Danish data on the minimum wage: The hourly wage jumps up by 40pct at the discontinuity of minimum wage rules; employment falls by 33pct and total input of hours decreases by 45pct

Do Lower Minimum Wages for Young Workers Raise Their Employment? Evidence From a Danish Discontinuity. Claus Thustrup Kreiner,  Daniel Reck and  Peer Ebbesen Skov. Review of Economics and Statistics, March 04, 2019. https://doi.org/10.1162/rest_a_00825


Abstract : We estimate the impact of youth minimum wages on youth employment by exploiting a large discontinuity in Danish minimum wage rules at age 18, using monthly payroll records for the Danish population. The hourly wage jumps up by 40 percent at the discontinuity. Employment falls by 33 percent and total input of hours decreases by 45 percent, leaving the aggregate wage payment almost unchanged. We show theoretically how the discontinuity may be exploited to evaluate policy changes. The relevant elasticity for evaluating the effect on youth employment of changes in their minimum wage is in the range 0.6-1.1.

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Minimumwages,setbylaworbycollectiveagreement,existin3/4ofOECDcountries(OECD,2015).IntheUnitedStates,minimumwageincreaseshavebeenhighonthepolicyagendainrecentyears,motivatedinpartbymanystudies ndingsmallemploymente ectsofminimumwagehikes.Somecities(e.g.LA,Seattle)andthestateofCaliforniahaverecentlylegislatedaminimumwagerateof$15,amuchhigherratethanthecurrentFederalminimumof$7.25perhour.Ashigherminimumwagesbecomecommon,policy-makersareconfrontedwithasecondquestion:shouldahighminimumwageapplytoeveryone?Inparticular,shoulditapplytoyoungerworkers?Youngworkersarelow-skilledandenterthelabormarketwithoutworkexperience,whichmakethempotentiallyvulnerabletohighminimumwages.ManyUSstatesandcities,includingCalifornia,Minnesota,SouthDakota,KansasCityandDesMoines,whichhaverecentlyincreasedtheirminimumwage,havedebated,andattimeslegislatedorplacedontheballot,anexceptionforyoungerworkers(Kreiner,ReckandSkov,2018).Similarly,manyEuropeancountrieswithhighminimumwageshavelowerminimumwagesforyoungerworkers(OECD,2015).Themainquestionweseektoansweris:Holdingtheadultminimumwage xedatagivenlevel,whatisthee ectofachangeintheminimumwageapplyingtoyoungworkersontheiremployment?ExistingUSevidenceandmostotherevidencecannotanswerthisquestionasitstudieschangesinaglobalminimumwageratherthanayouth-speci cminimumwage.Forexample,theelasticityofyouthemploymentwithrespecttotheminimumwageof0.075reportedbytheUSCongressionalBudgetO ceisbasedonchangesinaglobalminimumwage(CongressionalBudgetO ce,2014).OurempiricalevidenceexploitsalargediscontinuityinDanishminimumwagerulesoccurringwhenworkersreachage18.TheDanishcontextisidealforourpurpose.Denmarkhaslargechangesinminimumwagerateswhenworkersturn18(andnochangeatanyotherages)andahighadultminimumwagecomparabletothe$15levelinplaceinCaliforniaandunderconsiderationmoregenerallyintheUS.1Furthermore,wecanstudythee ectoftheagediscontinuityusinghigh-qualitymonthlydataonwages,employment,andhoursworkedfortheentireDanishworkforce.Ourmain ndingsarecontainedinFigure1,whichshowsthattheagediscontinuityinminimumwageshasalargeimpactonemploymentaroundage18.Weexplainthedetailsbehindtheconstructionofthedataset,measurementissues,andthesourceofidentifyingvariationbelow.Figure1aplotsaveragehourlywages,imputedbydividingreportedmonthlywagesbyreportedhoursworkedforeachindividual,asafunctionofage(measuredinmonths),fortwoyearsbeforeandaftertheir18thbirthday.TheaveragehourlywageratejumpsbyDKK46,orabout$7,correspondingtoa40percentchangeinthewagelevelatage18computedusingthemidpointmethod.Figure1bplotstheshareofindividualswhoareemployedbymonthlyage.Weobservea15percentage-pointdecreaseinemploymentatage18,whichcorrespondstoa33percentdecreaseinthenumberofemployedindividuals.Forcomparison,notethatthewageandemploymentratesdevelopsmoothlywhenindividualsturn17and19yearsold,andthatittakestwoyearsbeforetheemploymentrateisbackatthelevelitattainsjustbeforethejumpdownwardsatage18.Subsequentanalysesrevealthatthedropinemploymentwhenworkersturn18re ectsadiscretechangeinjoblosswithoutanydiscretechangeinhiring(wedoobserveasmallanticipatoryslow-downinhiringasworkersapproachage18).Asimpleestimateoftheemploymentelasticity(theextensivemargin)withrespecttothewagechangeisobtainedbydividingtheestimatesofthepercentagechangesinemploymentandhourlywage.Thisgivesanelasticityaround-0.8.Whenlookingattotalhoursworked(theintensiveandextensivemargin),we ndanelasticityof-1.1,indicatingthatmostoftheresponseoccursalongtheextensivemargin.Recallthataunitelasticitywouldimplythattheaveragewagepaymentofallindividuals,includingbothemployedandnon-employedworkers,shouldstayunchangedwhenthewagerateisraised,becauseitse ectontheaveragewagepaymentisfullyo setbyadecreaseinemployment.Consistentwiththisreasoning,we ndnearlynoe ectonaverageearnings.Thisprovidesalternativeevidenceofatotalhoursworkedelasticityaround-1,notdependingonthemeasurementofhourlywages.Weuseeconomictheorytomotivateourempiricalspeci cationandtoshowthat,un-derreasonableassumptions,theestimatedemploymentelasticitymaybeusedtocalculatethee ectonyouthemploymentofachangeintheminimumwagespeci callyforyoungerworkers.First,weprovideasimplemodelinwhichtheelasticityweestimateusingtheagediscontinuityisexactlythesameastheelasticityneededforthedesiredcounterfactualpolicyanalysis.Inthemodel,workershaveexogenous,heterogeneousproductivitiesandarehirediftheirproductivityexceedstheminimumwage(correspondingtoahorizontaldemandforlabormeasuredine ectiveunits).Inthissimplesetting,cross-workere ectsarezero.Accordingtothisbasicmodel,wemaycomputetheconsequencesofincreasingtheminimumwageforyoungworkers(thoseunder18)uptothehigherlevelapplyingtoadultsbyusingourestimatedelasticity.Thiscalculationgivesa15percentagepointdropinyouthemployment,correspondingto33percentofinitialemployment.Amodelwithdownwardslopinglabordemandforlow-skilledworkwouldinsteadsug-gestthattherearecross-workere ects,implyingthatahigheryouthminimumwagemayincreaselow-skilledadultemployment.Suchcross-workere ectsposeapotentialthreattotheidenti cationstrategy.However,weshowthatonecanobtainalowerboundfortheyouthemploymentelasticitybyconsideringtheextremecaseofa xeddemandforlow-skilledwork(implyingthattheemploymente ectfromthediscontinuityanalysisisentirelydrivenbycross-workere ects).Thelowerboundmaybecomputedfromourestimatedelasticityandthewageshareofyoungerworkersinthelow-skilledlabormarket.Wethuscomputethewageshareoflow-skilledworkersunderage18,usingvariousde nitionsofthelow-skilledworkersthatareperfectlysubstitutableforworkersunderage18.Inthemostex-tremeofthesecalculations,inwhichonlyworkersaged18-19aredeemedtobe low-skilled substitutesforworkersunderage18,thelowerboundoftheyouthemploymentelasticitybecomes0.6.Increasingtheminimumwageforyoungworkersuptothelevelofadultwork-erswouldthendecreaseemploymentbyatleast11percentagepoints,or25percentofyouthemployment,whichisstillasubstantialemploymente ect.Wealsoembedoursimplemodelinanequilibriumsearchframeworkincorporatingdy-namicsforaging.Inaccordancewiththeempiricalevidence,themodelpredictsthatthedropinemploymentatage18re ectsadiscretechangeinjobloss,ratherthanadiscretechangeinhiring.Themodelalsopredictsspillovere ectsofanincreaseintheyouthminimumwageonadultemployment,butinthiscasethesignofthespillovere ectisambiguous.Inanycase,ourelasticityestimateisagainagoodapproximationofthee ectonyouthemploymentifyoungworkersconstitutealowshareoftotallow-skilledemployment."Additionalanalysisdemonstratesthatourinterpretationoftheempiricalresultsiscor-rectandstudiesheterogeneityinemploymente ectsacrossworkers.Mostimportantly,wedemonstratethatotherpoliciesthatchangewhenworkersturn18,suchastheeligibilityforDanishsocialwelfareprograms,arenotdrivingourresults.Wealsoshowthatthesizeoftheemploymentelasticityisonlyslightlylargerforworkersoflowerability,asproxiedbyschoolGPAin9thgradeortheincomeofparents.Finally,weprovidesuggestiveevidencethatjoblosseshavepersistente ectsonworkers.Twoyearsaftertheworkers'18thbirthdays,theemploymentrateisabout15percentagepointslowerforworkersloosingtheirjobatage18relativetoworkerswhokepttheirjob.Ourpapercontributestothesizableliteratureonminimumwagesandemployment,asreviewedinCardandKrueger(2015)andNeumarkandWascher(2008).Mostofthislit-eraturestudiesemploymente ectsofglobalminimumwagehikes,whileourfocusisonthee ectsofage-speci cminimumwages,whereevidenceislimited.NeumarkandWascher(2004)showthatcountrieswithhighminimumwagesalsotendtohavehighyouthunem-ployment,but,consistentwithourresults,thiscorrelationisweakerwhencountrieshavealowerminimumwageforyoungworkers.Onenewstudy,Kabátek(2015),analyzesanagediscontinuity,inthiscaseseveralsmallagediscontinuitiesinDutchminimumwages.Theobservedchangesinwagesandemploymentaroundworkers'birthdaysarethereforemuchsmallerandmoredi usethaninourcontext.Theimpliedemploymentelasticityisslightlysmallerthanours.Combiningonelargediscontinuitywiththoroughtheoreticalrea-soningandrichdataallowsustointerpretoure ectsinmoredetailandtoperformcrediblecounterfactualpolicyexercises.Ourresultsmaymakesomereadersconcernedabouttheimpactofglobalincreasesintheminimumwageonemployment,asubjectofintenseongoingdebate.SeveralDDstudies,mostfamouslyCardandKrueger(1994), ndlittletonoimpactofglobalminimumwagehikesonemployment.2Ourestimatesofthee ectofanincreaseinminimumwagesonemploymentaremuchlargerthanthosetypicallyestimatedforglobalminimumwagehikesusingDDdesigns.Therearethreefactorsthatcouldexplainthisdi erence.First,estimatesinexistingDDstudiesmightbeattenuatedbyshort-runfrictions(Baker,BenjaminandStanger,1999;Sorkin,2015;MeerandWest,2015;Aaronson,FrenchandSorkin,2017),whicharenotrelevantinoursetting.Second,ourstudyisbasedonahighminimumwagelevelcomparedtomostpreviousstudies.Minimumwagesmaynotbebindingatlowlevelsand,ifbinding,theymayincreaseemploymentduetolabormarketimperfections(Manning,2003).Third,ourresultsmightbedrivenbycross-agesubstitutionratherthanpurelyadisemploymente ectoftheminimumwage.The rsttwoofthesefactorssuggestthatourresultsaddressshortcomingsoftheexistingliteratureonglobalminimumwagehikes.However,thethirdisanimportantlimitationofourstudy'sabilitytospeaktothisdebate.Cross-agesubstitutionwouldimplythatweestimatehigheremploymentelasticityinoursettingthanwouldbeseenwithaglobalminimumwagechange.Theextenttowhichthisparticularfactordrivesourlargeestimatedeterminestheextenttowhichreadersshouldupdatetheirbeliefsabouttheemploymente ectsofglobalminimumwagehikes.Onthewhole,therefore,itisdi culttoimaginethatour ndingswillmakereaderslessconcernedaboutemploymente ectsofhighminimumwages,butwhetherandtowhatextenttheyshouldbemoreconcerneddependsonwhattheybelieveaboutthemechanismsbehindourresults.Ourworkalsocontributestothetheoreticalliteratureonthee ectsofminimumwages.MuchoftheliteratureattemptstorationalizeearlyDDstudies ndingsmallorevenpositiveemploymente ectsusingmodelswithmonopsonypowerorotherlabormarketimperfections(RebitzerandTaylor,1995;Manning,2003;Flinn,2006).Our ndingsoflarge,negativeemploymente ectsaroundage-basedminimumwagesalignbetterwithbindingminimumwagesinacompetitivelabormarketmodel.Theminimumwageliteratureoftenassumesthatworkers/jobsarehomogenouswithadownwardslopinglabordemandduetoade-creasingmarginalproductoflabor.Thisisincontrasttotheoptimalincometaxliteraturenormallyassumingheterogeneousproductivities(Mirrlees,1971).Ourexplanationsoftheempirical ndingsarebasedontheorywithheterogeneousproductivities,similartootherrecentminimumwageresearch(ClemensandWither,2016;ClemensandStrain,2017).Thefactthatsomeindividualslosetheirjobwhentheyturn18,whileotherskeeptheirjob,stronglysuggeststhatheterogeneousproductivityisanimportantaspectofthelow-skilledlabormarket.