeS.4Q5491ot3Q1491 .leveltnecrep01tatnacfiingisyllacitsitatssisesahpssorcaecnereffidehttahtsetacidni† 18

NakamuraandSteinsson(2014)estimateatwo-stageinstrumentalvariablesregression. Inthefirst stage,thechangeinmilitaryspendingatthestatelevelisregressedontothechangeinnationalmilitary spendingandcontrols: ∆µ s,t =β s ∆µ nat,t +I s,t−1 (cid:161)α 1,s +ξ 1,s (L)z t (cid:162)+(cid:161) 1−I s,t−1 (cid:162)(cid:161)α 0,s +ξ 0,s (L)z t (cid:162)+Φ(cid:48) s c s,t +(cid:178) s,t , (6) whereµ andµ arebiannualchangesinstateandfederalmilitaryexpenditureasapercentageofGDP, s nat z isavectorofcontrols,andc arefixedeffects. I isthedummyvariablethatindicatesthestateofthe st businesscycleinstatesatperiodt. Thesecondstageregressionregressesthefittedvaluesfromthefirst stageontostate-levelGDP: ∆y s,t =I s,t−1 (cid:161)α 0,s +ψ 0,s (L)z t +γ 0 ∆µ (cid:98)s,t (cid:162)+(cid:161) 1−I s,t−1 (cid:162)(cid:161)α 1,s +ψ 1,s (L)z t +γ 1 ∆µ (cid:98)s,t (cid:162)+φ(cid:48) s c s,t +η s,t , (7) where ∆y measures biannual growth in state GDP while µ denotes the fitted value of equation 6. The (cid:98) parametersγ andγ capturethephase-dependentmultipliers.Itisworthemphasizingthattheseequa- 0 1 tionsestimateanopeneconomyrelativemultiplierforfederalspending, whichquantifiesincreasesin stateGDPrelativetoothersafterincreasesinmilitaryexpenditure. Thus,cautionshouldbeusedwhen comparingthesemultiplierstothosecalculatedinsection4.1.16 Table6presentestimatesoftheopen-economymultiplier. Thefirstrowofthetablepresentsregressionestimatesthatincludeonlytimefixedeffects.Again,eachsubsequentrowpresentsalternatespecifications.Thelinearregressionestimatesafiscalmultiplierof1.5–2.Thesevaluesimplythata1percentincreaseofrelativemilitaryspendingasapercentageofstateGDPincreasesitsGDPrelativetootherstates by1.5–2percentwithintwoyearsoftheincreaseinspending.Turningtothephase-dependentestimates, wefindverylittleevidencethattheopen-economyfiscalmultiplierdiffersacrossslumpsandbooms.Indeed,formanyoftheregressionspecifications,thepointestimateofthefiscalmultiplierduringslumps isactuallysmallerthanthatfrombooms,althoughneitherarepreciselyestimated. Incontrast,wefind evidence that the multiplier varies depending on whether the state is in recession or expansion. The pointestimateofthefiscalmultiplierinrecessionisnotablyhigher,around2.5,whereasinexpansions, 16IntheNakamuraandSteinsson(2014)dataset,thedatesthatmilitarycontractswereawardedareavailablebuttheexact timingoftheactualexpenditureisnotknown. Wecalculatethemultipliersatthehorizonoftwoyears,similartoouranalysis usingnationaldata. Thisbiannualspecificationisconsistentaslongasthemajorityoffundsisspentwithintwoyearsof assignment.However,theresultofthisassumptionisthattheexacttimingofthefiscalspendingshocksisunclear,andforthis reasonwearenotabletocalculatelocalprojections. 19

themultiplierisaboutone.However,thestandarderrorsoftheseestimatestendtobelarge,suchthatwe usuallycannotrejectthenullhypothesisthatthemultiplieristhesameinthetwophasesofthebusiness cycle. Table6:Open-economyfiscalmultipliersbybusinesscyclephase. Linear Above/belowtrend Peaktotrough(BBalg) All Slump Boom Recession Expansion 1.Baseline(yearfixedeffectsonly) Twoyearintegral 1.97 1.96 1.97 2.58 1.03 (0.66) (1.08) (0.94) (1.08) (1.57) 2.Yearfixedeffects;sizeofmilitary Twoyearintegral 1.60 1.18 1.46 3.07 -0.31† (0.68) (0.86) (0.82) (0.85) (0.96) 3.Yearandstatefixedeffects;sizeofmilitary Twoyearintegral 2.02 2.09 1.95 2.77 0.65 (0.68) (1.19) (1.01) (1.16) (1.57) 4.Yearandstatefixedeffects;sizeofmilitary;labormarket/industry Twoyearintegral 1.82 1.81 1.94 2.63 0.71 (0.58) (0.95) (1.12) (0.88) (1.30) 5.Yearandstatefixedeffects;sizeofmilitary;labormarket/industry;laggeddep.var. Twoyearintegral 1.69 1.59 1.61 2.33 0.74 (0.47) (0.77) (0.71) (0.72) (1.01) Notes:Standarderrorsclusteredbytimeandstate.Numberofobservationsvariesfrom1,223to1,325. †indicatesthatthedifferenceacrossphasesisstatisticallysignificantat10percentlevel. Rows2-5intable6showthattheresultsarebroadlyrobusttovariousregressionspecifications. The regressions in row 2 control for the level of military expenditure as a percent of state GDP, since particularcyclicallysensitiveindustriesarelikelyparticularlysensitivetodefensespending. Row3adjusts theregressionswithstatefixedeffects. Inrow4,weaddcontrolsforstatelabormarketinstitutionsand thesectoralcomposition. Finally,thelastspecificationadjustsforalaggeddependentvariable. Table7 presentsresultsfromidenticalspecificationsbutintheseregressions,militaryexpenditureincludesboth direct compensation and prime spending. Results across both sets of tables are qualitatively similar: whereaswefindnoevidencethatthemultiplierdiffersinperiodsofslackversusboom,thereisevidence thatthemultiplierislargerwhentheeconomyisinrecessionversusperiodsofexpansion. Lastly,giventhelargeamountofdatawenowhaveatourdisposal,weevaluatethemultiplierineach ofthefourstagesofthebusinesscyclewedescribedinfigure1.Table8reportsresultsforeachindividual businesscyclephase.WefindthatpointestimatesofthefiscalmultiplierinstagesIIandIIIofthecycle— periodswhentheunemploymentrateisincreasing—arealwayshigherthantheotherstages, although thedifferencesisnotalwaysstatistically meaningful. Thetablealso showswhy themultipliersarenot 20

Table7: Open-economyfiscalmultipliersbybusinesscyclephase(directcompensation+primespending). Linear Above/belowtrend Peaktotrough(BBalg) All Slump Boom Recession Expansion 1.Baseline(yearfixedeffectsonly) Twoyearintegral 1.71 1.50 1.86 2.34 0.83 (0.67) (0.92) (0.77) (0.93) (1.22) 2.Yearfixedeffects;sizeofmilitary Twoyearintegral 1.24 0.78 1.13 2.62 -0.40† (0.63) (0.78) (0.72) (0.77) (0.78) 3.Yearandstatefixedeffects;sizeofmilitary Twoyearintegral 2.57 2.55 2.58 3.30 1.45† (0.71) (0.98) (0.86) (1.01) (1.31) 4.Yearandstatefixedeffects;sizeofmilitary;labormarket/industry Twoyearintegral 2.17 2.31 2.30 2.96 1.29† (0.61) (0.81) (0.79) (0.74) (1.06) 5.Yearandstatefixedeffects;sizeofmilitary;labormarket/industry;laggeddep.var. Twoyearintegral 1.84 1.80 1.71 2.55 1.01† (0.44) (0.52) (0.43) (0.55) (0.68) Notes:Standarderrorsclusteredbytimeandstate.Numberofobservationsvariesfrom1,223to1,325. †indicatesthatthedifferenceacrossphasesisstatisticallysignificantat10percentlevel. differentbetweenslumpsandbooms, sinceeachoftheseperiodsiscomprisedofperiodsintimewith increasingordecreasingunemploymentrate,andthereforehighandlowmultipliers. 4.2.1 Robustnesschecks We perform several robustness checks of our estimated open-economy fiscal multipliers. As before, we check for the robustness using a different definition of recessions and/expansions.17 Results using thesealternativechronologies—theNBERdatesandthetwoprolongedBry-Boschanchronologies—are reportedintable9. The evidence for phase-dependence of the fiscal multiplier using these alternate specifications is moremixed. FortheNBERchronology, wefindthatthemultiplierisactuallysmaller inrecessionsfor certainregressionspecifications. Incontrast,alternativeBBalgorithmsagainshowevidencethatmultipliersdifferacrossrecessionsandexpansions.Indeed,thedifferencebetweenrecessionsandexpansions isoftenmorepronouncedunderthesealternativechronologiesandmoreoftenstatisticallysignificantat standardlevels. 17Becausewedonotbelievethe6.5percentthresholdissensibleforallstates,ourbaselineslump/boomchronologyisbased oneachstate’sHPfilteredunemploymentrate.Wedonotpresentresultsforanalternativeslump/boomchronology. 21

Table8:Estimatedopeneconomyfiscalmultipliersbyphaseofbusinesscycle. Linear StageI StageII All StageI Otherstages StageII Otherstages 1.Baseline(yearfixedeffectsonly) Twoyearintegral 1.97 0.88 2.37 2.93 1.58 (0.66) (1.41) (0.99) (1.24) (1.08) 2.Yearfixedeffects;sizeofmilitary Twoyearintegral 1.60 0.15 1.76 3.31 0.75† (0.68) (0.88) (0.87) (1.12) (0.74) 3.Yearandstatefixedeffects;sizeofmilitary Twoyearintegral 2.02 0.55 2.42 3.05 1.54 (0.68) (1.24) (1.10) (1.38) (1.16) 4.Yearandstatefixedeffects;sizeofmilitary;labormarket/industry Twoyearintegral 1.82 1.28 1.90 3.18 1.64 (0.58) (1.23) (0.99) (1.20) (0.95) 5.Yearandstatefixedeffects;sizeofmilitary;labormarket/industry;laggeddep.var. Twoyearintegral 1.69 1.37 1.65 2.29 1.51 (0.47) (0.89) (0.75) (0.98) (0.71) Linear StageIII StageIV All StageIII Otherstages StageIV Otherstages 1.Baseline(yearfixedeffectsonly) Twoyearintegral 1.97 2.22 1.85 1.46 2.04 (0.66) (1.28) (1.08) (2.12) (0.93) 2.Yearfixedeffects;sizeofmilitary Twoyearintegral 1.60 3.15 0.67† -0.36 1.84† (0.68) (0.82) (0.86) (1.28) (0.75) 3.Yearandstatefixedeffects;sizeofmilitary Twoyearintegral 2.02 2.48 1.79 1.34 2.13 (0.68) (1.38) (1.13) (1.94) (1.04) 4.Yearandstatefixedeffects;sizeofmilitary;labormarket/industry Twoyearintegral 1.82 2.43 1.33 1.23 1.97 (0.58) (0.91) (1.24) (1.57) (0.95) 5.Yearandstatefixedeffects;sizeofmilitary;labormarket/industry;laggeddep.var. Twoyearintegral 1.69 2.26 1.22 0.65 1.81 (0.47) (0.73) (0.85) (1.42) (0.71) Notes:Tablereportsestimatesfromthetwo-stageGMMestimatorinequations6and7.Phasescorrespondtothoselabeled infigure1. Numbersinparenthesesarestandarderrors,clusteredbytimeandstate. Numberofobservationsvariesfrom 1,223to1,325. †indicatesthatthedifferenceacrossphasesisstatisticallysignificantat10percentlevel. 5 Conclusion This paper studies fiscal multipliers over different stages of the business cycles using two distinct approaches to estimating the multiplier. The first is based on a long time-series of national-level data, whereasthesecondintroducesapanelelementbylookingattheeffectsoffiscalexpenditureacrossU.S. states. Weviewthebulkoftheevidencepresentedhereassupportingtheideathatthefiscalspending multiplier is likely larger in recessions than expansions. We usually find that the point estimate of the fiscalmultiplierishigherinperiodsoftimewhentheunemploymentrateisincreasingrelativetoperiods whenitisdecreasing. Incontrast,thereisscantevidencethatthemultipliervarieswhentheunemploy- 22

.seigolonorhcevitanretla,sreilpitlumlacsfiymonocenepodetamitsE:9elbaT )61degnolorp(BB )7degnolorp(BB REBN raeniL noisnapxE noisseceR noisnapxE noisseceR noisnapxE noisseceR llA )ylnostceffedexfiraey(enilesaB.1 27.1 01.2 41.1 60.2 20.2 58.1 79.1 largetniraeyowT )59.1( )51.1( )53.1( )10.1( )42.1( )08.0( )66.0( yratilimfoezis;stceffedexfiraeY.2 †14.0- 81.3 †55.0- 28.2 90.1 44.1 06.1 largetniraeyowT )20.1( )48.0( )97.0( )77.0( )48.0( )23.1( )86.0( yratilimfoezis;stceffedexfietatsdnaraeY.3 26.0 85.2 34.1 12.3 32.2 85.1 20.2 largetniraeyowT )12.2( )52.1( )06.1( )21.1( )33.1( )28.0( )86.0( yrtsudni/tekramrobal;yratilimfoezis;stceffedexfietatsdnaraeY.4 †71.0- 37.2 †75.0 81.3 90.2 56.0 28.1 largetniraeyowT )64.1( )17.0( )20.1( )66.0( )02.1( )28.0( )85.0( .rav.peddeggal;yrtsudni/tekramrobal;yratilimfoezis;stceffedexfietatsdnaraeY.5 †03.0- 06.2 †02.0 79.2 †97.1 86.0 96.1 largetniraeyowT )62.1( )36.0( )37.0( )65.0( )48.0( )75.0( )74.0( dradnatserasesehtnerapnisrebmuN .1erugfinidelebalesohtotdnopserrocsesahP .7dna6snoitauqenirotamitseMMGegats-owtehtmorfsetamitsestroperelbaT:setoN .523,1ot322,1morfseiravsnoitavresboforebmuN.etatsdnaemitybderetsulc,srorre .leveltnecrep01tatnacfiingisyllacitsitatssisesahpssorcaecnereffidehttahtsetacidni† 23

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A Onlineappendix(notforpublication) A.1 EstimatesfromathresholdVAR WealsoemployathresholdVARapproach,asinAuerbachandGorodnichenko(2012b)andsection6of RameyandZubairy(2018).WewritethethresholdVARinreduced-form: Y t =I t−1 Ψ 1 (L)Y t−1 +(cid:161) 1−I t−1 (cid:162)Ψ 0 (L)Y t−1 +u t , (8) where I indicatesthephaseoftheeconomy,Ψ(L)isalagpolynomialofVARcoefficients, u ∼N(0,Ω), t andΩ=I t−1 Ω 1 +(cid:161) 1−I t−1 (cid:162)Ω 0 . MilitarynewsshocksareidentifiedusingaCholeskidecompositionwiththefollowingorderingY = [news ,g ,y ].Ourmeasuresofgovernmentspending,g ,andoutput,y ,areasinthemaintext. t t t t t TableA.1presentstheresults. Eachpanelgivestheestimatedmultiplierusingaparticularestimated businesscyclechronology.Thetoprowgivesourbaselineresults,usingthe6.5percentthresholdandthe BBalgorithm,respectively. Themiddleandbottomrowspresentresultsusingthealternativechronologies. TableA.1:EstimatesofMultipliersacrosstheCycle Linear Above/belowtrend Peaktotrough(BBalg) All Slump Boom Recession Expansion 2yearintegral 0.66 0.81 0.55 1.04 0.60 4yearintegral 0.79 1.68 0.60 1.35 0.63 Linear NBERBusinessCycle ProlongedPeaktoTrough(BBalg) All Recession Expansion Recession Expansion 2yearintegral 0.66 1.26 0.55 1.96 0.61 4yearintegral 0.79 1.51 0.65 2.39 0.64 Linear Above/BelowTrend(HPfilter) Alt.PeaktoTrough(BBalg) All Recession Expansion Recession Expansion 2yearintegral 0.66 0.72 0.77 1.05 0.63 4yearintegral 0.79 1.28 0.68 1.35 0.65 Notes: TablegivesestimatedfiscalmultipliersfromathresholdVAR.Toprowgivesresultsfromourbaselineslump/boom andrecession/expansionchronologies. Middleandbottomrowsgiveresultsfromalternativechronologies. Seetextfor details. †indicatesthatthedifferenceacrossphasesisstatisticallysignificantat10percentlevel. 27

A.2 Additionalfiguresandtables FigureA.1:Realpercapitaoutputandgovernmentexpenditure. 1890 1900 1910 1920 1930 1940 1950 1960 1970 1980 1990 2000 2010 5 4 3 2 1 Log real per capita government spending 1890 1900 1910 1920 1930 1940 1950 1960 1970 1980 1990 2000 2010 3 2 1 Log real per capita GDP Notes: FigureshowsrawdatafromRameyandZubairy(2018). Verticaldashedlinesdenotestartofvariouswars(Spanish- American,WWI,WWII,Korean,Vietnam,responsetoSovietinvasionofAfghanistan,andSept11,2001). FigureA.2:Militaryspendingnews,Blanchard-Perottishock,andTreasurybill. 1890 1900 1910 1920 1930 1940 1950 1960 1970 1980 1990 2000 2010 008 002 004− Military news % of GDP 1890 1900 1910 1920 1930 1940 1950 1960 1970 1980 1990 2000 2010 01.0 00.0 01.0− Blanchard−Perotti shock 1890 1900 1910 1920 1930 1940 1950 1960 1970 1980 1990 2000 2010 02 51 01 5 0 Three month Treasury Bill % Notes:FigureshowsrawdatafromRameyandZubairy(2018).GrayshadedbarsdenotebaselineBB-definedrecessions. 28

FigureA.3:Alternativebusinesscyclechronologies. 1890 1900 1910 1920 1930 1940 1950 1960 1970 1980 1990 2000 2010 02 01 0 Unemployment rate and prolonged phases % 1890 1900 1910 1920 1930 1940 1950 1960 1970 1980 1990 2000 2010 02 01 0 Unemployment rate and alternative slumps % Unemployment rate HP filter trend 1890 1900 1910 1920 1930 1940 1950 1960 1970 1980 1990 2000 2010 02 01 0 Unemployment rate and prolonged cycle % Notes: ThebluelineineachpanelistheU.S.unemploymentrate,andisthesameacrosspanels. Reddashedlineinmiddle panelshowstheunemploymentratetrendasdefinedbytheHPfilter.Eachpanel’sgreybarsindicatethebusinesscyclephase asdeterminedby: BBalgorithmwithprolongedphases;alternativetrendunemploymentrate;BBalgorithmwithprolonged completecycle.Seethetextfordetails. TableA.2:SummarystatisticsofU.S.downturns1890–2015,alternativedefinitions. BBrecession:prolonged HPSlumps BBrecession:alternative N.phases 13 33 26 Meanduration(qtrs) 16 7 7 Medianduration(qtrs) 13 7 6 Minduration(qtrs) 7 1 3 Maxduration(qtrs) 31 15 13 Notes: Tableshowssummarystatisticsforthreealternativebusinesscycledownturns: theprolongedBry-Boschanrecession dates, thealternativeBry-Boschanrecessiondates, andHPfilterSlumps. Sampleperiod1890–2015, durationmeasuredin quartes.Seethetextfordetails. 29

TableA.3:Summarystatisticsforstate-levelrecessionsandexpansions. Recessions Expansions State Count Median Std.dev. Min. Max Count Median Std.dev. Min. Max AK 8 21 12 8 40 7 37 18 7 61 AL 5 25 16 17 55 5 69 29 12 89 AR 4 27 13 14 39 4 66 47 47 147 AZ 6 21 7 11 30 6 54 34 10 101 CA 4 39 6 33 46 4 71 23 39 94 CO 8 19 13 10 43 8 25 19 10 62 CT 6 37 19 11 57 6 41 13 18 58 DC 8 24 14 11 48 8 24 21 6 65 DE 7 24 10 11 42 7 28 25 7 70 FL 4 41 11 22 46 4 68 20 49 96 GA 9 11 10 8 36 9 23 23 6 70 HI 6 26 13 10 44 6 42 37 7 101 IA 5 39 17 12 54 5 46 36 17 107 ID 6 29 5 22 37 6 44 33 6 92 IL 7 20 15 13 55 7 34 21 6 71 IN 5 25 8 21 40 5 70 46 7 126 KS 7 20 14 11 55 7 43 26 10 75 KY 6 20 21 12 66 6 37 38 14 107 LA 9 29 15 8 49 9 16 19 8 63 MA 4 33 9 26 47 4 67 24 52 108 MD 6 26 12 12 43 6 45 16 34 70 ME 5 29 7 22 40 5 69 41 8 115 MI 5 27 12 19 47 5 74 40 10 105 MN 5 26 14 19 55 5 74 35 11 93 MO 5 22 20 11 58 5 70 42 10 105 MS 6 20 14 11 47 6 37 37 19 115 MT 6 19 14 14 46 6 42 24 19 84 NC 7 23 10 11 36 6 47 25 11 83 ND 7 18 5 12 26 7 54 27 12 79 NE 6 27 20 16 65 6 36 21 19 74 NH 4 31 16 19 52 4 71 25 55 111 NJ 6 25 14 10 41 6 47 37 8 92 NM 8 25 8 12 36 7 44 19 8 59 NV 4 48 10 38 57 4 63 16 48 87 NY 5 35 16 13 53 5 43 32 16 101 OH 5 40 16 13 54 5 61 21 30 74 OK 8 17 9 8 32 7 35 25 10 82 OR 6 25 10 11 39 6 42 29 9 86 PA 4 38 5 36 46 4 71 19 48 93 RI 4 42 8 31 48 4 71 21 44 95 SC 7 32 14 14 53 7 21 24 7 73 SD 5 23 18 14 59 5 33 70 7 179 TN 7 24 14 8 47 7 36 30 7 78 TX 7 27 9 9 32 7 41 23 10 74 UT 7 17 17 9 55 6 48 17 18 64 VA 5 34 11 14 38 5 59 31 18 102 VT 5 37 14 14 48 5 63 40 6 105 WA 4 36 16 30 64 4 67 19 46 92 WI 4 33 18 11 49 4 80 19 56 98 WV 5 23 17 12 57 4 74 28 49 113 WY 6 21 9 12 35 6 50 39 6 114 Notes: Tableshowscharacteristicsofcompletedstate-levelbusinesscyclephasesfromBry-Boschanalgorithm, January 1976–December2015. Median,standarddeviation,minimumandmaximumindicatephasedurationinmonths. Seetext fordetails. 30