THREEESSAYSINPUBLICECONOMICS By ChristopherLukeWatson ADISSERTATION Submittedto MichiganStateUniversity inpartialful˝llmentoftherequirements forthedegreeof EconomicsDoctorofPhilosophy 2021 ABSTRACT THREEESSAYSINPUBLICECONOMICS By ChristopherLukeWatson Thisdissertationiscomposedoftwochaptersontheeconomy-widee˙ectsoftheEarnedIncome TaxCreditandonechapteronthee˙ectsofmonopolisticmarketstructureinurbanrentalmarkets. Eachchapterconsidersunintendedconsequencesofpublicactionsgivenaninterconnectedmarket place.Forchapterthisisskillsubstitutability,chaptertwospatialconnections,andchapterthree preferencesandmarketpower. ChapteronestudiesthegeneralequilibriumincidenceoftheEarnIncomeTaxCredibyformal- izingthetheoreticalmechanismsandquantifyingitsempiricalimportance.TheEarnedIncome TaxCreditisa$67billiontaxexpenditurethatsubsidizes20%ofallworkers.Yetallprioranalysis usespartialequilibriumassumptionsongrosswages.Iderivethegeneralequilibriumincidence ofwagesubsidiesandquantifytheimportanceofEITCspilloversinthreeways.Icalculatethe GEincidenceofthe1993and2009EITCexpansionsusingnewelasticityestimates.Icontrast theincidenceofcounterfactualEITCandWelfareexpansions.Iquantifythee˙ectofequalizing theEITCforworkerswithandwithoutchildren.Inallcases,I˝ndspilloversareeconomically meaningfulrelativetotheintendeddirecte˙ects. Chaptertwostudiesthecountylevellabormarkete˙ectsofstatesupplementstotheEarned IncomeTaxCredit.Twentyeightstatesspend$4billiontosupplementthefederalEarnedIncome TaxCredit,withseveraljustifyingthetaxexpenditureasapro-workincentive.Yetnosystematic evaluationofthesesupplementsexists.Iusestateborderpolicyvariationtoidentifystatesupple- mentse˙ects.I˝rstdocumentthatsubsidyratesaregreaterwhenastate'sneighboralreadyhas asupplement.Next,Iassesswhethersupplementsa˙ectcountylevelEITCtake-up,migration, commuting,employment,andearnings.Estimatesaresensitivetotheestimationdesignandsample used.Whilesupplementsincreasebene˝tstolow-incomeworkers,resultsfailtoproviderobust evidenceofincreasedeconomicactivity. ChapterthreeisjointwithOrenZiv.Weinvestigatethesources,scope,andimplications oflandownermarketpowerinNewYorkCityrentalmarkets.Weshowhowzoningregula- tionsgeneratespilloversthroughincreasedmarkupsandderiveconditionsunderwhichrestricting landownershipconcentrationreducesrents.Usingnewbuilding-leveldatafromNewYorkCity, we˝ndthata10%increaseinownershipconcentrationinaCensustractiscorrelatedwitha1% increaseinrent.Marketpowerissubstantial:onaverage,markupsaccountfornearlyathirdof rentsinManhattan.Furthermore,pecuniaryspilloversbetweenzoningconstraintsandmarkupsat otherbuildingsareappreciable.Up-zoningthatresultsin417additionalhousingunitsatzoning- constrainedbuildingsreducesmarkupsonpolicy-unconstrainedunitsandgeneratesbetween5and 19additionalunitsthroughincreasedcompetition. Copyrightby CHRISTOPHERLUKEWATSON 2021 ToAlyssa,family,friends,mentors,andallloversofeconomics. v ACKNOWLEDGEMENTS Iacknowledgemywonderfulanddedicatedcommitteemembers.Ithankmyadvisor,Jay,whohas alwaysencouragedmeandhelpedfocusmyresearchafteraroughstart;Iappreciatehiswisdom andhisstories.IthankLesliePapkewhohasalwaysbeenencouragingyetruthlesswitharedpen. IthankOrenZivwhoIhavespentcountlesshoursworkingwithandwasalwaysavailableforme toventorshareadumbjoke.IthankEricChang,myoutsidecommitteemember,forhistimeand comments. Iacknowledgethefacultyandsta˙atMSU.IthankRileyActon,DylanBrewer,ChristianCox, PriyankarDatta,ChrisFowler,HannahGabriel,CodyOrr,AkankshaNegi,SJParsons,Gabrielle Pepin,andNickRowefortoomanyreasonstolist,butmostlyforbeingamazingcolleaguesand truefriends.IhopeIhavebeenanet-productivityboosterforyouall,asforsureyouwereforme.I thankStevenHaiderforhisimprovementstotheMSUgraduateprogramandrecruitingmyclass.I alsothankSorenAnderson,ProbhatBarnwal,MikeConlin,StacyDickert-Conlin,ToddElder,and BenZouforadditionalsupportandguidance.IthankLoriJeanNicholsandJayFeightforkeeping meontractandassistingwithnervousquestions. Iacknowledgethefacultyandsta˙atOldDominionUniversity.IthankGaryWagnerforhis generosity,wisdom,andfriendship.WithoutreservationIcansaythetrajectoryofmylifeishigher becauseofGary.IalsothankChipFilerandTimKomarekfortheirsupportandfriendship. Iacknowledgemyfamilyandfriends.Icannotthankmyfamilyenough.Byfarlargestsacri˝ce ofmytimeatMSUhasbeentimewithmylovedones.Ihopethatinthelong-runtheinvestment wasworthitandthatwewillhavemoreandbettertimestogether. IacknowledgeAlyssa.WemetatTAOrientationthe˝rstmonthatMSUandhavebeentogether foreversince.Alyssahasbeenaconstantsourceofinspirationandguidancethesepastsixyears. Shehaspushedmetoworkhardandalsotoslowdownandrelax.Allthewhile,sheearnedbothan MAandPhD,taughtawardwinningclasses,andconductedawardwinningresearch.Iloveyou. vi TABLEOFCONTENTS LISTOFTABLES ....................................... x LISTOFFIGURES ....................................... xiii KEYTOABBREVIATIONS .................................. xiv CHAPTER1THEGENERALEQUILIBRIUMINCIDENCEOFTHEEARNEDIN- COMETAXCREDIT ............................. 1 1.1Introduction......................................1 1.2OverviewoftheEITCandRelatedLiterature....................6 1.3Model.........................................9 1.3.1Workers....................................10 1.3.2Production...................................11 1.3.3TaxandTransferSystem...........................12 1.3.4Equilibrium..................................12 1.4Incidence.......................................13 1.4.1PartialEquilibrium..............................13 1.4.1.1ImplicationandInterpretationforPolicy.............14 1.4.2GeneralEquilibrium.............................15 1.4.2.1GeneralEquilibriumIncidencewithManyLaborMarkets....17 1.5EstimatingLaborMarketElasticities.........................18 1.5.1Data......................................18 1.5.2SummaryStatistics..............................20 1.5.3Identi˝cation.................................22 1.5.4EstimatingEquations.............................24 1.5.5ElasticityEstimates..............................26 1.6EmpiricalPolicyEvaluationMethodology......................28 1.6.1Data......................................29 1.6.2ModelWageandLaborChanges.......................29 1.6.3PerDollarE˙ects...............................30 1.6.4Caveats....................................30 1.7Incidenceof1993EITCExpansion..........................32 1.7.11993IncidenceResults............................32 1.8ComparingEITCandWelfareReforms........................36 1.8.1SimulatingtheTaxReforms.........................37 1.8.2SimulationResults..............................38 1.9StructuralModelParameterization..........................41 1.9.1StructuralModel...............................42 1.9.2RecoveringStructuralParameters......................43 1.10ChildlessWorkerReform...............................44 1.10.1ChildlessWorkerReformResults.......................45 vii 1.11Incidenceofthe2009EITCExpansion........................46 1.11.12009IncidenceResults............................48 1.12Conclusion......................................49 CHAPTER2THELOCALLABORMARKETEFFECTSOFSTATEEARNEDIN- COMETAXCREDITSUPPLEMENTS ................... 53 2.1Introduction......................................53 2.2StateEITCSupplements...............................56 2.2.1AcrossStateEITCPolicyCoordination...................59 2.2.1.1ImplicationsofCoordination....................60 2.3EvaluatingStateEITCSupplements.........................61 2.4EmpiricalDesigns...................................63 2.4.1MaxStateCreditVariation..........................64 2.4.2StateBorderFixedE˙ect...........................65 2.4.3StateBorderRegressionDiscontinuity....................66 2.5Data..........................................66 2.6Results.........................................69 2.6.1AllBorders..................................69 2.6.2One-SidedBorders..............................70 2.6.3StackedEventStudies.............................72 2.7Conclusion......................................73 CHAPTER3ISTHERENTTOOHIGH:LANDOWNERSHIPANDMONOPOLY POWER(WITHORENZIV) ......................... 76 3.1Introduction......................................76 3.2Model.........................................80 3.2.1Setup.....................................80 3.2.2Equilibrium..................................81 3.2.2.1EquilibriumUnderHorizontalDi˙erentiation...........82 3.2.2.2EquilibriumUnderVerticalDi˙erentiation............82 3.3PolicyImplications:Theory.............................84 3.3.1OldPolicies,NewImplications........................84 3.3.2NewPolicies,NewImplications.......................85 3.3.3AdditionalPolicies..............................86 3.4Data..........................................87 3.5ConcentrationandRentsinNewYorkCity......................92 3.6EstimatingElasticitiesandMarkups.........................96 3.6.1RenterDemandEconometricModel.....................96 3.6.2Identi˝cationandInstruments........................98 3.6.3EstimatingMarkupsinthePresenceofSupply-SideRestrictions......100 3.6.4ElasticitiesandMarkupCalculations.....................101 3.6.5EstimationRoutine..............................102 3.7EstimationResults...................................102 3.7.1ResultsusingManhattan...........................102 3.7.2ResultsforManhattan,theBronx,Brooklyn,andQueens..........104 viii 3.8Up-Zoning'sSpilloverE˙ectsThroughMonopolyPower..............104 3.9Conclusion......................................108 APPENDICES ......................................... 114 APPENDIXAAPPENDIXTOCHAPTERONE .................... 115 APPENDIXBAPPENDIXTOCHAPTERTWO .................... 151 APPENDIXCAPPENDIXTOCHAPTERTHREE .................. 159 BIBLIOGRAPHY ........................................ 184 ix LISTOFTABLES Table1.1:SummaryStatisticsforEstimationSample.....................21 Table1.2:LaborSupplyElasticityEstimatesbyLaborGroups: Y ! 3 .............27 Table1.3:LaborSubstitutionElasticityEstimatesAcrossLaborMarkets..........28 Table1.4:EmpiricalIncidenceofthe1993EITCExpansionon1993GrossWages.....33 Table1.5:EmpiricalIncidenceofthe1994EITCExpansiononLaborSupply.......33 Table1.6:EmpiricalIncidenceResults:ChangePerDollarofNewExpenditure......35 Table1.7:EmpiricalIncidenceResults:ChangePerDollarofNewExpenditure......36 Table1.8:IncidenceResults:AggregateE˙ects:AllWomen................40 Table1.9:IncidenceResults:AggregateE˙ects:SubgroupsofWomen...........41 Table1.10:IncidenceResults:AggregateE˙ects:WageQuintiles..............42 Table1.11:EmpiricalIncidenceResults:1994EITCExpansion+EqualizationofCredit Schedule......................................46 Table1.12:EmpiricalIncidenceResults:1994EITCExpansion+EqualizationofCredit ScheduleChangePerDollarofNewPlannedExpenditure............47 Table1.13:EmpiricalIncidenceofthe1993EITCExpansionon1993GrossWages.....49 Table1.14:EmpiricalIncidenceofthe2009EITCExpansiononLaborSupply.......49 Table1.15:EmpiricalIncidenceofthe2009EITCExpansion:ChangePerDollarofNew Expenditure.....................................50 Table2.1:StateEITCReturnsandAmountsTaxYears:2017-2020MostRecentValue...58 Table2.2:SummaryStatistics.................................68 Table2.3:E˙ectofStateEITCPrograms:AllBorders...................71 Table2.4:E˙ectofStateEITCPrograms:One-SidedStateBorders............72 x Table3.1:SummaryStats:2010ManhattanRentalBuildings................91 Table3.2:TheRelationshipBetweenOwnershipConcentrationandRent..........109 Table3.3:MainEstimationResults:Manhattan........................110 Table3.4:ModelParameterEstimatesforFourNYCBoroughs...............111 Table3.5:EstimationResults:FourNYCBoroughs.....................112 Table3.6:SpilloverE˙ectsfromUp-ZoningManhattanBuildings..............113 TableA.1:Summary:PercentChangeinGrossWageforLowWageMarketfrom 1% SubsidyIncrease..................................116 TableA.2:MarketStateYearObservationsforEstimationSample..............128 TableA.3:MarketStateYearObservationsforEstimationSample..............129 TableA.4:SummaryStatisticsforSimulationIncidenceSampleTaxYear1992.......131 TableA.5:SummaryStatisticsforSimulationIncidenceSampleTaxYear2009.......132 TableA.6:SummaryStatisticsforSimulationIncidenceSample1990Census........133 TableA.7:AdditionalElasticitySpeci˝cationsAveragewithinDemographicGroups....143 TableA.8:AdditionalElasticitySpeci˝cationsAveragewithinDemographicGroups....145 TableA.9:EITCDi˙erence-in-Di˙erenceResults......................146 TableA.10:IncidenceResults:IndividualE˙ectsof1993Expansion.............147 TableA.11:IncidenceResults:AggregateE˙ects:AllWomenRothstein(2010)Replica- tion&Extension..................................149 TableB.1:StateEITCReturnsandAmountsSources.....................151 TableB.2:AlternateSpeci˝cations:FedReturnsandEmployment.............153 TableB.3:StateSupplementRatesbyBorderStatus:One-vsTwo-sidedBorders......154 TableB.4:StateSupplementRatesbyBorderStatus:One-vsTwo-sidedBorders......155 TableB.5:StackedEventStudies:LogEITCReturns....................156 xi TableB.6:StackedEventStudies:LogEmployment:Women,LessHS...........157 TableB.7:StackedEventStudies:LogAvgMonthlyEarnings:Women,LessHS......158 TableC.1:SummaryStats:2008-2015NYCUnconstrainedRentalBuildings........167 TableC.2:MatchRateAcrossBoroughs............................171 TableC.3:Di˙erenceBetweenReportedandMDRCCCommonOwnership........172 TableC.4:TheRelationshipBetweenAggregateOwnershipConcentrationandPrices...173 TableC.5:TheRelationshipBetweenOwnershipConcentrationandPriceperSquareFoot.174 TableC.6:ExampleMappingofMarketValuetoIncome...................176 TableC.7:SummaryStats:2010NYCRentalBuildings...................182 xii LISTOFFIGURES Figure1.1:LaborSubsidyIncidenceinTwoFactorModel: f Œ g .............4 Figure1.2:EITCSchedulebyYearandNumberofChildren.................6 Figure1.3:IncidenceComparisonAcrossLaborSubstitutions................17 Figure1.4:LaborandWagesAcrossDemographicGroups.................22 Figure1.5:SimulatedvsTrueEITCParameters.......................22 Figure1.6:ModelImpliedChangeinLFPbyDemographicGroup.............34 Figure1.7:TrueandCounterfactual1992TransferPrograms.................38 Figure2.1:EITCPolicyandUseVariation..........................59 Figure2.2:E˙ectofStateSupplementImplementation...................61 Figure2.3:BorderCountiesbyTreatmentStatus.......................67 Figure2.4:StackedEventStudyPlots............................74 Figure3.1:Distributionof2010ManhattanRenters&Rents.................92 Figure3.2:DistributionofOwnershipConcentrationinManhattan.............94 Figure3.3:DistributionofResults..............................105 Figure3.4:ResultsforManhattan...............................106 FigureA.1:ModelImpliedParameters.............................150 FigureC.1:DistributionofBuildingUseinManhattan....................168 FigureC.2:DistributionofZoningConstraintsandRentStabilizationinManhattan....169 xiii KEYTOABBREVIATIONS 2SLS TwoStageLeastSquares ACS AmericanCommunitySurvey AFDC AidforFamilieswithDependentChildren ARRA AmericanRecoveryandReinvestmentActof2009 AR Anderson&Rubinteststatistic ASEC AnnualSocialandEconomicSupplementsample ATR AverageTaxRate Act ActualorTrue BA Bachelor'sDegree(4-yearCollegedegree) BBL Borough-Block-Lotbuildingidenti˝er BK Brooklyn(Kingscounty,NewYork) BLP Berry,Levinsohn,andPakes(1995) BX theBronx(Bronxcounty,NewYork) CBD CentralBusinessDistrict CES ConstantElasticityofSubstitution CI 95%Con˝denceInternal CPI ConsumerPriceIndex CPS CurrentPopulationSurvey CRS ConstandReturnstoScale Cft Counterfactual DHS Dickert,Houser,andScholz(1995) DOF DepartmentofFinance(speci˝callyinNewYorkCity) EITC EarnedIncomeTaxCredit FAR FloorAreaRatio FE FixedE˙ect xiv FTC FederalTradeCommision GDP GrossDomesticProduct GE GeneralEquilibrium GIM GrossIncomeMultiplier GMM GeneralMethodofMoments HHI Her˝ndahl-HirschmanIndex HS HighSchooldegree IGMM IteratedGeneralizedMethodofMoments IPUMS IntegratedPublicUseMicrodataSeries IRS InternalRevenueService IV InstrumentalVariable KPrk Kleibergen-Paap(2006)rankstatistic LATE LocalAverageTreatmentE˙ect LFP LaborForceParticipation LHS LessthanHighSchoolDegree(DidnotcompleteHighSchool) MDRC MultipleDwellingsRegistrationContacts MN Manhattan(NewYorkcounty,NewYork) MOP MontielOlea-P˛ueger(2013)e˙ectiveFstatistic MR Meyer&Rosenbaum(2001) MV MarketValue NBER NationalBureauofEconomicResearch NIT NegativeIncomeTax NPV NoticeofPropertyValue NTA NeighborhoodTabulationAreas NYC NewYorkCity OBRA OmnibusBudgetReconciliationActof1994 ORG OutgoingRotationGroupsample xv PE PartialEquilibrium PLUTO PrimaryLandUseTaxLotOutput PRWORA PersonalResponsibilityandWorkOpportunityReconciliationActof1996 QN Queens(Queenscounty,NewYork) RCL RandomCoe˚cientsLogit RCNL RandomCoe˚cientsNestedLogit SBFE StateBorderFixedE˙ect SBRD StateBorderRegressionDiscontinuity SE StandardErrors SI StatenIsland(Richmondcounty,NewYork) SQFT Square-foot SQUAREM SquaredExtrapolationMethodsforAcceleratingEM-LikeMonotoneAlgorithms TANF TemporaryAssistanceforNeedyFamilies TAXSIM TaxSimulation(speci˝callytheprogrambytheNationalBureauofEconomicResearch) TRIM3 UrbanInstitute'sTransferIncomeModel3 WIVRSE WeakInstrumentRobustStandardErrors xvi CHAPTER1 THEGENERALEQUILIBRIUMINCIDENCEOFTHEEARNEDINCOMETAX CREDIT 1.1Introduction TheEarnedIncomeTaxCredit(EITC)isoneofthelargestanti-povertyprogramsintheUnited States.Over20%ofallworkersand40%ofsingleparentworkersreceiveashareofthe $67 billion expenditure.Attheendofthe`phase-in'portion,theEITCyieldsa19%-34%subsidyongross earningsforworkerswithchildren.Lawmakersandpolicyadvocatesoftenproposeexpansionsof EITCbene˝tsandeligibility. Yetessentiallyallpriorresearchhasassumedawaythepossibilityofgrosswagedistortions whenanalyzingpolicye˙ectsonlaborsupply.SincetheEITCamountisbasedongrossearnings, iftheprogramfeeds-backintomarketwagese.g.,decreasingwagesforlow-incomeworkers thentheanti-povertypolicygoalswillbeundermined.Witheachexpansionthatincreasesbene˝ts orexpandseligibility,usingpartialequilibriumassumptionsseemslesstenable.Giventhescopeof theEITC,itsplaceinanti-povertypolicydiscussions,andtheimportanceoflabormarketearnings onitsoveralle˚cacy,thisoversightloomslarge. ImodelandevaluatetheEITCbyderivingageneralequilibriumincidenceequationthatrelates changesinaveragetaxratestochangesmarketwagesandlaborsupply. 1 Myapproachallowsme todecomposewagechangesintothedirectandindirecte˙ectsonboththetreatedanduntreated workers.IparameterizetheincidenceequationbyestimatingEITCspeci˝claborsupplyand substitutionelasticitiesandthenperformfourquantitativeevaluations.Icalculatetheempirical incidenceofthe1993expansionfordi˙erentdemographicgroups.Icomparecounterfactual marginalexpansionsofthepre-reform(1992)EITCandsocialsafety-net`Welfare'programsto 1 Irefertopre/post-taxwagesasgross/netwages.IreferenceEITCtaxratesassubsidiesare `negativetaxes.'Ide˝nea`partialequilibriume˙ect'asthedirecte˙ectofapolicychangeholding allelseequal;a`generalequilibriume˙ect'asthetotalpolicye˙ectallowingallendogenous variablestoadjust. 1 comparehowdi˙erenttaxincentivesa˙ectincidenceandspillovers.Usingtheestimatedelasticities toparameterizeastructurallaborsupplymodel,Icalculatetheincidenceoftheout-of-sample2009 EITCexpansion,andIconductacounterfactualEITCreformthatequalizesthecreditschedulefor workerswithandwithoutchildren. Toconducttheseexercises,Iestimatelaborsupplyelasticitiesfordi˙erentdemographicgroups andalaborsubstitutionelasticitythatgovernsthecurvatureoflabordemand.IuseEITCpolicy variationtiedtothe1993OmnibusBudgetReconciliationAct(OBRA)onlabormarketdata fromtheCurrentPopulationSurvey.Iassignworkerstodemographic-basedlabormarketcells andestimatethecell-speci˝cexpectedEITCpolicyreformexposureviaasimulatedinstrument approachthatusesa˝xeddistributionofworkercharacteristicsfromthe1990Census.This approachusesallpossibleEITCpolicyinformationbutpurgesendogenousbehavioralresponses fromthepolicychanges.Myestimationstrategyallowsmetoavoidtheassumptionthatwomenwith andwithoutchildrenrespondthesamewaytowagechanges,asintypicaldi˙erence-in-di˙erences basedanalysisoftheEITC. 2 Becausetheincidencedependsonthewageresponsivenessofdi˙erent labormarkets,capturinggranulardi˙erencesinsupplyresponsivenessisimportantforaccurately measuringincidencee˙ects. 3 Myprimarytheoreticalcontributionistoformalizethelabormarketforcesthatgenerate `spillovere˙ects'fromtargetedwagetaxesbetweentreatedanduntreatedworkersandacrosslabor marketsegments.Apolicythatincreasestheabsolutequantityofoneworkergroupincreasesthe marginalproductofcomplementaryworkersanddecreasesthatofsubstitutableworkers.These changesinmarginalproductcauselabordemandshiftsthatIinterpretasspillovere˙ects.I showthatthesespillovere˙ectshave`˝rstorder'importanceinmarketwageschanges,andfor treatedworkerspositivemarginalproductspilloversattenuatethenegativedirectwagee˙ect.The partialequilibriumincidence(ordirecte˙ect)isthe upperbound fortreatedworkersandthe lower 2 InAppendixA.3.3,Ishowhowpreviousestimationapproachesconfrontworkerheterogeneity and/orthepresenceofspilloversforidenti˝cation. 3 InAppendixA.5,Ishowthatusingaconstantlaborsupplyelasticityof 0 Ł 75 forallgroups impliesimplieslarger(inmagnitude)wagedeclines(upto 33% )yet 10% largernetearningse˙ects relativetomyestimatedelasticitiesresults. 2 bound foruntreatedworkersrelativetothegeneralequilibriumgrosswageincidence.Becausethe behaviorofall other economicagentsisheld˝xedinPE,themarginalproductchangesareignored sowagespillovere˙ectsarealsoignored.Sincethespillovere˙ectsare`˝rstorder'andopposite relativetothedirecte˙ects,thegeneralequilibriumincidenceistheoreticallyambiguousdueto cascadingfeedbackacrosslabormarkets. Forexample,supposetherearetwosetsofworkers, f Œ g thatarecomplementarytoeach otherintheproductionprocess, 4 andwetreatgroup toaworksubsidy.Thelaborsupplyincrease ofthe treated setofworkerswillincreasethemarginalproductofthe untreated set;thiscauses labordemandtoincreaseforthe untreated workers;theresultingquantityincreasein untreated workerswillthenincreasethemarginalproductofthe treated workers;andsoon...Figure1.1 displaystheseforcesgraphicallyusingatwofactormodelwithatargetedlaborsubsidy. MyprimaryempiricalcontributionistoquantifythemagnitudeofEITCinducedspillovers usingfourpolicyevaluations.Onanindividuallevel,spilloversaresmallbothinmagnitude andrelativetothedirecte˙ects;however,becausespilloversa˙ecteveryworker,spilloversare economicallyimportantwhenaggregated. 5 Intheempiricalincidenceevaluations,I˝ndspillovers increaseaggregatenetearningsbyabout 22 Ł 2% forthe1993OBRAEITCexpansionandby 17 Ł 6% forthe2009ARRAexpansion.WhencomparingtheEITCvsWelfare,thesuperiorityofanEITC expansionrelativetoaWelfareexpansionintermsofnet-earningsbecomes 21% largerwhen accountingforspillovers.EqualizingtheEITCforworkerswithandwithoutchildrenwouldcause a 395% increaseinnetearningschangeofunmarriedwomenwithoutchildrenbutattheexpenseof 88% decrease forunmarriedmothers.Ialsocalculatewagechanges,laborsupplychanges,andthe ˝scalexternalityofEITCreformsacrosseducation,marriage,andparentalstatusthathighlights theheterogeneousdistributionale˙ectsoftheEITC. MyresultshighlightimportantfeaturesoftheEITCandlabormarketprogramsingeneral.First, inducinglaborsupplymechanicallyexpandstheeconomy'spossibilitiesfrontier,whileprograms 4 Forexample,researchassistantsandprofessorsintheproductionofresearch,wheremoreRAs increaseproductivityofprofessorsandmore viceversa . 5 Ifocusonaggregatee˙ectsbutAppendixA.5displaysindividuale˙ects. 3 Figure1.1:LaborSubsidyIncidenceinTwoFactorModel: f Œ g ( a )PartialEquilibrium ( b )GeneralEquilibrium In( a ),asupplysubsidyshifts ( totheright.In( b ),assumingworkercomplementarity,the resultingmarginalproductspilloverscause both labordemandstoshiftright,whichattenuatesthe PEgrosswagedeclinefor -market.Labordemandsarederivedfromasupermodularproduction function. thatincentivizeleavingthelaborforcewillcontractthefrontier.Thus,policiesthatexpandthe laborforce,suchastheEITC,haveadditionalpro-growthbene˝ts,whilepoliciesthatsubsidize leisurehaveadditionalcoststotheeconomy.Second,thepositivespilloversontohigher-income workersseemslikeanunintendedtransfer;however,withprogressivetaxation,theseworkershave apositivetaxrateandthespilloversaretaxedback.Thus,theEITCcanhelp`payforitself'by indirectlyincreasingthetax-base,inadditiontothedirecte˙ectofmovingworkerstoemployment (BastianandJones,2018).TheseforcesareomittedinRothstein(2010)whosepartialequilibrium 4 approachshowstheEITCinitsworstlight. 6 Finally,untreated-substituteworkersfacedownward pressureonwageswhileuntreated-complementaryworkers,whoarealreadyhavehigherwages, getawagebump.Inthemediumtolongrun,thismayincentivizetheuntreated-substituteworkers toeitherbecomeeligible(havechildren)ortoup-skilloutofthelow-wagemarket. AnadditionalempiricalcontributionisthatbyisolatingEITCspeci˝cpolicyvariation,Iallow foramore˝ne-tunedestimateofthetreatmente˙ectsofthe1993EITCexpansion.Recently workbyKleven(2018)pointsoutthatWelfarereformduringthe1990'spotentiallycontami- natesestimatesoftheEITCexpansione˙ects.Partially,thisisbecauseprioranalysishasused `di˙erence-in-di˙erences'techniqueswheretreatmentissimplygroupmembershipinteractedwith yearindicators. 7 Myestimatesimplythatlaborsupplyforunmarriedwomenwithchildrenin- creased 1 Ł 27% duetothe1993EITCexpansion,whichislowerbyathirdtoatenthoftheestimates summarizedbyHotzandScholz(2003). 8 ThissupportstheclaimthatpriorEITCestimates werecontaminatedbymacroeconomicconditionswhilealsoshowingthattheEITC did increase women'slaborsupplyandtherebya˙ectedthemarketwagesoftheeconomy. Theoverarchingmessageofthispaperisthattheimpactofgeneralequilibriumspilloversof conditionalwagesubsidiessuchastheEITC,socialsafety-netprograms,orproposedUniversal BasicIncomeonlabormarketoutcomesareof˝rstorderimportance.Further,becausethe labormarketiscentraltothedistributionofgoodsandservicesintheeconomy,taxpolicyaimed atamelioratingthe˝nancialhardshipsoftheworkingpoorcanneverthelesshaveunintended consequencesacrossallsectorsoftheeconomy. 6 Section1.8andAppendixA.5replicateRothstein(2010)inalternatewayswitheach˝nding theEITCsuperiortoeitheraparameterizedAFDCorNITexpansioningeneralequilibrium. 7 Inastandardlaborsupplymodel,theDIDestimatorisequivalentthereduced-formregression wheregroupandtimeareinstrumentingnet-wages. 8 Table4inHotzandScholz(2003)summarizemuchoftheearlierempiricalliteratureand describethee˙ectsintermsofelasticities. 5 1.2OverviewoftheEITCandRelatedLiterature Thisworkispartofalongrunninge˙orttounderstandandquantifytheeconomicandsocial e˙ectsoftheEarnedIncomeTaxCredit.TheEITCisa$67billionfederaltaxexpenditureprogram designedtoencourageworkbysubsidizingearnedincomethrougharefundabletaxcreditusinga non-linearbene˝tschedule.Figure1.2showshowtheprogramhasexpandedsincetheearly1990's tothepresent. Figure1.2:EITCSchedulebyYearandNumberofChildren EITCschedulesforsingle˝linghouseholdforyears1993,1994,and2019byzero, one,andthreechildren.Joint˝lershaveahighermaximumcreditandextended plateauandphaseoutregions.Bothnominalandreal($2019)valuesplotted. ParametersfromTaxPolicyCenter(2019). Thede˝ningfeatureoftheEITCisthephase-inregionoftheschedule,whichincreasesthe subsidyasearningsincrease,andunambiguouslypromotesgreaterlaborsupply(HotzandScholz, 2003;NicholsandRothstein,2016).Thephase-indi˙erentiatestheEITCfromaNegativeIncome TaxandatraditionalWelfareprogram,whichstartatahighlevelandtaxawaythebene˝tas earningsincrease. Roughly 40% ofallsingleparentfamiliesand 25% ofmarriedparentfamiliesareeligiblefor theEITC,and 40% ofallfamilieswheretheprimaryearnerhaslessthanahighschooldegreeare EITCeligible(NicholsandRothstein,2016).Thismassiveinterventioninthelabormarketshould haveeconomicallymeaningfule˙ectsonlabormarketsortingandequilibrium. PreviousstudieshaveconsistentlyfoundthattheEITCbene˝tstructuresuccessfullyencourages 6 laborforceparticipationandincreasesemploymentratesforeligiblegroupsprimarilyunmarried womenworkerswithchildrenandlowlevelsofeducation.Twocomprehensivesurveyarticles HotzandScholz(2003);NicholsandRothstein(2016)ortwospeci˝capplicationsofthelabor supplye˙ectsEissaandLiebman(1996);EissaandHoynes(2004)provideageneraloverview ofpriorEITCstudies. 9 GiventhesizeoftheEITCasalabormarketintervention,weshouldexpect wageandpricedistortions.However,mostpapersintheEITClaborliteratureassumethatthe EITChashadnoe˙ectongrosswages(Dickertetal.,1995;EissaandLiebman,1996;Saez,2002; EissaandHoynes,2004;Chettyetal.,2013).AsnotedbyHotzandScholz(2003),thisassumption hadneverbeentestedin˝rstdecadeofEITCresearch. 10 Leigh(2010)andRothstein(2010)studythegrosswageincidenceoftheEITCinpartial equilibrium. 11 Leigh(2010),usingstateandfederalvariation,˝ndsthata10%increaseinthe maximumEITCamountleadstoa5%decreaseintherealwagesofhighschooldropouts,and, usingpredictedlaborsupplywithingender-age-educationlabormarketcells,˝ndsthat10%increase incelllaborsupplyleadstoa9%decreaseinrealwageswithinthelabormarketcell.Asmentioned earlier,Rothstein(2010)simulatesahypotheticalEITCexpansionchangeandreportsthatforevery dollarofintendedtransferrealwagesdecreaseby $0 Ł 34 (inpartialequilibrium).Theseresults implythattheEITCisnot ase˙ective aprogramaspolicymakersmaybelieveandmaybean 9 Morerecentpapersonlabormarkete˙ectsandnet-incomedistributionsincludeFitzpatrick andThompson(2010);Chettyetal.(2013);Jones(2017);Kasy(2017);HoynesandPatel(2018); Bastian(forthcoming).Inaddition,therearemanypapersthatassessthesocialimpactoftheEITC onvariousnon-labor-marketoutcomeshealth(DahlandLochner,2012;EvansandGarthwaite, 2014;Hoynesetal.,2015);education(Max˝eld,2015;BastianandMichelmore,2018);and marriage&fertility(Dickert-ConlinandHouser,2002;BaughmanandDickert-Conlin,2003). 10 Someofthesepapersareexplicit(EissaandLiebman,1996;Saez,2002;Chettyetal.,2013) andothersareimplicitinbyholdingwages˝xedwhensimulatinglabormarkete˙ects(Dickert etal.,1995;EissaandHoynes,2004).InChettyetal.(2013),theirmodel'stheproductionfunction impliesworkersareperfectsubstitutes(thusnospillovers)andtheirempiricalresultsdependonthe stableunittreatmentassumption.Onepotentialreasonfortheabsenceisagreaterinitialinterest intheindividualpolicytreatmente˙ectsoftaxreformsratherthanpolicye˙ectonlabormarkets. 11 Azmat(2019)studiestheincidence,alsoinpartialequilibrium,ofaconceptuallysimilar WorkingFamiliesTaxCreditprogramintheUK.She˝ndsthat,duetodi˙erencesinsalience uniquetotheUKprogram,grosswagesfallby7%forclaimantsand1.7%fornon-claimants.Also, HoynesandPatel(2018)lookatafter-taxincomedistributionale˙ectsoftheEITCandshowthat indirecte˙ectsincreasenet-incomeofworkersnearthepovertythreshold. 7 unintendedtransfertonon-targetedgroups,suchasbusinessownersandwealthierhouseholds. Mycontributiontothesepapersistoallowforlabormarketspilloversthata˙ectbothtreatedand untreatedworkers,toderiveananalyticalformulathatallowsmetoestimatetheempiricalincidence oftheEITCratherthanitsmaximumcreditorhypotheticalexpansion,andtocreateaframework topredictandevaluateout-of-sampleexpansions. AgrawalandHoyt(2018b)studygeneralequilibriumtaxincidenceinamulti-productconsumer goodsmarkets.They˝ndthattaxrateovershiftingispossiblewhenrelatedgoodsaresubstitutes and˝ndthatspilloversareempiricallyimportantinalcoholmarkets.Mypaperconsiderstaxesin multi-factor input markets,appliesthistoempiricallytotheEITCandWelfareprograms,andalso ˝ndsspilloversareempiricallyimportant. Intermsofgeneralequilibriume˙ectsoftheEITC,thisworkispartofasmallgroup.Lee andSaez(2012)allowforendogenouswagesandarguethatanEITCcombinedwithanoptimal minimumwagepolicycanpreventsomeoftheincidencee˙ect;however,theauthorsdonot actuallyattempttocalculatetheGEincidence.Tobuildontheirwork,Iincorporatespillover e˙ectsbetweenlabormarketsand˝rmentrydecisionsallowingforanarbitrarynumberoffactors withheterogeneoussupplyresponsesandtaxchanges.Kasy(2017)developsanovelestimation procedureusingmaximumEITCamountstocalculatethechangeingrosswagesandlaborsupply alongage,education,gender,andincomedistributioncellsand˝ndsnegativeearningse˙ects thatdominatethecredit,asiflabordemandwerecompletelyinelasticsimilartoLeigh(2010); Rothstein(2010).BecauseIdonotrelyonadi˙erence-in-di˙erencestrategybetweenthosewith andwithoutchildren,Iallowforlaborsupplyheterogeneityalongparentalstatus. 12 Inaddition, becauseIusedempiricaltaxrates,Icancomputebothgrossandnetearningse˙ects.Finally, FroemelandGottlieb(2019)developamacroeconomicmodeltoanalyzeconsumption,savings, andwagedetermination,and˝ndthatboththegrossearningsandwealthgapincreasebutthe netearningsgapshrinksduetotheEITC.Tocometotheseconclusions,theauthorsuseatwo 12 Additionally,theauthoromitscommon-policy-shocke˙ectsbyusingyearindicatorvariables inhisempiricalspeci˝cation.Thismaybeonereasonthathisempiricalestimatesaresimilarto partialequilibriumanalysis. 8 skillmodel,focussolelyonmarriedhouseholds,useanapproximatedEITCpolicyfunction,and ignorethedistinctionbetweenworkerswithandwithoutchildren.Myworkisabletoaccountfor mostoftheseforceswhilemaintainingarichdegreeofindividualheterogeneityinskillsandwage responsivenessandexactlymodelingtheEITC. Finally,myresultsareabletorationalizeastartlingnull-˝ndingbyKleven(2019).The authoruseseverystateandfederalEITCreformsincetheprogram'sinceptionandonly˝nds employmentincreasesfromtheOBRAexpansion,whichhenotesoccurredalongwith confoundingmacroeconomicandpolicyforces.Icontributetohisworkbyestimatinglaborsupply elasticitiesusingpurelyEITCpolicyvariationandbycalculatingtheincidencebyastructural approachthatholdstheseconfoundingvariablesconstant.Additionally,byseparatelycalculating thelabormarkete˙ectsoftheOBRAandARRAexpansion,IshowthatmostEITCexpansions likelydonotgenerateeconomicforceslargeenoughtobeobservedusingdi˙erence-in-di˙erence methods. 1.3Model Inthissection,Idescribeageneralequilibriumlabormarketmodeltoinvestigatethee˙ect oftargetedlaborsubsidies.Theprimaryassumptionsarethatworkerutilityisquasi-linearina compositeconsumptiongood,productiontechnologyhasconstantelasticityofsubstitutionbetween factorsandisconstantreturnstoscale,andworkercharacteristicsareobservedbyallmarket participants.Tomakeanalysissimpler,Iabstractfromothertaxationissuesbyassumingthe subsidyis˝nancedbylump-sumtaxesonworkers,exceptIallowforanunemploymentbene˝t. Forexposition,Ipresentamodelwithonlytwolaborskilllevels.InAppendixA.1,Iderive welfaremeasuresforthemodel,showthatthemodeleasilygeneralizestoarbitrarylabortypeswith type-speci˝ctaxchanges,anddiscusstwoextensions:allowinglabormarket`switching'andtwo outputsectors. 9 1.3.1Workers Lettherebeamass # ofworkers,whereeachisde˝nedbyaskilllevel, 4 2f 0 Œ 1 g ,aparental status, 2 2f 0 Œ 1 g ,andacontinuousandstochasticdisutilityoflabor, a ˘ ˙ 4Œ2 ¹ a º .Supposethat onlyskilldeterminesworkerproductivity,sowagesarepositivelyrelatedtoskillsbutunrelatedto parentalstatusconditionalonskill.Givenperfectinformationandperfectlaborcompetition,all workerswiththesameskillwillearnthesamewage. Eachworkerhaspreferencesoverahomogeneousconsumptiongood, - ,andlabor, ! ,repre- sentablebyaquasi-linearutilityfunction, * ¹ -Œ! ; a º = - a ! .Workersmaximizeutilityby choosingafeasiblelabor-consumptionbundlegivenwages( F )andthetaxsystem.Thatis,each workersolves: max -Œ! f - a ! g s Ł t Ł- ) 2 ¹ F 4 ! º & ! 2f 0 Œ 1 g Œ (1.1) where ) 2 ¹ F 4 º isthenetearningsaftertaxation,whichdependsongrossearningsandparental status. 13 Aftersubstitutingthebudgetconstraint,theutilitymaximizationproblembecomesadiscrete choiceproblem: max ! = f 0 Œ 1 g 8 > > >< > > > : ) 2 ¹ 0 º |{z} ! = 0 Œ) 2 ¹ F 4 º a | {z } ! = 1 9 > > >= > > > ; (1.2) Thesolutionyieldsworkeroutputdemandandlaborsupplyfunctions, - ˇ 8 and ! ( 8 .Let v 4Œ2 = ) 2 ¹ F 4 º ) 2 ¹ 0 º ,thenbyde˝nition Pr ¹ a v 4Œ2 j 4Œ2 º = ˙ 4Œ2 ¹ v 4Œ2 º .Withspeci˝cdensityfunctions, ˙ 4Œ2 ¹ v º ,thelaborsupplyprobabilityofeachtypeofworkerisknown;e.g.,withType-1Extreme Valuedraws,laborsupplyhasalogitform: ˙ 4Œ2 ¹ v º = e v š¹ 1 ¸ e v º . Thus,theaggregatelaborsupplyfunctionsare: ! ( 4Œ2 = ˙ 4Œ2 ¹ v 4Œ2 º # 4Œ2 & ! ( 4 = Õ 2 2C ! ( 4Œ2 & ! ( = Õ 4 2E ! ( 4 Ł (1.3) 13 InthissectionIignorenon-laborincomeastherearenoincomee˙ects;however,inthe empiricalsectionsIincorporatenon-laborincomewhencalculatinge˙ectivetaxrates. 10 Thelaborsupplyelasticityfordemographicgroup ¹ 4Œ2 º is: m! ( 4Œ2 mF F 4 ! 4Œ2 = m) 4Œ2 mF 5 4Œ2 ¹ v 4Œ2 º F 4 ! 4Œ2 : = Y ! 4Œ2 Ł (1.4) Usingthelogitexample, Y ! 4Œ2 = m) 4Œ2 mF F 4 ¹ 1 ˙ 4Œ2 ¹ v 4Œ2 ºº .Astherearenoincomee˙ectsforlabor supply,theMarshallianandHicksianelasticitiesareequivalent. 1.3.2Production Lettherebemass ˜ ofpotentialproducersindexedby 9 2J ,eachendowedwithoneunitof capital( ),thatcanhirelabortoproduceahomogeneousconsumptiongood.Firmsdrawacapital supplycost(orentrycost), b 9 ,fromacontinuousdistribution, ˝ ¹ b º .Technologyisrepresentedby anestedconstantelasticityofsubstitution(CES)productionfunction: @ ( 9 = & ¹f ! 4 ; 9 g 4 Œ 9 º = 9 2 6 6 6 6 6 4 Õ 4 2E o 4 ¹ ! ˇ 4 ; 9 º 1 ¸ d d ! d 1 ¸ d 3 7 7 7 7 7 5 U ¹ 1 U º 9 (1.5) = 9 L U 9 ¹ 1 U º 9 Œ (1.6) where 9 isaHick-neutralproductivityterm, ! ˇ 4 ; 9 isthe˝rm- 9 type- 4 labordemand,and L 9 denotes theaggregatelaborindexforthe˝rm.Theelasticityofsubstitutionbetweenlaborskill-groupsis parameterizedby: d = d ln » ! 4 00 š ! 4 0 ¼š d ln » F 4 00 š F 4 0 ¼ 0 Œ for 4 0 Œ4 00 2E Ł (1.7) Thistechnologyfeaturesconstantreturnstoscale(CRS)andassumes˝xedsubstitutionelastic- itiesbetweenfactors. 14 Firmsmaximizepro˝ts: c 9 = ? & ¹f ! 4 ; 9 g 4 2E Œ 9 º Í 4 2E F 4 ! 4 ; 9 A 9 . Aggregateoutputisde˝nedas @ ( = ¯ 9 @ ( 9 d 9 .Pricetaking,zeropro˝ts,andidenticalproduction functionsimplyall˝rmschoosethesamefactorinputbundle,sobyCRStheaggregateproduction functionisalsonestedCES.Inormalizetheoutputpricetoone, ? = 1 ,sowagesandcapitalrents areintermsofthe˝nalgood. 14 Note,whentherearemorethantwoskillgroups, d isthe partial elasticityofsubstitution.The primarymodelingbene˝ttothistechnologyisthatitallowsfortractableanalyticsolutionswithan arbitrarynumberoflabortypes,asIuseinthegeneralizedmodelfortheempiricalapplications. 11 Undertheseassumptions,the˝rmcapitalsupplyissynonymouswith˝rmentryandisendoge- nouslydeterminedby˝rmcapitalsupplycosts, b 9 ,andthepriceofcapital, A .Firm 9 willenter if b 9 A .Inequilibrium,thisdeterminestheaggregatecapitalsupplyfunction, ( ¹ A º ,andthe aggregatecapitalsupplyelasticity, Y ( = A 6 ¹ A º ˝ ¹ A º . 1.3.3TaxandTransferSystem Forsimplicity,supposethatinitiallythegovernmentraisesrevenueusinglump-sumtaxationatthe level = ,providesanunemploymentbene˝tatlevel 1 ,andbalancesitsbudget.Then,thegovernment reformsthetaxsystemtoprovidealaborsubsidyforlowskillworkerswithchildren, g ¹ 0 Œ 1 º (thatis paidforbylump-sumtaxchanges).Thisimpliesthefollowingskillspeci˝caggregatelaborsupply functions(recallingequation1.3): ! ( 0 = ! ( 0 Œ 0 ¹ F 0 º¸ ! ( 0 Œ 1 ¹ F 0 ¸ g ¹ 0 Œ 1 º º (1.8) ! ( 1 = ! ( 1 Œ 0 ¹ F 1 º¸ ! ( 1 Œ 1 ¹ F 1 º (1.9) Equation1.8providesintuitionfortheincidenceformulaIwilldemonstrateinthenextsection. Thesubsidydirectlycreatesawork-incentiveforthesubsidizedgroup.However,theequilibrium e˙ectongrosswagesdistortslaborsupplyforunsubsidizedworkers. 1.3.4Equilibrium Anequilibriumintheeconomyisawageandrentschedulesuchthatthefactormarketclearsand ˝rmsmakezeropro˝ts(thusclearingtheoutputmarket).Theeconomyisinequilibriumwhenno workerwishestoadjustherlaborsupplyandno˝rmwishestoadjustitsinputbundle. DuetotheCRSassumption,thescaleoffactordemandscannotbedetermined.Fortunately, themodelcanbesolvedintermsofdemandratios.Inequilibrium,thelabordemandbundlemust satisfy: ! ˇ 0 ! ˇ 1 = F 0 š o 0 F 1 š o 1 d (1.10) 12 Whilethelabor-aggregateandcapitaldemandbundlemustsatisfy: L ˇ ˇ = F š U A š¹ 1 U º 1 Œ (1.11) where F = o 0 F 0 o 0 1 ¸ d ¸ o 1 F 1 o 1 1 ¸ d 1 1 ¸ d isalaborcostindex.Theunitcostfunctionhasthe followingform: 2 ¹ F 0 ŒF 1 ŒA º = ¹ 1 š º F U U A 1 U 1 U . I˝ndthethemodel'sequilibriumconditionsbyequatingthefactordemandandsupplyfunctions andenforcingzeropro˝tsusingtheunitcostfunction,withoutputpricenormalizedtoone.Thus, thegeneralequilibriumoftheeconomyisany f F 0 ŒF 1 ŒA g thatsolvesthefollowingequations: LaborClearing ! ( 4 0 ! ( 4 1 = F 0 š o 0 F 1 š o 1 d (1.12) FactorClearing ! ( 4 0 ¸ ! ( 4 1 ( = F š U A š 1 U 1 (1.13) ZeroPro˝ts 1 = 2 ¹ F 0 ŒF 1 ŒA º Ł (1.14) 1.4Incidence Inthissection,Ipresentthepartialandgeneralequilibriumincidenceoftargetedlaborsubsidies forthetwoskillmodelwhichprovidesallnecessaryeconomicintuition.Attheend,Ipresentthe incidenceresultforthefullmodelthatallowsforarbitrarylabortypeswhichIuseintheempirical applications.ThepartialequilibriumsectionessentiallyreplicatesRothstein(2010)usingtheabove modelnotation. 1.4.1PartialEquilibrium Thetaxreformintroducesalaborsubsidyforlowskillworkerswithchildren, g 0 Œ 1 .Becausethere isnosubsidyforothertypesofworkers,Ireferto g 0 Œ 1 simplyas g .I˝ndthepartialequilibrium incidencebytotallydi˙erentiatingthelaborclearingcondition(equation1.12)whileholding f ! 1 Œ ŒF 1 ŒA g constant.Inthelimitwhenthemarketsizeofsubsidizedgroupgoestozero,this 13 resultisequivalenttothegeneralequilibriumresult,discussednext.Thisyields(when ^ g¡ 0 ): ^ F PE 0 = Y ! 0 Œ 1 Y ! 0 d ! \ 0 Œ 1 ^ g : = W 0 ^ g 0 (1.15) where ^ G 4 = G 4 š F 4 isthepercentofwagechangeforthe 4 -group, \ 4Œ2 = ! 4Œ2 š ! 4 isthewithin skillshareofsubsidizedworkers,and Y ! 4 and Y ! 4Œ2 arethegroupandsub-groupsupplyelasticities, respectively,where Y ! 4 = \ 4Œ 1 Y ! 4Œ 1 ¸¹ 1 \ 4Œ 1 º Y ! 4Œ 0 .Recallequation1.8andnotethatthenumerator usestheelasticityofthesubsidizedgroupwhilethedenominatorusestheaggregatesupplyelasticity forthelowskillmarket. Interestingly,themodelimpliesthatthepartialequilibriumlabordemandelasticityforlaboris constant,equivalentforalllabortypes,andequaltothelaborelasticityofsubstitution.Toseewhy thisisthecase,considerthefollowing: 15 ! ˇ 0 ¹ F 0 º = ! ( 1 ¹ F 1 ¹ F 0 ºº F 0 š o 0 F 1 ¹ F 0 ºš o 1 d = ) [ ˇ 0 = d ¸ mF 1 mF 0 Y ! 1 d Ł (1.16) When mF 1 mF 0 = 0 bypartialequilibriumassumption,thedemandelasticityequalsthesubstitu- tionelasticitybetweenfactors. 16 Holding F 1 and A ˝xedisequivalenttoholdingthosefactors' marginalproductconstant,butthisisinvalidwhen ! 0 increases(exceptwhenthelowskillgroup isin˝nitesimal). 1.4.1.1ImplicationandInterpretationforPolicy Whentherearemultiplelabortypeswithheterogeneoussubsidychanges,aggregatingthePEresults yieldsan`employmentweightedaveragepartialequilibriume˙ect.'Thisisnotoftheoreticalor practicalinterestunlessitis ex-ante knownthatspillovere˙ectswillbenegligible.ThePE assumptionsrequirethatforanyspeci˝claborgroupnoothergroupadjustsitssupply,which createsasetofmutuallyexclusiveassumptions. 15 InthetwofactorCRScase,LeeandSaez(2012)showthatinequilibrium,thesupplyresponses ofthesecondfactorcanbeusedtopindownthe˝rstfactor'sdemandandsecondfactor'spriceas onlyafunctionofthe˝rstfactor'sprice,despitetheunknownscaleofproduction. 16 Anotherwaytoseethisisthat: [ ˇ 4 = d ln » ! ˇ 4 ¼ d ln » F 4 ¼ = d ln » ! ˇ 4 š ! ˇ 4 0 ¼ d ln » F 4 š F 4 0 ¼ = d if d ln » ! ˇ 4 0 ¼ = d ln » F 4 0 ¼ = 0 . 14 Rothstein(2010)impliesthatdecreasesingrosswagesareatransferto ˝rms attheexpenseof workers:impliesthatemployersoflow-skilllaborcaptureaportionoftheintendedEITC transferandgetedworksubsidiesproduceunintendedtransferstoemploy 17 While Rothstein'spartialequilibriumanalysisistechnicallycorrect,theinterpretationofhisresultdoes notnecessarilyfollowfortworeasons. First,withzeropro˝ts,therearenoexplicitpro˝tsfor˝rms.WithCRStechnology,ifone factorpricegoesdown,thenanothermustincrease,sothe owners oftheotherfactorsbene˝tif lowskillwagesfall. 18 Second,ifentrepreneursownsomeoftheotherfactors(suchascapital), thenentrepreneursmay`capture'thewagesubsidybecausetheirownfactorpaymentsincrease. However,theproductionfunctioninRothstein(2010)onlyincludeslaborfactors,sothereisno possiblefactortobeownedbyentrepreneurs. 19 However,the`allelseequal'forthePEincidencerequiresthepricesandquantitiesofallother factorsbeheld ˝xed ,whichmeansthatownersofotherfactors cannot actuallyrealizeanyfactor priceincreases.Thus,apartialequilibriumstoryisincapableofyieldingRothstein'sconclusion abouttransfersto˝rmsattheexpenseofworkers.Inordertorendertheconclusionabout˝rm ownersbene˝tingfromchangesingrosswages,onemustuseageneralequilibriumanalysis. 1.4.2GeneralEquilibrium Tocalculatetheincidence,Itotallydi˙erentiateequations1.12,1.13,and1.14withrespect to f F 0 ŒF 1 ŒAŒg g .Sincethetwotypemodelsystemhasthreeequationsandthreeunknowns ( d F 0 Œ d F 1 Œ d A ),Icansolvetheforachangeinlowskillwagesusingiterativesubstitution.Use thezeropro˝tsconditiontosolve d A = 5 ¹ d F 0 Œ d F 1 º ,usethelaborclearingconditiontosolve d F 1 = 6 ¹ d F 0 Œ d g º ,andthensubstituteintothefactorclearingconditionfor d F 0 = ¹ d g º .This 17 Kasy(2017)makesasimilarclaimbasedonhisresults. 18 Alternatively,holdingotherwagesandrentsconstant,theoutputpricemustdecreasewhich bene˝tsconsumersespeciallylowincomeratherthan˝rmowners. 19 Inanearlierworkingpaper,Rothstein'sproductionfunctiondidincludecapitalbutthiswas omittedinthepublishedversion. 15 yields: ^ F GE 0 = © « Y ! 0 Œ 1 \ 0 Œ 1 Y ! 0 d ¸ B ! 0 Y ! 0 Œ 1 \ 0 Œ 1 ¹ Y ! 0 d º ! Y ¸ 1 B ¸ 1 ¸ d B ! ¹ Y ! 0 d º 1 ¸ Y ¸ 1 B ¸ 1 ¸ d B ! 0 ¸ B ! 1 B ! 0 Y ! 0 d ¸ B ! 1 Y ! 1 d !! ª ® ® ® ® ® ® ¬ ^ g (1.17) : = ¹ W 0 ¸ 0 º ^ gŒ where W 0 isthePEgrosswagee˙ectand 0 istheGEspilloverterm,and B arefactorcostshares. Thus,theGEincidenceisthedirect(PE)e˙ectplusaweightedsumofcross-factore˙ects. 20 Since 0 0 ,asubsidyincreaseforlowskilllaborimpliesthatthespillovere˙ectsattenuatethePE wagee˙ects,soworkersretainmoreofthesubsidythanisimpliedbythePEanalysis. Solvingfortheotherpricee˙ects(when ^ g¡ 0 ): ^ F GE 1 = Y ! 0 d Y ! 1 d ! 0 ^ g 0 and ^ A GE = B ! 0 B ^ F GE 0 ¸ B ! 1 B ^ F GE 1 . 21 Withonlyalowskilllaborsubsidy,thePEanalysisprovidesanupper boundforthelowskilllabormarketwagee˙ect,butPEiscompletelyuninformativeaboutthe magnitudeoftheotherinputpricee˙ectssincethesedependonGEspilloverterms. Asalludedtobefore, ^ F PE 0 = ^ F GE 0 onlyif B ! 0 = 0 ,whichisasmall-marketassumptionthat makeslittlesenseinatwotypemodel. 22 Figure1.3providesavisualcomparisonofPEandGE incidencefora1%e˙ectivesubsidyincreasefor ! 0 asimpliedbydi˙erentendogenouscostshares. Figure1.3alsoshowstheimportanceofthesubstitutionelasticity, d .Wheninelastic,asin Rothstein(2010),thePEincidenceimplieslargewagee˙ects;however,whenmoreelastic,asin myestimatespresentedinSection1.5,thewagee˙ectsaresmaller.Thispatternisbecausealarger elasticityimpliesa˝rmcanmoreeasilyadjustitsfactordemandbundletotakeadvantageofcost savings. 20 Equation1.17resemblestheresultinAgrawalandHoyt(2018b)inthatthegeneralequilibrium incidenceisalinearfunctionofthePEincidenceandGEspillovere˙ects. 21 Asu˚cientconditionfor ^ A GE ¡ 0 isthat ¹ B ! š B º Y ¸¹ 1 š B º ¡ d .If B = 0 Ł 33 and Y = 1 , then ^ A GE ¡ 0 when d¡ 5 ,whichotherauthorsandI˝ndempirically(KatzandMurphy,1992; GoldinandKatz,2009;Borjasetal.,2012). 22 Asnotedearlier,around20%oftaxunitsreceivetheEITCand40%ofallworkerswithchildren (NicholsandRothstein,2016). 16 Figure1.3:IncidenceComparisonAcrossLaborSubstitutions Thisplotsthepercentchangeingrosswagesforlowskillworkersfroma 1% subsidyincreaseat di˙erentsubstitutionelasticitiesandcostshares.Otherparameters: Y ! 0 = 0 Ł 75 ŒY ! 1 = 0 Ł 6 ŒY = 1 . DetailsinAppendixA.1. 1.4.2.1GeneralEquilibriumIncidencewithManyLaborMarkets Addingadditionaltypesoflaborinthiscontextisrelativelysimplegiventhesymmetryofthe model. 23 Letskillsbeindexedby 4 2f 0 Œ 1 Œ 2 ŒŁŁŁŒˆ g = E .Iallowarbitraryskill-speci˝csubsidies ( ^ g 4 ),andthensolvetheequationsinthesamemannerasbeforeusingiterativesubstitutionafter totallydi˙erentiating.FulldetailsareinAppendixA.1. Thegeneralequilibriumincidencefortype 4 0 laboris: ^ F GE 4 0 = Y ! 4 0 Œ 1 \ 4 0 Œ 1 ^ g 4 0 Y ! 4 0 d ¸ Í 4 B 4 Y ! 4Œ 1 \ 4Œ 1 ^ g 4 Y ! 4 d ! ¹ Y ! 4 0 d º 1 ¸ Í 4 B 4 Y ! 4 d (1.18) = W 4 0 ¸ 4 0 ^ g 4 0 ¸ 4 0 ¹f g 4 g 4 2En 4 0 º (1.19) where = Y ¸ 1 B ¸ 1 ¸ d B ! Ł (1.20) Generally,onecannotsignequation1.18withoutknowingthemagnitudeofeach f g 4 0 g 4 .For example,ifthetaxchangeforonegroupissmall but allotherchangesarelargeandpositive,then theGEspilloversmaydominate,sothewagechangewouldbepositive. Equation1.18showsthree˝rstordertermswithrespecttoataxreform:thedirecte˙ect,the 23 Intheempiricalapplications, jEj = 72 basedonage,education,andmaritalstatusofwomen. 17 own-supplyinducedmarginalproductspillovers,andthereceivedmarginalproductspilloversfrom othertaxchanges.Onlyifbothspillovertermsaresmallwill F GE ˇ F PE ;e.g.,ifthecostshare weightedaveragetaxchangeiszero: E » B 4 g 4 \ 4Œ 1 ¼ = 0 . 24 1.5EstimatingLaborMarketElasticities Inthissection,IdescribehowIestimatelaborsupplyandsubstitutionelasticities: f Y 4 0 g Œd , whichareusedintheempiricalapplicationsinsections1.7-1.11.Insummary,Icombinetwodata setstocalculatethelabormarketvariables:the1986-2000CurrentPopulationSurveys(Floodetal., 2018)andthe1990USCensus5%sample,(Rugglesetal.,2018). 25 Next,IuseNBER'sTAXSIM (FeenbergandCoutts,1993)tocreateEITCinducedaveragetaxratechangesastheempirical analogueof ^ g .Finally,Iuseatwo-stepe˚cientGMMtoestimatethesupplyandsubstitution elasticities.AdditionaldetailsandresultsareinAppendicesA.2-A.4. 1.5.1Data Iusethe1986to2000CPSOutgoingRotationGroup(ORG)samplesforlabormarketinformation bystateandyear.Thesampleasksdetailedemployment,earnings,andhouseholdstructure informationfromroughly100khouseholdspermonth.Ipoolthemonthlysamplesforannuallevel labormarketvariables. 26 Iassignworkerstotheirlaborskilllevelsbasedonobservabledemographiccharacteristics. Laborskilllevelsarede˝nedbyfoureducationcategories,nineagegroups,andmarriagestatus thisimplies72skilllevels. 27 Iassignworkerstoalabormarketsbasedontheworker'sskilllevel, 24 AgrawalandHoyt(2018b)makethispointbysupposingthatthemarketshareoftaxedgoods issmallrelativetoacompositeconsumptiongood. 25 IusetwosubsamplesfromtheCPS:theOutgoingRotationGroups(ORG)andtheAnnual SocialandEconomic(ASEC)samples. 26 Idropindividualswhowerenotinterviewedoringroupquarters,variablevaluesthatwere allocated,marriedworkerswithoutacohabitatingspouse,fulltimestudentsoutofthelaborforce, andhouseholdswithgreaterthan10membersbecauseofthedi˚cultyinassigningchildrenfor complexfamilystructures(lessthan0.5percentofthesample). 27 Thatis,72skilllevelsforeachgenderthoughIfocusonlyonwomenworkersformyempirical analysis. 18 state,andyear.Additionally,Iassignworkerstodemographicgroupsbydividingthelabormarket betweenworkerswithandwithoutchildren.Thisyields 72 51 15 labormarketcells 4 2E and 2 72 51 15 demographiccells ¹ 4Œ2 º = 3 2fEf 0 Œ 1 gg . 28 Forlabormarketquantities,Iusetotalhoursworkeddividedbytotalpotentialworkersatthe labormarketlevel. 29 Forlabormarketprices,Icalculateaworker'sreale˙ectivewageasearnings perweekdividedusualweeklyhoursde˛atedusingthetheBureauofLaborStatisticsConsumer PriceIndex(BLSCPI)AllItemsResearchSeries(BureauofLaborStatistics,2019). 30 Appendix A.2includesadditionaldetailsandsummarystatistics. Iusethe1990USCensus5%sampletocalculatedemographic-speci˝csimulatedinstruments fortheEITCpolicychanges. 31 Speci˝cally,IcalculateEITCtaxparametersforeverytaxyear usingNBER'sInternetTAXSIMforthe˝xed1990workerpopulation.TheprimaryEITCtax parameteristheaveragetaxrateassociatedwiththeEITC(EITCATR),de˝nedas g EITCATR = EITC ¹ Actual º EITC ¹ NoWork º TrueEarnings .IalsocalculateanindicatorforifaworkeriseligiblefortheEITC andthechangeinEITCamountfromonetax-yeartothenextholdingearningsconstant. Ifurtherdescribetheinstrumentconstructionandformalizetheexogeneityrequirementsin Section1.5.3andAppendixA.3,butthevirtueofusingtheCensusisthatbyusingthe˝xed population,allvariationinthetaxparametersisduetopolicyreformsovertimeandspaceand initialexposurelevelsoftheEITCtothesereforms. 32 Thatis,thevariationinthesimulatedtax 28 Thisfollowsthebaselinemarketde˝nitioninRothstein(2010),exceptIaddgeographic delineationbystate.Thebene˝ttothisde˝nitionisthatI`observe'theskilllevelofunemployed workers. 29 Thismeasurecapturesbothextensiveandintensivemarginresponsesthatarerelevantforlabor marketequilibrium.InAppendixA.4,Ipresentresultsusingthetotalnumberofworkersthat capturesonlytheextensivemarginresponse. 30 Thisvariableistheloggeometricmeanwage,whichinterpretableasanhoursweighted productivityindex(Borjasetal.,2012). 31 Simulatingtaxparameterstogenerateinstrumentsisalsousedinnumerouspriorstudiessuch as:Dickert-ConlinandHouser(2002);GruberandSaez(2002);Rothstein(2008);Leigh(2010); BastianandMichelmore(2018). 32 Inthisway,thetaxinstrumentsaresimilarto`shift-share'instruments.Seethefollowingon recentanalysisconcerningthegeneralidentifyingassumptionsoftheseinstruments:Adao,Kolesár andMorales(2018);Borusyak,HullandJaravel(2018);Goldsmith-Pinkham,SorkinandSwift (2018). 19 parametersis not duetoanyendogenousbehavioralresponsetothepolicyreformsseeFigure1.5 below. 1.5.2SummaryStatistics Table1.1displaysthedi˙erenceinlabormarketvariablemeansbeforeandaftertaxyear1993 conditionalonmarriageandparentalstatustohighlighttheidenti˝cationusingEITCpolicytax changes.The˝rsttwovariablesareaveragesoftheEITCAverageTaxRates,wherethe˝rstisthe instrumentcalculatedfromthe1990CensusandthesecondusevaluesfromtheASECsamples (describedlater),whichincorporateendogenousbehavioralresponses.Beforethereform,thetrue andsimulatedtaxratesaresimilar,butpost-OBRAthetruetaxratesarelower(implyingalarger credit).Thisisduetoendogenouslaborsupplyincreasesinthetrueratesbutnotthesimulated rates,astheinstrumentcalculationholds˝xedlaborsupplydecisions. 33 Additionally,Table1.1showsthatlaborsupplyincreasedforunmarriedwomenwithchildren andmarriedwomenbutdecreasedslightlyforunmarriedwomenwithoutchildren.Despitethese supplyincreases,therearemeaningfulwageincreasesforeverygroupinthisperiod.Thesummary statisticsshowthatthelabordemandmustdominatethesupplyincreasestoresultinpositivewage growth. 34 Forthisreason,IuseEITC-speci˝cpolicyvariationthatisunrelatedtodemandshocks tountanglethesecompetingforces. IplotthedatafromTable1.1inFigures1.4and1.5.InFigure1.4Iplotlogtotalhoursper workerandmeanloggrosswagesbydemographicgroupsduringthe1990's.Thesearetheprimary outcomeandandendogenousexplanatoryvariableintheempiricalspeci˝cation,respectively. InFigure1.5,IplotthesimulatedEITCATRsandEITCtake-upsharesagainsttheempirical measuresfromtheASEC.Theprimarypolicychangeforunmarriedmothersoccurredovertax 33 Whilethiscouldbeduetoearningsdecreases(fromlowerwagesorlesssupply)thatcause workerstoqualifyformorecredits,Table1.1showswageandlaborsupplyincreasedforunmarried mothers. 34 The1990swereatimeoftechnologicalchangeandfavorablemacroeconomicconditionswhich canexaggerateEITCe˙ectsonlaborsupplyandconfoundthewagee˙ects(NicholsandRothstein, 2016;Kleven,2019). 20 Table1.1:SummaryStatisticsforEstimationSample TaxYears 1989-19931995-1999Di˙erence MeanSD MeanSD bt UnmarriedWomenw/Children EITCATR-1990Census -0.080.04 -0.140.08 -0.06***-40.86 EITCATR-ASEC -0.080.06 -0.160.11 -0.08***-34.20 LogHoursPerPerson-ORG 3.080.54 3.190.44 0.11***8.55 LogRealWage-ORG 2.150.31 2.470.33 0.32***39.09 Observations 2560 3854 6414 UnmarriedWomenw/oChildren EITCATR-1990Census 0.000.00 -0.010.01 -0.01***-69.49 EITCATR-ASEC 0.000.00 -0.010.01 -0.01***-32.69 LogHoursPerPerson-ORG 3.320.37 3.280.35 -0.05***-5.01 LogRealWage-ORG 2.150.31 2.470.33 0.32***39.47 Observations 2589 3864 6453 MarriedWomenw/Children EITCATR-1990Census 0.000.00 0.000.01 0.00***14.72 EITCATR-ASEC 0.000.01 0.000.02 0.001.92 LogHoursPerPerson-ORG 3.030.40 3.100.34 0.07***8.34 LogRealWage-ORG 2.230.30 2.580.32 0.35***54.45 Observations 3809 5349 9158 MarriedWomenw/oChildren EITCATR-1990Census 0.000.00 0.000.00 -0.00***-7.65 EITCATR-ASEC 0.000.00 0.000.00 -0.00***-4.53 LogHoursPerPerson-ORG 3.270.39 3.290.34 0.02**2.68 LogRealWage-ORG 2.230.30 2.580.32 0.35***54.49 Observations 3844 5336 9180 AlldatafromCPSSamples1990to2000and1990USCensus.EITCATRscalculatedusing TAXSIM. years1993to1996,whiletheonlypolicychangeforunmarriedwomenwithoutchildrenwasin taxyear1993.Forunmarriedmothers,thetrueATRislessthanthesimulatedATRthatholds laborsupply˝xed,whichisconsistentwithworkersenteringthelaborforceatlowerearnings.The simulatedsharepredictsthatfewerunmarriedmotherswouldclaimtheEITCstartingintaxyear 1996duetoanaddedincometest. ManyempiricalEITCstudiesassumethattheEITCpolicychangesforworkerswithoutchildren isnotenoughtoa˙ectbehavior.The˝guresshowthisisareasonableassumptionbecauseIcan 21 Figure1.4:LaborandWagesAcrossDemographicGroups (a)LogHoursperWorker (b)LogWage Thisplotslogtotalhoursperworker( a )andmeanlogrealwage( b )usingCPSORGsamplesof women(1990-2000)bymarriageandparentalstatus.Logtotalhoursperworkerisusedasthe measureoflaborquantityandmeanlogrealwageaslaborprices. predictthetheEITCATRandshareusingonlythe1990distributionoflaborsupplyandin˛ation. Figure1.5:SimulatedvsTrueEITCParameters (a)EITCATR (b)Sharew/EITC ThisplotstheaverageEITCATR( a )andsharewithEITC( b )forunmarriedwomen-headedtax unitscalculatedusingASEC(`true')or1990Census(`sim')samplesandNBERTAXSIM.The 1990CensusvaluesareusesassimulatedIVsforlabormarketoutcomes. 1.5.3Identi˝cation Succinctly,theincidencemodelandFigure1.1elucidatesthattheEITCcreatesbothsupply anddemandvariationinwagesthatcanbeusedtoidentifylaborsupplyandlaborsubstitution 22 elasticities: d F 4BC |{z} WageVariation intheData = W 4 d g 4BC | {z } SupplyShift ¸ 4BC ¹f g 4 0 BC g 4 0 º | {z } DemandShift | {z } IncidenceModel ¸ E F 4BC |{z} Unobserved Variation Ł (1.21) AsdiscussedinWatson(2020),supplyelasticitiesareidenti˝edusingspilloverbaseddemand variationandconditioningontheowntaxratethatcontrolsforsupplyshifts;whereas,demand elasticitiesareidenti˝edusingthetaxreformsupplyshockandconditioningonthedemand spillovers. Asu˚cientsetofidentifyingassumptionsforbothlaborsupplyandsubstitutionelasticitiesis that: E » g 4BC D ˇ 4 0 BC j 4BC Œ- ¼ = 0 Œ 8 4Œ4 0 2E (1.22) E » 4BC D ( 4 0 2BC j g 42BC Œ- ¼ = 0 Œ 8 4Œ4 0 2E Œ (1.23) where g 4BC = \ 4 0 BC g 4 0 BC ¸ \ 4 1 BC g 4 1 BC . 35 Inwords,taxratevariationisuncorrelatedtobothunobserved non-spilloverdemandshockse.g.,skillbiasedtechnicalchangeorchangesinhiringcostsand tounobservedsupplyshockse.g.,employmentopportunitycosts.SeeAppendixA.3.1formore detailsandderivation. Toempiricallyimplementthis,IcreatetwosetsofIVsusingthe1990Censussample,whichI calltheown-marketIVsandthesubstitute-marketIVs.Theown-marketIVsarecalculatedusinga simpleaverageofsimulatedindividualEITCvariableswithinagivendemographic-skillstate-year group.Thesevariablesmeasurethedirecte˙ectoftheEITConagivenmarketgroup.Thisiswhat isplottedinFigure1.5. Thesubstitute-marketIVsarecalculatedusingtwosetsof`leave-out'averagesinthesame state-year.The˝rstsetisbasedonsimilareducationgroupsandthesecondisbasedonsimilarage group.Forexample,considerthegroup`young,unmarriedwomenwithlessthanahighschool degree,'thenthe˝rstIVsetisbasedonaveragingacrossallwomenwithlessthanahighschool 35 Theseassumptionsareslightlystrongerthannecessary,particularlyforthesubstitutionelas- ticity,butwouldimplythenecessaryassumptionIshowinAppendixA.3.1. 23 degreebutleavingouttheyoung,unmarriedgroupinthataverage.Further,byconditioningon theown-marketEITCparameters,theremainingvariationisorthogonaltothedirecttaxshockto anyparticulargroup.TheseIVsuseEITCexposure,butnotresponsiveness,ofclose-substitute workers. 1.5.4EstimatingEquations Toestimatethelaborsupplyandsubstitutionelasticities, f Y 4 0 g Œd ,Iusetwo-stepe˚cientGMM withstandarderrorsclusteredatthelabormarketlevel(Hansen,1982). 36 Whiletheoretically possibletoestimatethesupplyandsubstitutionelasticitiesjointly,Iestimatetheparametersintwo separatesteps(Zoutmanetal.,2018;Watson,2020). 37 Iidentifythelaborsupplyelasticities, Y ! 3 ,usingvariation within demographiccellsacross state-years.Thatis,identi˝cationcomesfromthedi˙erencesinEITCinducedwagespillovers i.e.,demandshockswithinademographicgroupduetodi˙erentialexposuretoEITCreforms inagivenstate-year.Forexample,supposeinstateArelativetoBtherearemoreunmarried mothers,thenstateAhasgreaterexposuretoEITCreforms,sotheresultingsupplyshockwill createlargerdemandspillovers.Additionally,ifAandBhavesimilarsharesofunmarriedmothers butAimplementsastateEITC,thenAwillhavealargerEITCpolicyshock. 38 Byconditioning onthedemographicgroup'sownEITCchange,theremainingskill-levelvariationintheEITCis duetodemandshocks.IdescribethisargumentingreaterdetailinAppendixA.3.1. Toestimatetheheterogeneouslaborsupplyelasticitieswhilecontrollingformarketconditions via˝xede˙ects,Ispecifythecoe˚cientonlogmarketwageasfunctionofmarriage,parental,and 36 AppendixA.4additionalempiricalspeci˝cations. 37 Thelinearizeddeviationsfromequilibrium,usedtoarriveatequation1.18,formalinear systemofequationsthatcouldbeestimatedusingGMM,similartoSuárezSerratoandZidar (2016).Attheexpenseofe˚ciency,separatingtheestimationtasksallowsfortheparametersto betransparentlyidenti˝edandmorerobusttomisspeci˝cation. 38 Fourteenstates(andDC)hadanstateEITCprogrambetween1990and2000:CO,IA,IL,KS, MA,MD,ME,MN,NJ,NY,OR,RI,VT,WI. 24 educationstatus.Thisleadstothefollowingestimationequations: ln » , ¼ 3BC = c 0 ¸ / 3BC 1 ¸ » / 3BC g 3 ¼ 3 ¸ c 2 g 3BC ¸ c 3 ln » % 3BC ¼ ¸ d 3 ¸ d BC ¸ d F % 0 ŒC ¸ d BMW ;BC ¸ d waiver :BC ¸ 4 F 3BC (1.24) ln » ! ¼ 3BC = V 0 ¸ Y ! 1 ln » , ¼ 3BC ¸ Y ! 6 » ln » , ¼ 3BC g 3 ¼ ¸ V 2 g 3BC ¸ V 3 ln » % 3BC ¼ ¸ d 3 ¸ d BC ¸ d F % 0 ŒC ¸ d BMW ;BC ¸ d waiver :BC ¸ 4 ! 3BC (1.25) where / aremarketlevelsimulatedEITCinstrumentsfromthe1990Census, g 3BC istheownEITC ATRsimulatedfromthe1990Census, ln » % 3BC ¼ islogcellpopulation, g 3 areindicatorvariablesfor marriage,parental,andeducationstatus, d 3 aredemographicgroup˝xede˙ects(FEs), d BC arestate- yearFEs, d F % 0 ŒC areFEsforinitial(1989)wagepercentilesinteractedwithyearindicators, d BMW ;BC areFEsforpercentofworkersin1990thatarehavewagesatorbelowtheprevailingstateminimum wageinteractedwithyearindicators,and d waiver 3BC areFEsforstatewelfarewaiversinteractedwith parentalstatusindicators.Theimpliedelasticityforagivenlabormarketis Y ! 3 = Y ! 1 ¸ Y ! 6 ¹ 3 º . ThecontrolsaremeanttoabsorbanydemandorsupplyshocksotherthantheEITCpolicy changesthatmaya˙ectlaborsupply.ThedemographicgroupFEs, d 3 ,controlforanytime invariantcorrelationbetweenwagesandlaborsupplythatisspeci˝ctoademographicgroup;e.g., demographicleveltastesforworking.Thestate-yearFEs, d BC ,controlforanystate-yearlevel correlationsacrossdemographicgroups;e.g.,astatepolicychangethata˙ectthecostofworking forallworkers.TheinitialwagepercentileFEs, d F % 0 ŒC ,controlforanycorrelationsatspeci˝ctoa market'swagesegmentbeforetheEITCexpansions;e.g.,mean-reversioninwagesorskillbiased technologicalchange.Thebinding-minimum-wageFEs, d BMW ;BC ,controlforthedegreetowhich supplyresponsesarelimitedbybindingminimumwages 39 ,Finally,thewaiverFEs, d waiver 3BC ,control forcorrelationsthatareduetostatewelfarechangespriortothePersonalResponsibilityandWork OpportunityReconciliationActof1996(PRWORA),providedbyKleven(2019). Iidentifythesubstitutionelasticitybyusingusingvariation between skilllevelsacrossstate- years.IuserelativeEITCsupplyshocksacrossskillsastheidentifyingvariation,andconditionon 39 Asdiscussedearlier,abinding-minimum-wagelimitsthedegreeofpriceresponsivenesswhich inturnlimitsthechangesinmarketquantitiesunderlyingthegeneralequilibriumforces. 25 marketspillovers.Iestimateasinglesubstitutionelasticityforallskillgroupsusingthefollowing equation: ž ln » , ¼ 4BC = W 0 ¸ W 1 ~ g 4BC ¸ W 2 ~ / 4BC ¸ W 3 š ln » % ¼ 4BC ¸ d 4C ¸ d BC ¸ d F % 0 ŒC ¸ D F 4BC (1.26) š ln » ! ¼ 4BC = U 0 ¸ d ž ln » , ¼ 4BC ¸ U 2 ~ / 4BC ¸ U 3 š ln » % ¼ 4BC ¸ d 4C ¸ d BC ¸ d F % 0 ŒC ¸ D ! 4BC Œ (1.27) where ~ G 4BC = G 4BC G 0 BC ,thelogdi˙erence.Iusecontrolsanalogoustothesupplymodelbutwith interpretationbasedonrelativequantitiesandwages. 40 ImakeoneimportantchangeinFEs:the marketlevelFE d 4C poolsmarriedandunmarriedmarkets(i.e.,onlyinteractsageandeducation) andisadditionallyinteractedwithyeartoabsorbskill-speci˝cshockstolabordemand. 41 1.5.5ElasticityEstimates Table1.2displaystheestimatedelasticities. 42 Theresultsshowthatlaborsupplyresponsiveness decreaseswitheducation,thathavingchildrenmakesonelessresponsivetowages,andthatmarried womenaremoreresponsivethanunmarriedwomen. Myestimateforthelaborsupplyelasticityforunmarriedmotherswithloweducationattainment isquitesimilartootherestimates.Iestimatethevalue 0 Ł 82 whileRothstein(2008)estimatesa valueof 0 Ł 75 andMeyerandRosenbaum(2001)estimate 0 Ł 83 forparticipationforworkinan 40 IdonotusestateWelfareWaiversinthisspeci˝cationbecauseatthemarketleveltheyare perfectlycolinearwiththestate-yearFEs.Idonotusebinding-minimum-wageFEs,butunreported robustnesstestsshownomeaningfulchangeinelasticityestimates. 41 Eachchangeisof˝rstorderimportancefortheestimatedelasticity.Interactingskillwith yearisjusti˝edbythetheoreticalrelationship: ln » ! C š ! C ¼ = d ln » F C š F C ¼ ln » \ C š \ C ¼ .The decisionnottoincludemarriagestatusintheFEisofnecessityasitsinclusionabsorbstoomuch variationintheinstrumentsandcausesthecovariancematrixtobenearlysingular.SeeAppendix A.4foradditionalempiricalspeci˝cationsthatdisplaytheissue. 42 InAppendixA.4,Ipresentadditionalspeci˝cationresults,includingalternativedependent variables. 26 averageweek. 43 I˝ndthatunmarriedwomenwithoutchildrenandlessthanahighschooldegree haveanelasticityof 1 Ł 16 ,andIcanrejectthatthelaborsupplyelasticitiesforunmarriedwomen withandwithoutchildrenareequal.Thiscanimplyaviolationoftrendswhenusing di˙erence-in-di˙erencemethodsbecauseworkerswillresponddi˙erentlytolabormarkete˙ects ongrosswages. Myestimatesformarriedwomenwithloweducationarehigherthanpreviousestimates.I estimatethevalue 0 Ł 89 whileEissaandHoynes(2004)estimate 0 Ł 27 forsimilarlyeducatedmarried women. 44 BargainandPeichl(2016)surveylaborsupplyelasticitiesacrosscountriesandshow estimatesformarriedwomenrangefromalmostperfectlyinelasticto 1 Ł 50 fortheUnitedStates. Table1.2:LaborSupplyElasticityEstimatesbyLaborGroups: Y ! 3 HoursperWorker w/oChildrenw/Children UnmarriedMarriedUnmarriedMarried LessHS1.161.360.820.89 (0.07)(0.07)(0.08)(0.08) HS0.851.050.510.58 (0.06)(0.05)(0.06)(0.06) SomeCollege0.821.020.480.55 (0.05)(0.05)(0.05)(0.05) BAPlus0.530.730.190.26 (0.05)(0.04)(0.6)(0.05) ObsARFKPrkWaldFMOPE˙ective-F 47,33939.8439.7616.68 AlldatafromORG86-00,1990Census;EITCATRscalculatedusingTAXSIM.StandardErrorsclusteredby (144)demographicgroupings.Weightedbynumberofobservationsineachlabormarket.Modelcontrols: logcellpopulation,FEsfordemographics,State-Year,Initial-Wage-Pct-Year,andWelfareReforms.KPrk WaldFisclusterrobustCragg-Donaldstat;ARisclusterrobustFstatofIVsonstructuralequationresiduals. MOPE˙ective-Fisanalternativeweak-IVF-statistic,calculatedusingalinearfunctionofwages(Oleaand P˛ueger,2013;P˛ueger,2015) 43 Additionally,Dickertetal.(1995)calibratealaborsupplyestimateof 0 Ł 85 andthedi˙erence-in- di˙erencesresultfromEissaandLiebman(1996)impliesanelasticityof 1 Ł 16 ,whichcoincidentally ismyestimateforunmarriedwomenwithloweducationbutnochildren. 44 Onereasonforthedi˙erencecouldbethatEissaandHoynes(2004)estimateajointlabor supplydecisionattheindividuallevelwhileIholdconstantthemarriedpartner'slaborsupplyand treatthisannon-laborincomeforthewife.AnotherreasoncouldbethatEissaandHoynes(2004) usealongertimeseriesofpolicyvariation,whilemyvariationlinkedtothe1993OBRAexpansion only. 27 Table1.3presentsestimatesofthelaborsubstitutionelasticitybetweenlabormarketsforthe tworelativelaborsupplymeasures.Column(1)isjustidenti˝edusingthe`relative'EITCATRand column(2)isoveridenti˝edusingthe`relative'EITCATR,changeinEITCamount,andsharein withEITC.ForeachestimateIreporttheclusterrobuststandarderrorinparentheses.Additionally, IreporttheWeakIVRobustcon˝denceintervalbasedonAndrews(2018).Forbothspeci˝cations, Icanrejectthatthesubstitutionelasticityisinelastic,whichisinlinewiththeimmigrationliterature estimatesaround 1 Ł 4 (KatzandMurphy,1992;GoldinandKatz,2009;Borjasetal.,2012).A moreinelasticestimateof d willtendtoimplylargermagnitudeincidencee˙ectssince d isinthe denominatorofequations1.15and1.18. Table1.3:LaborSubstitutionElasticityEstimatesAcrossLaborMarkets HoursperWorker (1)(2) d -1.81-1.57 WaldSE(0.30)(0.45) WIVRCI[-2.43,-1.29][-3.11,-1.38] KPrkWaldF67.2813.77 Anderson-RubinF39.475.68 MOPE˙ective-F110.0815.74 #IVs13 Obs19,50119,501 AlldatafromORG86-00,1990Census;EITCATRscalculatedusingTAXSIM.Column(1) isjustidenti˝edusingrelativeEITCATRs;columns(2)usesadditionalIVs.Weightedby geometricmeanoflabormarketobservationpairs.StandardErrorsclusteredby(63)labormarket groupings.WeakIVRobustCIsbasedusingAR(1)orLCtest(2,3)(Andrews,2018;Sun,2018). Modelcontrols:logrelativecellpopulation,FEsforEdu-Age-Year,State-Year,andInitial-Wage- Quintile-Year.KPrkWaldFisclusterrobustCragg-Donaldstat;ARisclusterrobustFstatof IVsonstructuralequationresiduals.MOPE˙ective-Fisanalternativeweak-IVF-statistic(Olea andP˛ueger,2013;P˛ueger,2015). 1.6EmpiricalPolicyEvaluationMethodology Inthissection,IoutlinehowIcombinetheincidencemodel,estimatedelasticities,anddata toderivethepolicyevaluationresults.Ipresentthreetypesofresults:modelimpliedgrosswage changes,laborchanges,andperdollare˙ects(multipliers).Thewageandlaborchangesarebased 28 onestimateselasticitiesandtax/subsidychanges.Theperdollare˙ectscloselyfollowRothstein (2010)butincorporatespilloversandupdateformulastoallowforchangesinwelfareprogram usageandtaxpaymentsgivenearningschanges. 1.6.1Data IusetheAnnualSocialandEconomicsamplefromtheMarchCPSasthissamplecontains employmentandincomeinformationinthepreviouscalendaryearthatisnecessarytocalculate FederalaveragetaxratesandEITCspeci˝cATRs(Floodetal.,2018).Speci˝cally,Iusethe1994 ASECforthe1993OBRAexpansionandthe2009ASECforthe2009ARRAexpansion.This sampledeliversbaselinelaborandwagelevels,unearnedincomelevels,costshares(laborshare bydemographicgroup),andaveragetaxrates(FederalandEITC).Iusethesamede˝nitionof skillsanddemographicsasintheempiricalsection.However,forthepolicyevaluations,Ino longerdistinguishbetweenstatesandonlyuseFederalEITCvariationduetotheASECbeing about1/10thesamplesizeastheORGsamplesintheempiricalsection.WhiletheASECsample asksaboutwelfareprogramusage,IcombinethissamplewiththeoutputoftheUrbanInstitute's TransferIncomeModel3(UrbanInstitute,2020)tocomplementthereportedamount. 45 The TRIM3simulateshouseholdandfamilyleveltransferprogramamountsthatisanalogoustothe NBER'sTAXSIMmodelfortaxratesandcredits.Formoredetailsaboutthesample,seeAppendix A.2.2. 1.6.2ModelWageandLaborChanges Tocalculatemodelimpliedwageandlaborchanges,Icombinethedatadescribedaboveandthe elasticitiesfromtheSection1.5results.Icalculateandreportthemodelimpliedwagespercent 45 Ateverypointintheearningsdistribution,I˝ndselfreportedamountsarelessthanfromthe TRIMmodel(Meyeretal.,2015;MeyerandMittag,2019).FortheEmpirical1993Incidence results,Itakethesimpleaverageofthetwomeasuresforwelfareusage;usingtheselfreported amountismoreconservativewhiletheTRIMimplieslargere˙ects.FortheEITCvsWelfare ReformcounterfactualsIusetheTRIM3modelexclusivelysinceIamalteringtheprogram's parametersdirectly. 29 changes, ^ F 4 ,usingthegeneralincidenceformulainequation1.18.Icalculatethemodelimplied laborpercentchangesas: ^ ! 4Œ2 = Y 4Œ2 ^ F 4 ^ g 4Œ2 .Ithenreportthepercentagepointchangesin laborforceparticipationas d ! 4Œ2 = ^ ! 4Œ2 ! 4Œ2 . 1.6.3PerDollarE˙ects Icalculateperdollare˙ectsbysummingthechangesintotalincomefortheeconomydividedby thechangeinEITCexpenditure.Byde˝ninggrossearningsas / ˝ = F ! andnetearningsas / # = ¹ 1 g º / ˝ ,IcanlookatsourcesofchangeintotalincomefromtheEITCreformsbytotally di˙erentiatingtheincomemeasures.Thetotalchangeingrossearningsis d / ˝ = F d ! ¸ d F ! ¸ d F d ! andthetotalchangeinnetearningsis d / # = ¹ 1 g º d / ˝ d g ¹ / ˝ ¸ d / ˝ º . Ireportthechangeingrossearningsduetolaborchanges( F d ! ),thechangeduetowage changes( d F ! ),thetotalgrossearningschange( d / ˝ ),andthetotalnetearningschange( d / # ).I additionallyincludewhatRothstein(2010)referstoasthechangeinnet-transfers( d / ˝ ¸ d g/ ˝ ) andthenet-earnings( d / ˝ ¸ d g/ ˝ ),whichholdallothertaxesandtransfersconstantratherthan allowingthemtoadjustgiventhegrossearningschanges.Finally,thetablereportsthe expost `˝scalexternality'thatmeasuresthepolicyreform'se˙ectonthegovernmentbudgetconstraint incorporatingextensivelaborsupplye˙ects, dFE = gF d ! (Hendren,2016a;Kleven,2018). 46 , 47 Toputtheseinperdollarterms,IdividethemeasuresbythetotalnewEITCexpenditure. 1.6.4Caveats TherearetwocaveatstotheresultsIwishtomakesalient.First,Iholdworkers'marketdesignation ˝xed,whichcouldbeinterpretedasashort-runassumption.Thatis,whileIallowforwages(`skill 46 Icalculatetheextensivemarginchangeinwelfareusage, ,as d = ¹ j ! = 0 º d Pr ¹ ! = 1 º 1 Pr ¹ ! = 1 º ¸ j ! = 1 Œ Phase-In d Pr ¹ ! = 1 º Pr ¹ ! = 1 º ,whichassumesthatlaborforceentrants,originallyreceivingmaximal demographicaveragewelfarebene˝t,enterintotheEITCPhase-InearningsregionanduseWelfare programsatthepre-reformdemographicaveragelevelforthePhase-Inregionearnings. 47 Assumingautilitariansocialwelfarefunctionwithaunitmarginalvalueofcostofgovernment revenue,onecaninterpretthisasConsumerWelfaremeasure.SeeSectionA.1.2.2foraderivation ofthisresult 30 prices')toadjust,Idonotallowworkerstorespondtothepriceadjustmentotherthanthrough stayingorleavingthelabormarket.Thisignoreshumancapitalinvestmentresponses,suchas througheducation(Max˝eld,2015;Bastian,forthcoming),health(DahlandLochner,2012),and marriageandfertility(Dickert-ConlinandHouser,2002).However,incorporatingtheseresponses isoutsidethescopeofthispaper. 48 Second,mymodelignorespotentialfrictionsinthewage-laboradjustmentprocess.Theclearest exampleofafrictionistheminimumwage.Recallthetwotypemodelaspresentedearlier,where group issubsidized.Theincidencemodelsupposesthatasthelaborsupplyfor increases,the grosswagefor fallsthatthenshiftslabordemandforthe marketoutward.Supposethat isthe low-wagegroupwithandthatthereisabindingminimumwage.If˝rmscannotabsorbadditional workersatthebindingwage,thenunemploymentrisesratherthanemploymentandsothereisno increaseinlabordemandforthe market. Whilethemodelissilentaboutthis,Imaketwopointsabouthowtheresultsincorporate thispotentialfriction.First,theelasticityestimatesareultimatelylocalaveragetreatmente˙ects (LATEs)forthee˙ectofthe1993EITCexpansiononwages.Thus,anymarketfrictionsthatexisted withtheEITCshouldbecapturedintheelasticityestimates.Forexample,ifabindingminimum wagepreventsworkersfromresponding,thenIwouldestimateperfectlyinelasticlaborsupple shownabovethisisnotthecase.BecauseIamultimatelyinterestedinthee˙ectsof thisprogram,theLATEsexactlyprovidethevariationIwishtouseinestimatingprograme˙ects. Next,unlikeintheelasticityestimation,theincidenceresultspoolworkersnationallyratherthanuse statespeci˝cmarketde˝nitions.Thus,whileimperfect,ifnationallymarketfrictions`wash-out', thentheresultscanbetrusted.Exactlydealingwiththisissueisbeyondthescopeofthepaper,and Iamcurrentlyunawareofanystudyempiricallydealingwiththisissue. 49 48 InAppendixA.1,Ipresentatwo-skillmodelthatallowsforhigh-skillworkerstoswitchtothe lower-skillmarket,similartoSaez(2002),andshowhowthisaugmentstotheincidenceequation. 49 LeeandSaez(2012)theoreticallyconsideranoptimalEITCwithaminimumwage,butdonot empiricallytestanyresults. 31 1.7Incidenceof1993EITCExpansion Inthissection,Iusetheestimatedelasticitiesandtheempiricalaveragetaxchangestocalculate thegeneralequilibriumincidenceofthe1993EITCexpansion.Iusedatafromthe1994Annual SocialandEconomicSupplement(ASEC)oftheCPSthatincludeslabormarketinformationfor taxyear1993(Floodetal.,2018).TheASECincludeslaborandnon-laborincomeinformationthat allowsmetocalculatetaxparametersnecessaryforestimatingthee˙ectofthe1993expansion.In AppendixA.2,Idescribethevariableconstructionandpresentsummarystatisticsfortheempirical incidencesample.Here,Ifocusonaggregatee˙ects,butinAppendixA.5Idisplayindividuallevel e˙ectsalongwithalternativeelasticityspeci˝cations. 1.7.11993IncidenceResults InTable1.4,Ipresentmyestimatesofthegrosswageincidencee˙ectsofthe1993OBRAEITC expansion.ThetabledisplaysownEITCATRchange,PEIncidence(directe˙ect),GEIncidence (direct+spillover),andtherelativemagnitude(`Size')ofthespilloveranddirecte˙ects.Note, theincidencee˙ectsare not normalizedbya 1% taxchangesincetheincidencee˙ectsdependon multipletaxchangesacrossskillgroups.Unmarriedwomenwithoutahighschooldegree,which hadthelargesttaxdecrease,seethelargestgrosswagechanges.Inaggregate,spilloversrepresent between11-18%ofthetotalgrosswagee˙ectsforunmarriedwomenand56-60%formarried women. Table1.5translatesthenetwagechangesintolaborsupplye˙ectsusingtheestimatedlaborsup- plyelasticities.Asexpected,unmarriedwomenwithchildrenandlowlevelsofeducationincrease theirlaborsupply,butothergroupshavemarginallaborsupplychanges.Figure1.6visuallyshows themodelimpliedGEchangeinlaborforceparticipationbydemographicgroupandcomparesit tothreealternativeempiricalstrategies,Dickertetal.(1995);MeyerandRosenbaum(2001),and asimpledi˙erenceindi˙erencemodel,describedinAppendixA.4.1. 50 This˝guresupportsthe 50 TheseestimatesareselectedfromHotzandScholz(2003)whodocumentseveralempirical estimatesofEITCexpansionsfrom1986to2002. 32 Table1.4:EmpiricalIncidenceofthe1993EITCExpansionon1993GrossWages Unmarried NoChildren Unmarried w/Children ¹ % º d g PEGESize d g PEGESize LessHS -1.47-0.41-0.397.20 -2.98-0.95-0.934.30 HS -1.16-0.28-0.2510.20 -1.73-0.41-0.387.20 SomeCollege -0.71-0.15-0.1219.30 -1.11-0.24-0.2112.30 BA+ -0.25-0.04-0.0147.30 -0.29-0.04-0.0144.00 Total -0.94-0.23-0.2118.70 -1.70-0.45-0.4311.70 Married NoChildren Married w/Children ¹ % º d g PEGESize d g PEGESize LessHS -0.42-0.16-0.1319.40 -0.04-0.020.0134.10 HS -0.05-0.020.0053.10 0.050.010.0466.50 SomeCollege 0.050.010.0463.50 0.120.030.0650.20 BA+ 0.060.010.0479.80 0.080.010.0474.30 Total -0.06-0.030.0056.50 0.060.010.0459.60 Alldatafrom1994MarchCPS,WomenfromTaxUnits,andTRIM3model.Note:GE=PE+ Spillover;Size= abs (Spillover)/( abs (PE)+ abs (Spillover)).Valuesareaveragepercentchanges. LaborsupplyelasticitiesfromTable1.2andcolumn1inTable1.3. claimbyKleven(2018)thatpriorEITCelasticityestimatesmayhavebeencontaminatedbycon- currentfactorsandbiasedup.UsingmysimulatedIVandmodelbasedestimate,I˝ndattenuated (butclearlypositive,non-zero)laborsupplye˙ectsthatarebelowallotherestimates. Table1.5:EmpiricalIncidenceofthe1994EITCExpansiononLaborSupply Total Unmarried NoChildren Unmarried w/Children Married NoChildren Married w/Children d ! PEGE PEGE PEGE PEGE PEGE LessHS 0.310.33 -0.010.01 2.112.12 0.040.06 0.060.07 HS 0.170.18 0.060.07 1.371.38 0.030.05 -0.02-0.01 SomeCollege 0.100.12 -0.010.01 1.111.12 0.020.04 -0.06-0.05 BA+ 0.010.02 0.040.06 0.160.17 -0.010.01 -0.02-0.01 Total 0.150.16 0.020.04 1.351.36 0.020.04 -0.02-0.01 Note: % ! 4Œ: = Y ! 4 % F 4 d g 4Œ: .Alldatafrom1994MarchCPS,WomenfromTaxUnits, andTRIM3model.Valuesareaveragepercentagepointchanges.Laborsupplyelasticitiesfrom Table1.2andcolumn1inTable1.3. 33 Figure1.6:ModelImpliedChangeinLFPbyDemographicGroup ThisplotstheGEchangeinLFPbymarriage,parental,andeducationgroupfromtheincidence modelaswellastheestimatedchangefromalternativeempiricalstrategies,Dickertetal.(1995); MeyerandRosenbaum(2001),andasimpledi˙erenceindi˙erencemodel,describedinAppendix A.4.1. Table1.6displaystheincidencee˙ectsintermsofaggregateearningschangesperdollarofnew EITCexpendituretomakethee˙ects. 51 The1993EITCexpansione˙ectonearningsisdominated bythelaborsupplye˙ect.Theaggregatechangeingrossearningsincreasesby $0 Ł 14 inpartial equilibriumand $0 Ł 24 accountingforspillovere˙ects,whichisa 71% increase.TheaggregateGE e˙ectonnetearningholdingtaxesconstantis $1 Ł 24 butis $0 Ł 55 afteraccountingforchangesin taxesandtransfersduetoearningschanges.Note,thisdi˙erenceisalmostentirelyduetolower netearningsformarriedmothers,whoaremorelikelytobehigherincomeworkerswithpositive taxrates,ratherthanunmarriedwomenwhoarelowerincomeworkers. The˝scalexternalityisa $0 Ł 09 increaseperdollarofnewEITCspending,implyingasmallnet 51 InAppendixA.5.1,Ipresentindividuallevele˙ectsofthe1993expansion. 34 Table1.6:EmpiricalIncidenceResults:ChangePerDollarofNewExpenditure Total Unmarried NoChildren Unmarried w/Children Married NoChildren Married w/Children Dollars PEGE PEGE PEGE PEGE PEGE Labor 0.320.36 0.050.06 0.290.29 0.010.03 -0.03-0.02 Wages -0.18-0.12 -0.12-0.10 -0.07-0.07 -0.000.01 0.010.03 GrossEarnings 0.140.24 -0.07-0.04 0.220.23 0.010.04 -0.020.02 NetTransfer,FixedTaxes 0.820.88 -0.06-0.05 0.320.33 0.020.03 0.540.56 NetEarn,FixedTaxes 1.141.24 -0.020.1 0.610.62 0.030.06 0.510.55 NetEarnings 0.450.55 -0.010.02 0.580.59 0.010.03 -0.12-0.09 FiscalExternality 0.090.09 0.010.01 0.080.08 0.000.00 -0.00-0.00 Unitsintablearechangesindollarsofearningssummedacrossdemographicgroups.Note: / ˝ = F !Œ/ # = ¹ 1 g º F ! .Alldatafrom1994MarchCPS,WomenfromTaxUnits,and TRIM3model.LaborelasticitiesfromTable1.2andcolumn1inTable1.3. increaseingovernmentspendingdespitethelargeEITCexpansion!Thisresultcomplementsthe empirical˝ndingbyBastianandMichelmore(2018)thattheEITC`paysforitself'asunmarried motherswhodonotworktendtoreceivethemaximalwelfarebene˝tswhichislargerthanthe maximalEITCcreditamount.Thus,movinganunmarriedmotherfromnon-worktothephase-in regionoftheEITCscheduleresultsinanetpositivepositionforthegovernmentbudget. 52 Acrossdemographicgroupsthereisconsiderableheterogeneity.Grossearningsdeclinefor unmarriedwomenwithoutchildrenbutriseforothergroupsofwomenbecausetheformergroup facesgrosswagelosseswithessentiallynoincreaseintransfers.Netearningsdecreaseonlyfor marriedwomenwithchildrenforthreereasons.Firstandforemost,theOBRAreformimplemented anassettestthat decreased EITCamountsforhigherincometaxunits,whichtendtobemarried workers.Additionally,alargeportionofmarriedworkerswithpositiveEITCalsofacepositivetax ratesduetospousalearnings,sotheEITCis`taxedback.'Finally,sincemanymarriedtax˝lers areinthephase-outregion,increasedgrossearningsduetospilloversdecreasestheEITCamounts evenmore. 52 Hendren(2016a)useslaborsupplyelasticitiesfromtheEITCliteraturetocalculatea˝scal externalityof $0 Ł 09 potentiallyduetoholdingconstantwelfareexpenditurechanges.IfIhold welfareprogramexpenditureconstant,thenI˝nda˝scalexternalityof 0 Ł 03 thatisnownegative butstillsmaller,whichlikelyduetothesmallerlaborsupplyelasticitiesthatIestimate. 35 Interestingly,althoughwagesfallforunmarriedwomenwithoutchildren,I˝ndthat inGE net earningsactuallyriseforthisgroup.Whilethechangeisquitesmall,giventhatthePEnetearnings e˙ectisnegative,thepositiveGEforcescounteracttheincidencee˙ectswhichwasoneofthe principalconcernsofEITCexpansions. InTable1.7,Ishowtheincidencea˙ectsbyrealwagequintilespoolingacrossdemographic groups.Asexpectedthelaborsupplye˙ects,wagedeclines,andtransfersareconcentratedin low-wagegroups.Forthehighestwagegroup,GEspilloverscauseswagestobenet-positive.One interestingresultoftheEITCreformisthatwageinequalityincreases,whichimpliesagreater`skill premium,'butincomeinequalitygoesdownduetothetransfer.Asdiscussedearlier,whilemain modelignores`marketswitcAppendixA.1foramodelthatallowsforsuchchang thechangein`skillprices'maychangehumancapitalinvestmentdecisionsinthemedium/long run. Table1.7:EmpiricalIncidenceResults:ChangePerDollarofNewExpenditure Quintile1 Quintile2 Quintile3 Quintile4 Quintile5 Dollars PEGE PEGE PEGE PEGE PEGE Labor 0.110.11 0.090.10 0.070.07 0.050.06 0.000.01 Wages -0.05-0.05 -0.06-0.05 -0.03-0.02 -0.04-0.03 -0.000.02 GrossEarnings 0.060.07 0.030.06 0.040.05 0.010.03 -0.000.03 NetTransfer,FixedTaxes 0.340.35 0.280.30 0.090.09 0.070.08 0.040.06 NetEarn,FixedTaxes 0.450.46 0.370.40 0.160.17 0.110.14 0.040.07 NetEarnings 0.200.21 0.110.14 0.110.12 0.050.07 -0.020.01 FiscalExternality 0.030.03 0.020.02 0.020.02 0.020.02 0.000.00 MeanWage $5.63 $8.06 $9.72 $11.21 $15.68 Unitsintablearechangesindollarsofearningssummedacrossdemographicgroups.Note: / ˝ = F !Œ/ # = ¹ 1 g º F ! .Alldatafrom1994MarchCPS,WomenfromTaxUnits,and TRIM3model.LaborelasticitiesfromTable1.2andcolumn1inTable1.3. 1.8ComparingEITCandWelfareReforms Inthissection,Iusemyestimatedlabormarketelasticitiestocomparethreehypotheticalpolicy reformsbasedontheOBRAandPRWORAreformsinthemid-1990's.The˝rstisanexogenously 36 funded$100milliondollarexpansionsofthe1992EITC.Thesecondisequalsizedexpansionof thecombined1992ADFCandFoodStampsprograms(whichIrefertoassimply`Welfare'). 53 The thirdexperiment,whichIcalltheNetEITCreform,simultaneouslyexpandstheEITCandcontracts Welfarebene˝tstocreatean exante revenueneutralEITCexpansionwithnodistortionsonhigher wagemarkets. 54 Thisallowsmetoignorethedistortionarye˙ectsof˝nancingtheexpansionas wellasmirroringthetaxandtransfersystempolicyreformsofthe1990s. 1.8.1SimulatingtheTaxReforms Toimplementthesimulation,Icharacterizethetaxsystemwithtransferinclusiveaveragetaxrates, calculatedusingthereportedincomedata,NBERTAXSIM,andtheUrbanInstitute'sTRIM3 welfaresimulator(FeenbergandCoutts,1993;UrbanInstitute,2020). 55 Foreachreform,Isuppose thatthegovernmentwishestoincreasethegenerosityofitstaxandtransfersystemforlowincome taxunitsby$100millionthrougheitheranEITCexpansionorWelfareexpansion,butdoesnot considerbehavioralchangesinresponsetothereforms.ToimplementtheEITCexpansion,Isolve forthenewmaximumcreditamountholding˝xedtheexisting`kinkpoints'suchthatthetotal expenditureequalsthetargetedamount.Toimplementthewelfareexpansion,Iapproximatethe existingwelfaresystemasa˝xedbene˝tandarateatthebene˝tistaxedaway,andthensolvefor thechangeinthebene˝tsuchthattotalnewexpenditureequalsthetargetedamountwhilekeeping thesamerate.TheNetEITCreformimplementstheEITCexpansionaboveandthe negative of thewelfareexpansiontomakethereform ex-ante revenueneutral. 56 Figure1.7visuallyshowsthe reformtransferprograms. 53 ThisreformisroughlythesameasthehypotheticalNegativeIncomeTaxreformRothstein (2010)considers.InAppendixA.5,Ireplicatehisexperimentsand˝ndqualitativelysimilarresults. 54 Becausetheexperimentisa`marginalreform,'takingthenegativeofthevaluesreportedfor theNetEITCreformwouldbethesameasconductingaNetWelfareexpansion. 55 Idonotconsideranintensivehoursmargin,soIdonotconsidermarginaltaxrates.This accordswiththepreferredspeci˝cationinRothstein(2010),andmostempiricalliteratureonthe EITC. 56 Thesereformsroughlymirrortheactualreformsinthe1990'sbutatasmallerscale. 37 Figure1.7:TrueandCounterfactual1992TransferPrograms PlotsEITCandCompositeWelfareforsinglewomenwithonechildin1992usingdatafromCPS ASEC1993,NBERTAXSIM,andUrbanInstitute'sTRIM3.ThecounterfactualEITCexpansion raisesthemaxcreditholdingthe˝rsttwokinkpoints˝xed;thecounterfactualWelfareexpansion increasesthebasetransferamountholdingthee˙ectivemarginaltaxrateconstant. 1.8.2SimulationResults Table1.8and1.9displaytheincidenceresultsfortheEITC,Welfare,andNetEITCsimulated taxreformsattheaggregateanddemographiclevel,respectively,andareinterpretedthesameas Table1.6.Forbothtables,columns(1-3)showthepartialequilibriumresultsandcolumns(4-6) incorporatespillovers.Themaintakeawayisthatthe`bad'aspectsoftheEITCexpansions(gross wagedecreases)andthe`good'aspectsofWelfareexpansions(grosswageincreasesandpositive welfare)areattenuatedbytheGEforces. FortheEITC,thedollarchangeduetowagesis $0 Ł 12 inPEbutonly $0 Ł 04 inGE,but fortheWelfarereformthe $0 Ł 06 wagegrowthinPEbecomes $0 Ł 02 inGE.FortheNetEITC reform,thewagedeclinegoesfrom $0 Ł 18 to $0 Ł 06 ,atwo-thirdsdecreaseduetospillover e˙ects.AggregategrossearningsincreasefortheEITCandNetEITCprogramsbutdecreasefor theWelfareexpansion.ThisisbecausetheWelfareexpansionincentivizesworkerstoexitthelabor force,andthissourceofearningslossdominatesthescarcityinducedwageincreases. 38 Thedi˙erencebetweenNetEarningswithFixedTaxes,whichRothstein(2010)reports,and NetEarningsisthatthelattermeasureaccountsforthefactthattheincreaseingrosswageswill betaxed.Ifoneholdstaxes˝xed,thenthewholeintendedtransferisaddedtogrossearnings, whichoverestimatesthenetearningsgain.Thenetearningsmeasurereportedallowsforadditional earningstobetaxed(holdingtheATRconstant),sothesomeoftheintendedtransfergoestotaxes aswellasincidencee˙ects.FortheWelfareexpansion,netearningswith˝xedtaxesis $0 Ł 89 in GEbutallowingfortaxchangesnetearningsactuallydecreaseby $0 Ł 41 !FortheEITCreforms, bothmeasuresofnetearningsarepositive. Asnotedearlier,thewelfaremeasureisthe expost ˝scalexternalityofthereform.TheEITC andnet-EITCreformshavedecreaseof $0 Ł 08 and $0 Ł 09 ,respectively,buttheWelfareexpansion essentiallyhasnoexternality.ThismeanstheEITCexpansionsimposeanadditionalcosttothe governmenttobalancethebudgetbuttheWelfarereformdoesnot.However,thisshouldbe consideredalong-sidethegrossandnetearningse˙ects.TheEITCexpansionincreasesaggregate grossearnings(analogoustoGDP)andnetearningsbyshiftingsomeeconomicresourcestolower incomeworkers. Theimplicationofzero˝scalexternalityoftheWelfarereformisworthdelvinginto.Letthere bethreegroups:highincome( H )whoalwayswork,stable-laborlowincome( S )whoalwayswork, andmarginal-laborlowincome( M )whowouldworklessifable,where{ M,S }areinsamelabor market.Conceptually,thegovernmentistransferringincomefrom H to M ,whichallows M toexit market.Equilibriumforcesincreasethewagesof S (duetoinducedscarcity)andlowerwagesof H (duetonegativespillovers).Thisimpliesthat H paylesstaxesand S paymoretaxes,andon balancethesecanceloutthepaymentto M .ThepaymentoftheWelfarereformcomesfromother lowincomeworkersratherthanhighincomeworkers! Table1.9decomposestheaggregatee˙ectsbydemographicgroupsforeachreform.TheEITC reformGEnetearningschangeforunmarriedwomenwithchildrenis $0 Ł 79 and 0 Ł 04 formarried womenwithchildren,whilenetearningsfallformarriedandunmarriedwomenwithoutchildren by $0 Ł 10 ,sincethelattergroupsreceivealmostnosubsidybutareexposedtowagedecreases. 39 Table1.8:IncidenceResults: AggregateE˙ects:AllWomen GE Dollars EITC Welfare Net EITC EITC Welfare Net EITC (1)(2)(3) (4)(5)(6) Intended 1.000.650.35 1.000.650.35 Labor 0.22-0.100.32 0.27-0.130.40 Wages -0.120.06-0.18 -0.040.02-0.06 GrossEarnings 0.10-0.050.14 0.23-0.110.34 NetTransfer,FixedTaxes 0.881.06-0.18 0.961.02-0.6 NetEarn,FixedTaxes 1.100.950.14 1.230.890.34 NetEarnings 0.50-0.360.21 0.63-0.410.39 FiscalExternality -0.090.01-0.09 -0.080.00-0.09 Unitsintablearechangesindollarsofearningssummedacrossdemographicgroups.Note: / ˝ = F !Œ/ # = ¹ 1 g º F ! .Alldatafrom1993MarchCPS,WomenfromTaxUnits.Laborsupply elasticitiesfromModel1inTable1.2andcolumn1inTable1.3. TheWelfarereformGEnetearningschangeisnegativeforwomenwithchildrenande˙ectively zeroforwomenwithchildren. Theaggregate˝scalexternalitychangesarealmostentirelyduetochangesfromunmarried womenwithchildren.BecausetheEITCandWelfarereformsprimarilya˙ectunmarriedmothers' laborsupply,thisgroupdrivesthe˝scalexternality. Finally,Table1.10decomposestheincidencee˙ectsbywagequintile,wherethemeanwage foreachis{ 5 Ł 85 Œ $7 Ł 74 Œ $9 Ł 29 Œ $10 Ł 91 Œ $15 Ł 04 g ,respectively.Thewagegroupspoolthedi˙erent demographicgroupstoshowthereforme˙ectsondi˙erent`skillgroups'inaggregate,which maya˙ecthumancapitaldecisions.Asdiscussedearlier,theEITCreformsdecreasewagesfor low-wagegroupsbutincreaseeverygroup'slaborsupplyandnetearnings.TheWelfarereforms ontheotherhanddecreasenetearningsforallwagegroups,evenforthosewhohavesmallwage increases.TheWelfarereformsraisewagesthroughcreatingarti˝cialscarcity(throughreduced laborsupplyincentives)butthelossresourcestotheeconomylowerthetotalpossibleincometo bedistributed. 40 Table1.9:IncidenceResults: AggregateE˙ects:SubgroupsofWomen GE Dollars EITC Welfare Net EITC EITC Welfare Net EITC (1)(2)(3) (4)(5)(6) UnmarriedMothers NetEarn,FixedTaxes 0.720.660.07 0.740.650.09 NetEarnings 0.78-0.260.38 0.79-0.270.40 FiscalExternality -0.070.01-0.08 -0.080.01-0.08 UnmarriedWomen NetEarn,FixedTaxes -0.150.03-0.19 -0.110.01-0.13 NetEarnings -0.140.03-0.17 -0.100.01-0.12 FiscalExternality -0.010.00-0.01 -0.010.00-0.01 MarriedMothers NetEarn,FixedTaxes 0.520.250.27 0.560.230.33 NetEarnings -0.14-0.140.01 -0.10-0.150.07 FiscalExternality 0.000.000.00 0.000.000.00 MarriedWomen NetEarn,FixedTaxes 0.010.01-0.01 0.050.000.05 NetEarnings 0.010.01-0.01 0.040.000.05 FiscalExternality 0.000.000.00 0.000.000.00 Unitsintablearechangesindollarsofearningssummedacrossdemographicgroups.Note: / ˝ = F !Œ/ # = ¹ 1 g º F ! .Alldatafrom1993MarchCPS,WomenfromTaxUnits.Laborsupply elasticitiesfromModel1inTable1.2andcolumn1inTable1.3. 1.9StructuralModelParameterization Thepreviousresultswereallderivedusingonlytheassumptionofquasi-linearityoftheutility function.Inthissection,Iaddadistributionalassumptionabouttheworkerspeci˝cdisutility oflaborthatallowsmetoparameterizedemographicspeci˝claborsupplyfunctionstocalculate generalequilibriumresultsfornon-marginalandout-of-samplereforms.Speci˝cally,Iuselabor participationprobabilitiesandmyelasticityestimatestoparameterizeastandard`logit'binary choicemodel. 41 Table1.10:IncidenceResults: AggregateE˙ects:WageQuintiles GE Dollars EITC Welfare Net EITC EITC Welfare Net EITC (1)(2)(3) (4)(5)(6) Quintile1 Wages -0.020.00-0.03 -0.020.00-0.02 GrossEarnings 0.03-0.010.03 0.04-0.010.05 NetEarnings 0.14-0.030.07 0.15-0.030.09 FiscalExternality -0.040.00-0.05 -0.040.00-0.05 Quintile2 Wages -0.040.01-0.05 -0.030.010.02 GrossEarnings 0.04-0.010.05 0.06-0.020.05 NetEarnings 0.19-0.080.08 0.21-0.080.04 FiscalExternality -0.030.00-0.03 -0.030.000.00 Quintile3 Wages -0.030.01-0.04 -0.020.010.02 GrossEarnings 0.01-0.010.02 0.06-0.020.05 NetEarnings 0.10-0.070.03 0.12-0.080.04 FiscalExternality -0.010.00-0.01 -0.010.000.00 Quintile4 Wages -0.020.02-0.03 0.000.010.02 GrossEarnings 0.03-0.020.05 0.07-0.030.05 NetEarnings 0.10-0.110.05 0.13-0.120.04 FiscalExternality -0.000.00-0.00 -0.00-0.000.00 Quintile5 Wages -0.010.01-0.02 0.02-0.000.02 GrossEarnings -0.020.00-0.02 0.03-0.020.05 NetEarnings -0.03-0.08-0.02 0.02-0.100.04 FiscalExternality -0.00-0.00-0.00 0.00-0.000.00 Unitsintablearechangesindollarsofearningssummedacrossdemographicgroups.Note: / ˝ = F !Œ/ # = ¹ 1 g º F ! .Alldatafrom1993MarchCPS,WomenfromTaxUnits.Laborsupply elasticitiesfromModel1inTable1.2andcolumn1inTable1.3.MeanwageforQ1is $5 Ł 85 ,Q2is $7 Ł 74 , Q3is $9 Ł 29 ,Q4 $10 Ł 91 ,andQ5is $15 Ł 04 . 1.9.1StructuralModel Theutilityproblemforworkersisthefollowingdiscretechoice: max ! = f 0 Œ 1 g f D 8 ¹ ) 2 ¹ 0 Œ< 8 º º a 8 ¹ 0 º | {z } ! = 0 ŒD 8 ¹ ) 2 ¹ F 8 Œ< 8 º º a 8 ¹ 1 º | {z } ! = 1 g Œ (1.28) where a 8 istheidiosyncraticdisutilityoflabordrawnfromsomedistribution, ˙ 4Œ2 ¹ a º .Initially,I assumedthat D 8 ¹ G º = G ,butnowsupposethat D 8 ¹ G º = V 4Œ2 G ,where V 4Œ2 canbeinterpretedastype- 42 specifcmarginalutilityofconsumption(orincome).Additionally,suppose a 8 ¹ 0 º a 8 ¹ 1 º = X 4Œ2 ¸ n 8 , where n 8 distributedindependentType1ExtremeValue( ˙ ¹ n º = e e n )and X 4Œ2 isinterpreted asanunobservedutilitycostoflabor(asupply`shifter').Then,demographic-speci˝c(expected) laborsupplyfunctionis: Pr ¹ ! 8 = 1 j F 4 Œ< 4Œ2 Œ) 2 º = e V 4Œ2 ) 2 ¹ F 4 Œ< 4Œ2 º¸ X 4Œ2 e V 4Œ2 ) 2 ¹ 0 Œ< 4Œ2 º ¸ e V 4Œ2 ) 2 ¹ F 4 Œ< 4Œ2 º¸ X 4Œ2 : = c 4Œ2 Ł (1.29) 1.9.2RecoveringStructuralParameters De˝ning v 4Œ2 : = ) 4Œ2 ¹ F 4 Œ< 4Œ2 º ) 4Œ2 ¹ 0 Œ< 4Œ2 º asthenetwage,themodelimpliesthat: GrossWageElasticity: Y ! 4Œ2 = mc 4Œ2 mF 4 F 4 c 4Œ2 = V 4Œ2 m v 4Œ2 mF F 4 ¹ 1 c 4Œ2 º (1.30) NetWageElasticity: [ ! 4Œ2 = mc 4Œ2 m v 4Œ2 v 4Œ2 c 4Œ2 = V 4Œ2 v 4Œ2 ¹ 1 c 4Œ2 º Ł (1.31) Ifthetransferfunctionis ) 4Œ2 ¹ F 4 Œ< 4Œ2 º = ¹ 1 g 4Œ2 º¹ F 4 ! º¸ 1 4Œ2 ¹ 1 ! º¸ C ¹ < º ,sothatthenet wageis ¹ 1 g 4Œ2 º¹ F 4 º ,then m v 4Œ2 mF F 4 = v 4Œ2 sothat Y ! 4Œ2 = [ ! 4Œ2 .Thus,Icanrecoverthemarginal utilityofconsumptionparametersusingthefollowing: Y ! 4Œ2 v 4Œ2 ¹ 1 c 4Œ2 º = V 4Œ2 Ł (1.32) Withanestimateof V 4Œ2 ,IcanthenrecovertheunobservablenetsupplyshiftersusingaBerry (1994)styleinversiontechnique: ln c 4Œ2 ln ¹ 1 c 4Œ2 º V 4Œ2 v 4Œ2 = X 4Œ2 Ł (1.33) Withtheestimatedstructuralutilityparameters f¹ b V 4Œ2 Œ b X 4Œ2 ºg ¹ 4Œ2 º2D ,Icansimulatenon- di˙erentialEITCreforms.Note,Iestimatetheseparametersbasedontheelasticitiesestimates fromthe1990's,sotheunderlyingassumptionoftheseparametersisthat V isa˝xedutility parameterandanychangesovertime(conditionalonthenetwage)occurthroughtheshifter, X . 43 1.10ChildlessWorkerReform AdvocacygroupsencouragepolicymakerstoreformtheEITCschedulesuchthatworkers withoutchildrenaretreatedthesameasworkerswithchildren. 57 Advocatesciteissuesrelatedto horizontalequityonthebasisofskillaswellasliftingmoreworkersoutofpoverty.Anotherreason is,giventhattherearenegativeearningse˙ectsforchildlessworkerswhoareclosesubstitutes, expandingtheEITCfortheseworkerscano˙settheincidencee˙ectsjustlikeforunmarriedwomen withchildren. Toquantifythee˙ectsofthisreform,Iequalizethe1994EITCscheduleforworkerswithout childrenandworkerswithonequalifyingdependent. 58 Thatis,IcreateacounterfactualOBRA expansionwherethecreditforworkerswithoutchildrenwasequalizedratherthansetwithamax of $306 .Mymodelbasedapproachcandescribethelaborsupplyandearningse˙ectsofthisand predictanyadditionaltake-upthatmayoccur. Note,thestructuralmodelresultsbelowandtheincidencemodelresultsabovedonotyield thesamequantitativevaluesfortworeasons.First,theincidenceresultsuseanalyticresultsfor changesinATRs,whilethestructuralresultsnumericallysolveformarketclearingprices.Second, theincidenceresults,basedonmarginalchangesinATRs,holdconstantotherfeaturesofthetax andtransfersystem,whilethestructuralresultsincorporatetaxliabilitychangeswhencalculating laborsupply.Thus,theincidencemodeldescribeshowtheEITCexpansionsaresharedbetween workersandthestructuralmodelshowsthetotale˙ectofequalizingtheEITCschedulesonmarket equilibriumincorporatingspillovers. 57 SeediscussionsinNicholsandRothstein(2016);Marretal.(2016);Maagetal.(2019). NicholsandRothstein(2016)notethatbothformerPresidentObamaandthenformerHouseWays andMeanscommitteechairmanRyanbothadvocatedforincreasingthegenerosityforchildless workers. 58 Myreformislargerthanmanyexistingproposals.Maagetal.(2019)usethe2016American CommunitySurveytoparameterizeanequalizationreformthattriplesthechildlessworkermaxi- mumcreditanddoublesthekink-pointthresholds,butholdgrosswagesandlaborsupplyconstant, whichignoresbehavioralresponsesorincidencee˙ects.PresidentObama'sproposaldoubledthe maximumcreditandextendedthesecondkink-pointbyhalfExecutiveO˚ceofthePresidentand USDepartmentofTreasury(2014). 44 1.10.1ChildlessWorkerReformResults InTables1.11and1.12,Idisplaytheresultsofthepolicyreform.Tomakecomparisonsasclose aspossible,IsolvethemodelusingtheactualEITCscheduleintaxyear1993asabaseline,next solvethemodelusingtheactual1994schedule,andthensolvethemodelusingthecounterfactual 1994schedule.Thisholdsallnon-labor-marketvariablesconstant,suchaslaborsupplyshifters, aggregateproductivityordemandshifts,andcapitalsupplyshifts.Ithencalculatethechangesfor eachexpansionfromthebaseline. Therearetwostrikingelementsfromtheresults.First,equalizingthecreditscheduleswould substantiallyincreaselaborsupplyforunmarriedworkerswithoutchildrenan 4 Ł 8 percentagepoint (ppt)increaseinaggregate.Thisisbecausetheseworkershaveagreaterlaborsupplyelasticitythan workerswithchildrenandtheexpandedcreditsubstantiallyincreasestheirnetincome.Second, equalizationcreatesacountervailinge˙ectonunmarriedmothers'thelaborsupplyfrom 1 Ł 5 to 1 Ł 0 pptsinaggregateand 2 Ł 5 to 1 Ł 4 pptsforthosewithoutahighschooldegree.Thisisduethe samegrosswageincidencee˙ectsfromthemuchlargerlaborsupplyshockthatadvocatescitewhen promotingachildlessworkerexpansion.Grosswagesforunmarriedworkersinitiallydecreaseby about 0 Ł 6 0 Ł 7% undertheactualexpansionbutdecreasebetween 2 Ł 4 3 Ł 6% undertheexpansion regime. 59 Table1.12putsthee˙ectsintermsofdollarsofplannednewexpenditureandshowsthree importantfacts.First,neithertheactualorcounterfactualreformhasmuche˙ectonmarried womenmostlybecausetheseworkershavehouseholdearningsthataretoohightobea˙ectedby thepolicy.Second,thereformshavesimilaraggregatee˙ectsintermsofearningsandwelfare measures.Third,thereformshavesimilaraggregatee˙ectsbecausethelaborsupplye˙ectsofthe policyarealmostexactlyreversedfortheunmarriedwomen.Thosewithoutchildrensupplymore laborbutthosewithchildrenbecomemuchlesslikelytojointhelaborforce. WhileequalizingtheEITCschedulemaybemore`fair'andcertainlywillhelpmanylow 59 ThewagechangesinTable1.11areslightlydi˙erentbetweenunmarriedworkerswithand childrenbecauseworkersdonotperfectlyoverlapindemographic-skillbasedmarkets. 45 Table1.11:EmpiricalIncidenceResults: 1994EITCExpansion+EqualizationofCreditSchedule PercentChangeinWages Unmarried NoChildren Unmarried w/Children Married NoChildren Married w/Children % F ActCftDi˙ ActCftDi˙ ActCftDi˙ ActCftDi˙ LessHS -2.33-7.63-5.44 -2.10-6.21-4.21 -0.10-1.87-1.78 -0.30-0.42-0.13 HS -0.17-2.35-2.19 -0.25-1.79-1.54 0.050.310.26 0.050.330.28 SomeCollege -0.36-3.03-2.69 -0.19-0.98-0.90 0.050.310.26 0.050.330.28 BA+ 0.05-0.09-0.15 0.060.270.21 0.060.360.30 0.060.380.32 Total -0.76-3.55-2.84 -0.65-2.41-1.79 0.030.01-0.02 0.010.250.24 PercentagePointChangeinLaborSupply Unmarried NoChildren Unmarried w/Children Married NoChildren Married w/Children d ! ActCftDi˙ ActCftDi˙ ActCftDi˙ ActCftDi˙ LessHS 1.547.946.17 2.521.38-1.07 -0.061.451.52 0.490.510.02 HS -0.124.985.11 1.461.02-0.42 0.030.190.16 0.020.140.12 SomeCollege 0.405.935.47 1.050.82-0.22 0.040.250.21 0.020.140.12 BA+ 0.020.940.92 0.070.130.06 0.030.200.17 0.010.080.06 Total 0.505.334.76 1.450.96-0.47 0.020.390.37 0.080.170.10 `Act':ActualEITCschedules;`Cft':CounterfactualEITCschedulewhereworkerswithno childrengetsamecreditasworkerswithonechild;`Di˙':Equalizationspeci˝ce˙ectsAlldata from1994MarchCPS,WomenfromTaxUnits.Valuesareaveragepercentchanges,weighted population. incomeworkers,theseresultsimplythatsuchareformdoesnotcomewithoutacost.Policymakers wishingtoreformtheEITCfaceadilemma:thecurrentstructuredisadvantagesworkerswithout childrenbutreformingtheEITCmayharmworkerswithchildren(andthroughsecondarye˙ects theirchildren).Justaspolicymakersshouldconsiderthespillovere˙ectsfromthecurrentEITC structure,theyshouldbesuretounderstandthetrade-o˙sintermsoffamiliesfromastructural reformoftheEITC. 1.11Incidenceofthe2009EITCExpansion Inthissection,Iconsiderthelabormarkete˙ectsofthe2009EITCexpansionthatwaspart oftheAmericanRecoveryandReinvestmentActof2009.Thereformmadethecreditschedule moregenerousforworkerswiththreeormorequalifyingchildrenaswellasformarriedworkers 46 Table1.12:EmpiricalIncidenceResults: 1994EITCExpansion+EqualizationofCreditSchedule ChangePerDollarofNewPlannedExpenditure Total Unmarried NoChildren Unmarried w/Children Married NoChildren Married w/Children Dollars ActCft ActCft ActCft ActCft ActCft Labor 0.620.65 0.110.51 0.420.05 0.030.05 0.050.03 Wages -0.12-0.11 -0.14-0.16 -0.07-0.04 0.040.04 0.050.06 GrossEarnings 0.500.51 -0.030.33 0.350.01 0.070.08 0.110.09 NetTransfer,FixedTaxes 0.880.89 0.120.70 0.640.07 0.040.05 0.080.06 NetEarn,FixedTaxes 1.501.51 0.231.19 1.060.12 0.070.10 0.140.09 NetEarnings 1.371.41 0.231.14 0.970.12 0.050.08 0.110.07 Welfare -0.10-0.09 -0.01-0.06 -0.07-0.01 -0.01-0.01 -0.01-0.01 `Act':ActualEITCschedules;`Cft':CounterfactualEITCschedulewhereworkerswithno childrengetsamecreditasworkerswithonechild.Unitsintablearechangesindollarsofearnings summedacrossdemographicgroups.Note: / ˝ = F !Œ/ # = ¹ 1 g º F ! .Alldatafrom1994 MarchCPS,WomenfromTaxUnits. byextendingthe`maxcredit'portionoftheEITCtoreduce`marriagepenalties'(Nicholsand Rothstein,2016). 60 Thereformwasintendedtoprovidecounter-cyclicalincomesupportfor lowwageworkersratherthanstrengtheninglaborforceattachment. 61 Nevertheless,becausethe expansionisthesecondlargestEITCreformafterthe1993expansion,thereformgaveeconomists anopportunitytorevisittheEITC'slabormarkete˙ects.Inshort,Iribarren(2016)andKleven (2019)˝ndnostatisticallysigni˝cante˙ectfromthisreform. Therearethreepotentialexplanationsforthis.First,therewasnoe˙ect,whichisaconjecture recentlyadvancedbyKleven(2019).Second,therewereprevailingforcesthatdominatedany EITCe˙ectandacleanexperimentisnotpossible.Theexistingpapersrelyontreatmentand controlgroupbasedestimatesthatshouldpurgetheoveralleconomicforcesduringtherecession period,sotheresultsdependonappropriatenessofthesegroupingdecisions.Third,thereform wastoosmalltoseealargelaborsupplye˙ect,evenholdingeconomicconditionsconstant.The 60 Theexpansionsweresettoexpirein2017buthavesincebeenmadepermanent. 61 ItistheoreticallyambiguoushowtheEITCfaresinarecessionsincethelaid-o˙workerwill likelyloseeligibilitywhereasworkerswithreducedhoursmaybecomeeligible.Jones(2017)uses linkedCPS-IRSdatatoshowthatunmarriedmotherswithloweducationhadahigherlikelihood oflosingeligibilityandlowerlikelihoodofgainingeligibilitythroughlostearnings. 47 expansionincreasedthemaximumcreditby $600 ,whichmaynotbeenoughtocreatelargelabor supplychanges,andthetargetedgroupsworkerswith3+children,marriedworkersareasmall proportionoftheEITCclaimers. Myincidenceanalysisallowsmetoprovideabenchmarkestimateofthe2009expansion e˙ects.Ifthelabormarkete˙ectsaresmallevenwhenIamabletoholdallothereconomic conditionsconstant,thenthisimpliesthatstandarddi˙erence-in-di˙erenceevidencemaysimply beunder-poweredtodetectane˙ect.However,ifthee˙ectsoftheexpansionarecomparableto thelarger1993expansion,thentheachangeinlabormarketfundamentalsisnecessarytoexplain theempiricalnull˝ndings.Additionally,theresultsprovideinsightinto why EITCexpansionmay havedi˙erente˙ectsovertime.Iflaborsupplyelasticitiesarefallingorcostsincreasing,then largerandlargerEITCexpansionsarenecessarytoachievethesamelaborsupplye˙ects. 1.11.12009IncidenceResults ComparedtoTable1.4,Table1.13showsthatthetaxratechangeforunmarriedwomenwasless thanathirdofthe1993EITCexpansionbuttheexpansionsweresimilarformarriedwomen.As such,the2009directandspillovere˙ectsaremuchsmallerthanthe1993case;infact,thespillover e˙ectsaree˙ectivelyzero. Table1.14showsthatunmarriedmothers'aggregatelaborsupplyshouldhaveincreasedby 0 Ł 6% whileothergroupsshowessentiallynochange,comparedwith 1 Ł 4% forthe1993expansion. Despitethefactthatthe2009expansionreducedthetwoearners`marriagepenalty,'thereis essentiallynoe˙ectformarriedworkers.Theaggregategeneralequilibriumlaborsupplychange e˙ectisonly 0 Ł 05% . Finally,inTable1.15,Ishowtheperdollare˙ectofthe2009expansion.Again,thedirectand spillovere˙ectsaremuchsmallerthanthe1993expansion,withessentiallynoscopeforspillovers. Theaggregategrossandnetearningschangesarebothlessthanhalfofthe1993perdollare˙ects. Thisimpliesnearzero˝scalexternalitybecausetherewaslittlebehavioralchange. 48 Table1.13:EmpiricalIncidenceofthe1993EITCExpansionon1993GrossWages Unmarried NoChildren Unmarried w/Children % d g PEGESize d g PEGESize LessHS -0.40-0.12-0.125.00 -0.85-0.31-0.312.90 HS -0.38-0.09-0.098.60 -0.66-0.15-0.154.80 SomeCol. -0.23-0.06-0.0513.60 -0.45-0.11-0.117.10 BA+ -0.08-0.02-0.0134.40 -0.12-0.02-0.0224.20 Total -0.27-0.07-0.0615.30 -0.53-0.14-0.148.40 Married NoChildren Married w/Children % d g PEGESize d g PEGESize LessHS -0.19-0.07-0.0715.80 -0.21-0.08-0.0723.00 HS -0.02-0.010.0035.80 0.040.010.0233.20 SomeCol. 0.040.010.0249.70 0.130.030.0420.30 BA+ 0.050.010.0149.40 0.100.010.0233.20 Total 0.010.000.0042.20 0.060.010.0228.60 Alldatafrom2009MarchCPS,WomenfromTaxUnits.Note:GE=PE+Spillover;Size= abs (Spillover)/( abs (PE)+ abs (Spillover)).Valuesareaveragepercentchanges,weighedby population.Laborsupplyelasticitiesfromstructuralmodelimpliedbyequation1.32. Table1.14:EmpiricalIncidenceofthe2009EITCExpansiononLaborSupply Total Unmarried NoChildren Unmarried w/Children Married NoChildren Married w/Children d ! PEGE PEGE PEGE PEGE PEGE LessHS 0.110.11 -0.05-0.05 1.001.00 0.000.01 0.100.10 HS 0.060.07 -0.06-0.06 0.650.65 0.010.01 -0.02-0.02 SomeCollege 0.030.04 -0.04-0.04 0.560.56 0.010.02 -0.07-0.07 BA+ -0.000.00 -0.00-0.00 0.180.18 0.010.01 -0.03-0.03 Total 0.040.05 -0.04-0.04 0.600.60 0.010.01 -0.03-0.03 Note: % ! 4Œ: = Y ! 4 % F 4 d g 4Œ: .Alldatafrom2009MarchCPS,WomenfromTaxUnits. Valuesareaveragepercentpointchanges,weighedbypopulation.Laborsupplyelasticitiesfrom structuralmodelimpliedbyequation1.32. 1.12Conclusion IevaluatetheEarnedIncomeTaxCreditallowingforgeneralequilibriuminteractionsinthe labormarketandheterogeneouswageresponsiveness.Myapproachallowsonetoevaluateany 49 Table1.15:EmpiricalIncidenceofthe2009EITCExpansion: ChangePerDollarofNewExpenditure Total Unmarried NoChildren Unmarried w/Children Married NoChildren Married w/Children Dollars PEGE PEGE. PEGE PEGE PEGE Labor 0.120.14 -0.04-0.04 0.210.21 0.010.02 -0.05-0.05 Wages -0.07-0.05 -0.05-0.05 -0.04-0.04 0.000.01 0.020.03 GrossEarnings 0.050.09 -0.10-0.09 0.170.17 0.020.03 -0.03-0.02 NetTransfer,FixedTaxes 0.930.95 -0.05-0.04 0.210.21 0.020.03 0.750.75 NetEarn,FixedTaxes 1.051.09 -0.09-0.08 0.420.42 0.030.04 0.690.70 NetEarnings 0.170.20 -0.08-0.07 0.430.43 0.010.02 -0.200-0.19 Welfare 0.000.00 -0.00-0.00 0.010.01 0.000.00 -0.01-0.01 Unitsintablearechangesindollarsofearningssummedacrossdemographicgroups.Note: / ˝ = F !Œ/ # = ¹ 1 g º F ! .Alldatafrom2009MarchCPS,WomenfromTaxUnits.Labor supplyelasticitiesfromstructuralmodelimpliedbyequation1.32. largescaleprogramthata˙ectsaveragetaxratesbymappingthosechangestogrosswagesand laborsupplyaslongasonehasinformationoninitialwages,quantities,andelasticities.When labormarketsareimperfectsubstitutes,ataxinducedsupplychangeinonemarketwilla˙ect themarginalproductofworkersinothermarkets,creatingcascadingmarginalproductandwage spilloversacrosslabormarkets.Becausethegeneralequilibriumwagechangesaretheoretically ambiguous,Iquanti˝edtheimportanceofgeneralequilibriume˙ectsinthreeways. First,Icalculatedtheempiricalincidenceofthe1993OBRAand2009ARRAEITCexpansion. I˝ndthatspilloversrepresentabout15-30%ofaggregatewageandnetearningse˙ectsinthe directionofincreasingdollarstoworkers.Second,tocomparehowdi˙erentlabormarketpolicies a˙ectspillovers,Isimulateda$100millionexpansionoftheEITC,oftheAFDCandFoodStamps programs,andareformthatpaysfortheEITCexpansionbyreducingWelfarebene˝ts.Forall threepolicyreformsexperiments,theGEincidenceislessthanone-thirdthePEincidencefor theEITCreformsthisimpliesmoredollarsgotoworkerswhilefortheWelfarereformworkers receivefewerdollars.Third,Iusedmyelasticitiestoparameterizeastructurallaborsupplymodel toconsiderthee˙ectofequalizingthetheEITCscheduleforworkerswithandwithoutchildren. I˝ndthatequalizingtheEITCwouldhavetheoppositeissueofcurrentEITCexpansions:gross 50 wagedecreaseswouldcausesmarginalworkerswithchildren not toenterthelabormarket. Overall,theseresultsshowthattheEITCisacoste˙ectiveprogramintransferringincometo lowwageworkers.Inallcases,the˝scalexternalityoftheEITCexpansionsisalwaysquitesmall relativetotheincreasesinnetearnings.The1993expansioncreatedlargelabormarketdirectand indirecte˙ects;however,the2009expansionappearsnottohavecausedlabormarketdisruptions. Thebestexplanationforthisseemstobesimplythatthe2009expansionwassmaller,focusedon asmallergroup,andinanenvironmentwheremanypeoplewerealreadyworking.Whenlabor marketdisruptionsaresmall,theprogramisprimarilyfunctioningasanimmediateanti-poverty toolinthatdollarsgotolowincomeworkerswithoutdistortinguntreatedworkers'behaviors.When theyarelarge,theprogramisactingasaimmediateandlong-runanti-povertytoolbyincreasing theearningspotentialofworkersandtheeconomyasawhole. TheaboveassessmentoftheEITC'scoste˙ectivenessisnotwithoutsomecaveats.First, theEITChasapositive˝scalexternalityonlybecausenettransfersfromnon-employmentto employmentarepositiveratherthanduetospillovers.Thus,whilepositivemarginalproduct spilloversexpandtheeconomiccapacityoftheeconomyandtaxbase,ignoringthisinteraction withothertransfers,theEITCwouldnot`payforitself.'Second,theEITChasheterogeneouse˙ects thatmaynotyieldhorizontalequity.Similarskilledworkerswithoutchildrenwillbesubjectto grossearningse˙ectsbutwillnotreceivethesubsidy.I˝ndthatthewelfaree˙ectsareultimately smallfortheseworkers;nevertheless,proponentsofexpandingtheEITCmustacceptthatsome workerswillbe˝nanciallyhurt.Asindicated,thisalsoholdsforthosewhowanttoexpandthe EITCforworkerwithoutchildren.Third,choosinganEITCexpansionoveraWelfareexpansion oranyotherpolicythatlinksbene˝tlevelswithnon-employmentimpliesajudgementaboutthe marginalvalueofleisureforworkersonthemarginofthelaborsupplythreshold. Finally,myapproachstillmakesanumberofsimpli˝cationsworthpointingout.First,the productiontechnologyassumesaconstantelasticityofsubstitution,soallfactorsare(imperfectly) substitutableinthesameway.Second,theincidenceisderivedassumingfrictionlesslabormarket assumptions;e.g.,perfectcompetition,pricetaking.Third,themodelhasabstractedfromfully 51 modelingthetaxsystemorincorporatingdi˙erentindustriesortradepatterns.Incorporatingand resolvingtheseissueswouldbeaninteresting,informative,andpotentiallyimportantcontribution tounderstandingtheincidencee˙ectsofgovernmentprograms. 52 CHAPTER2 THELOCALLABORMARKETEFFECTSOFSTATEEARNEDINCOMETAX CREDITSUPPLEMENTS 2.1Introduction Twentyeightstatesspendover$4billionannuallytosupplementthefederalEarnedIncomeTax Credit. 1 Intaxexpenditurereports,severalstatesexplicitlyjustifythesupplementsasapro-work incentive,whileothersjustifytheirprogramsusingananti-povertyrationale.Yet,thereismuch wedonotknowaboutthesestatelevelprograms.DotheyincreasefederalEITCtakeup?Dothey causeworkerstomigrateorcommuteacrossborders?Dotheyspurlaborsupplyandemployment? WhilepreviousanalyseshaveusedstateEITCpolicyvariationforidenti˝cation,therehasbeen nosystematicevaluationofthesesupplementsonlocallabormarketsabsentthefederalportion oftheprogram. 2 Kleven(2019)usesstackedeventstudydesignstoinvestigateindividuallevel e˙ectsoftheprogramsand˝ndsaprecisezero. 3 NeumarkandWilliams(2016)˝ndusingstate leveltaxreturndatathatstateexpansionsdoincreasefederalEITCtake-up.Additionally,Neumark andShirley(2017)considerlongrune˙ectsofanti-povertypoliciesforurbancensustractsand ˝ndmixedevidenceoflong-runemploymentresponses.Icomplementthesee˙ortsbyfocusing onlocalaggregateoutcomesusingdi˙erentdata,methods,andvariation. 4 Ievaluatethesequestionsatthecountylevelusingtwoempiricaldesignsthatexploitpolicy 1 Thisisbasedonstatetaxreturnandtaxexpenditurereportsfromtaxyears2017to TableasfarasIamaware,thisfacthasnotbeendocumentedgiventhedecentralized natureofstatetaxexpenditures. 2 Forexample,considerLeigh(2010);NeumarkandWilliams(2016);Kasy(2017);Bastian (forthcoming)usethemaximumstateEITCcreditasacontinuousdi˙erenceindi˙erencestyle design. 3 Speci˝cally,heusestwodi˙erentmethodsforthis.Inthe˝rsthecreatesasyntheticcontrol stateforeachexpansionstateforunmarriedwomenwithchildren(andacheckusingatriple di˙erenceincludingunmarriedwomenwithoutchildren)foranaggregatestatelevelregression, andintheseconditisamoreconventionaleventstudydesignusingindividualleveldata. 4 Buhlmannetal.(2018)useaneventstudyandborderpairdesigntolookattaxbunchingat EITCkinkpoints,butdonotlookatotheroutcomes. 53 variationacrossstateborders.First,Iuseastateborderpair˝xede˙ectdesign(SBFE)that generalizesacase-studyapproachwhilecontrollingforlocaleconomicconditions,similarto Holmes(1998);Huang(2008);Dube,LesterandReich(2010).Second,Iuseastateborder distanceregressiondiscontinuitydesign(SBRD)thataccountsforthedegreeacounty'seconomic activityoccursnearastateborder,similartoDieterle,BartalottiandBrummet(2020).These designsallowmetocontrolforlocalmacroeconomicshocksthatpreviousEITCstudieshavenot controlled,whichwouldbiasresultsifpresent. 5 I˝rstdescribetheEITCpolicyvariationacrossstatesalongwithsuggestiveevidenceofstrategic subsidycompetitionbetweenstates.Second,Idescribeamodelthatyieldsameasureofthe˝scal externalityofthestatepoliciesintermsofestimableelasticitiesthatcanbeusedforeconomic evaluationoftheprograms.ThemodelisbasedonMonteetal.(2018)andallowsformigration, commuting,andanextensivelaborsupplychoice.Finally,Iconductandreportmyempirical ˝ndings,whichIbrie˛ysummarizebelow. Formyoutcomevariables,IusedatafromtheIRSStatisticsofIncome(EITCtakeupandmi- gration),theCensusLongitudinalOriginandDestinationStatistics(commutingandemployment), andtheCensusQuarterlyWorkforceIndicators(employmentandearnings).Likepreviousstudies, Iusestatemaximumcreditamountsandstateexpansiontimingtomeasurestatepolicyvariation. AnovelfactthatIdocumentisthatstatesthatborderotherstatesthathavealreadyimplemented anEITCsupplementtendtothemselvesimplementmoregeneroussupplementstomatchtheir neighbor'sincumbentprogram.I˝ndthatthesesecond-moverstatesmaketheirstateEITCsubsidy ratesonaverage7percentagepointsmoregenerous,whichisover50%moregenerousthanstates thatdonothaveaneighboringincumbentprogram.Additionally,Ipresentsuggestiveevidence thatthestatesthathavealreadyimplementedsupplementstendtomaketheirsupplementsroughly 2percentagepointsmoregenerousthe˝veyearsaftertheirneighborimplementsasupplement. Thiscouldimplythatstatesupplementvariationissubjecttounderlyingtrendsinnear-by statesthatarealsocorrelatedwithlabormarketvariablesintheexpansionstate.Thisthreatto 5 Theprimaryreasonisthatstatesupplementratesvaryatthestate-yearlevel,thusatmost state-linear-trendscouldbeused. 54 identi˝cationofcausalEITCe˙ectshasnotbeenexploredpreviously,asfarasIamaware. Giventheabove,Iseparatetheresultsbycomparingallstateborderpolicyvariationandthe subsetofborderswhereonlyonesideoftheborderhasastatesupplement(one-sidedborders).I ˝ndthattheresultsarehighlydependentonempiricalstrategyandthesampleused.Whenpooling allpossiblestateborders,resultsaretypicallylargerinmagnitudeandestimatesignsareconsistent withtheEITCboostinglabormarketactivity.However,whenusingthesubsetofborderswithonly onestatesupplementandmorerecentstateprograms,resultsareoftensmallerinmagnitudeand/or oppositesignasthepooledresults. Forexample,usingtheSBFEstrategy,I˝ndthatthesemi-elasticity(anditsrobuststandard error)betweencountyfederalEITCreturnsandstatesupplementratesis0.16(0.05)usingall bordersbut0.07(0.12)usingonlyone-sidedborders,wherestate-borderclusteredstandarderrors areinparentheses.UsingtheSBRDstrategyforthesamethreesubsets,theelasticityis0.23 (0.17)and-0.06(0.25),respectively.WhenIuseanevent-studyapproach,I˝ndthatthedynamic treatmente˙ectsforone-sidedbordersappearcenteredaroundzeroimplyingnoshort-orlong-run e˙ects. Inaggregate,myresultssuggestamodestincreaseinfederalEITCtake-up,noe˙ectonmi- grationorcommuting,andaninconclusivee˙ectonemploymentandearnings.Statesupplements increasebene˝tstolowincomeworkersbutdonotnecessarilyincreaselocalemploymenttoo˙set stateexpenditures.ThisimpliesthatstateEITCsupplementsfunctionasaconditionalcashtrans- fer,wheretheconditionishavinglowgrossearningsandqualifyingchildren,ratherthanasan economicdevelopmenttool,whichistheexplicitrationalforseveralofthestateprograms. Thus,whilestateEITCprogramsmaybeaworthwhileanti-povertyprogram,itisnotobvious thattheprogramspayforthemselvesintermsoflabormarkete˙ects.Thisresultimpliesthatstate EITCsupplementsdonotful˝lltheeconomicdevelopmentjusti˝cationofsomestatesfortheir implementation.However,itmaybepossiblethatstateprogramsgeneratedemande˙ects,which couldindirectlyincreasetaxincometaxrevenue.Thisremainstobeexplored. 55 2.2StateEITCSupplements Currently,28states,theDistrictofColumbia,andtwomunicipalitieshaveimplementedsup- plementstothefederalEITC.Collectively,thesegovernmentsspend$4billionintaxexpendi- tures.Collectively,thesegovernmentsspend$4billionintaxexpenditures. 6 Forsomecontext, thestateshareofmedicaidexpenditureforthesestates(andDC)is$138billion(KaiserFamily Foundation,2021).StatemedicaidandCHIPexpendituresrepresentabout16%ofstatebudgets (MedicaidandCHIPPaymentandAccessCommission,2021),whilestateEITCareroughly0.4% ofstatebudgets.Nevertheless,thepro-workincentivesofstateEITCsupplementsmaycausethem tobemorepoliticallypopulartotoutthanmedicaidexpenditureswhendiscussingaidtolowincome families. Twojusti˝cationsforEITCprogramsarethattheyprovideeconomicstimulusbene˝tsand/or provideeconomicrelieftolowincomeworkers.Michiganjusti˝esitsprogramusingtheformer: Theearnedincometaxcredit,atboththefederalandstatelevels,isintendedtoincreaseworke˙ort andattachmenttothelaborforceandisagoodexampleofataxexpendituredesignedtoin˛uence taxpayerbehavior (ExecutiveBudgetAppendixonTaxCredits,Deductions,andEx WhileCaliforniaincludesthelatterjusti˝cationinthetextofthelawitself: ...Thepurposeof theCaliforniaEarnedIncomeTaxCreditistoreducepovertyamongCalifornia'spoorestworking familiesandindividuals (CARev&TaxCode 7 Table2.1reportsseveralpolicyfeaturesofstatesupplementsandusage.Columns(b)-(e) reportstatesupplementrates,thetaxyear2020average 8 maximumcreditinthestate(equaltothe supplementratetimestheaveragefederalmaxcredit),whetherthestatesupplementisrefundable, andhowthestatesupplementtreatsnon-residentworkers.StatesthatmaketheEITCrefundable 6 FormorediscussiononstateEITCsupplements,seeWaxmanandLegendre(2021). 7 Foreightstates,I˝ndjusti˝cationsofstateEITCfromlaws,taxexpenditurereports,orother o˚cialy:CA,CO,LA,ME,MI,NJ,NM,andVY.Oregontaxexpenditure reportsexplicitlystatealackofo˚cialpurposefromthelegislature;Ihavefoundo˚cialstatements forotherprograms. 8 Forthisaverage,Iuseaconstantweightingof 0 Ł 4 forsinglequalifyingchildcredit, 0 Ł 4 fortwo children,and 0 Ł 2 forthreepluschildren. 56 e˙ectivelycanmakeaveragestatetaxratesnegative,whilenon-refundabilityreducesthesalience ande˙ectofastatesupplement. 9 Moststatesmakenonresidentsineligibleforstatecredits; however,sevenmakethemavailableataproratedrateequaltotheportionof`stateAGI'to`total AGI'andfourplacenolimitonthecredit(thoughnoneofthesearerefundable). Columns(f)-(i)reporttotalstateEITCclaims,stateexpenditures,andthesevaluesasafraction offederalEITCusageinthestates.ThetableshowsthatnumberofstateEITCclaimroughly matchesfederalclaims.NewYorkandtheDistrictofColumbiahaveclaimsabovethefederal amountwhileHawaii,Virginia,Wisconsin,andSouthCarolinahavemuchfewerclaimsthanthe federalprogram. 10 However,thetaxexpenditureofeachstateistypicallymuchlowergiventhat statesupplementratesareboundedbetween0%and40%acrossstates.Theaverageofcolumn(i) is15.7%thatisslightlylowertheaveragestatesupplementrateincolumn(b),17.1%,because(i) incorporatesdi˙erentialtake-upofstateEITCs. Next,Figure2.1showsthevariationinStateEITCsupplementratesovertime.Thestatesin pinkdonotsupplementtheFederalEITC,whiledarkershadesofbluecorrespondtolargerstate supplementrates. 11 Interestingly,thereseemstobesomespatialcorrelationinStateEITCspread, wheremoststateswithaprogramborderanotherstatewithaprogram. Figure2.1alsoshowsfor2017thestatevariationinStateEITCprogramsupplementratesand maximumcreditsandcountyleveldistributionofFederalEITCreturnsandaverageEITCamount deciles.ThereappearstobeanegativecorrelationbetweenStateEITCprogramsandFederal EITCusage.FederalEITCusageappearstobeconcentratedintheSouthandSunbeltwhile StateEITCprogramsaremostlyinthePlainsandandMidwest.The˝gurealsoshowsthe2000 distributionofunmarriedmothersandofallmothers(marriedandunmarried)inthelaborforceat 9 Whilerefundabilityshouldmakethestatesupplementmoresalientandbene˝cialtoworkers, inunreportedresultsI˝ndnodi˙erentiale˙ectofstatesupplements. 10 SouthCarolina'sprogramwasenactedin2018andisrelativelynew,sothislownumbermay beduetosalienceissues. 11 StatesinredsupplementtheFedEITCbutdosousinganon-standardsupplementschedule; i.e.,donotusea`top-up'rule.Intheregressionspeci˝cations,Iincludethesestatesby˝ndingthe maximumstatecreditassociatedwiththeirstatepolicy. 57 Table2.1:StateEITCReturnsandAmounts TaxYears:2017-2020MostRecentValue StateSubsidyRateStateMaxRefundableNon-ResidentStateClaimsStateAmountState%ofState%of (%)($)(Y/N)Treatment(1000s)($millions)FedClaimsFedAmount (a)(b)(c)(d)(e)(f)(g)(h)(i) CAYIneligible2,04638872.55.9 CO10513YIneligible34374103.310.2 CT27.51412YIneligible1939589.519.7 DE201027NIneligible147.8 DC402053YIneligible6379127.668.5 HI201027NFraction561559.27.5 IL18924YFraction91431699.113.7 IN9462YFraction1048.7 IA15770YFraction20869107.515.2 KS17873YIneligible19779100.916.9 LA3.5180YIneligible493.5 ME5257YNoRefund10010105.35.1 MD281437YIneligible16618 MA231181YIneligible20525.2 MI6308YNoRefund1186.2 MNYIneligible31524499.834.9 MT3154YIneligible NE10513YIneligible12029959.5 NJ371899YIneligible44031.5 NM10513YIneligible1985099.410.1 NY301540YNoRefund2,3321,082143.928.5 OH10513NNoLimit78317988.38.2 OK5257NIneligible3001693.31.9 OR8411YFraction24749969 RI15770YFraction932811615.5 SC20.11032NIneligible602112.71.8 VT361848YIneligible402796.634.2 VA201027NNoLimit34713659.59.7 WI15770YIneligible239936811.8 StateEITCreturnsandamountsdataaccessedfromindividualstatewebsites;typicallystatetax expenditurereports.Mostrecentvalueisreported.FederalEITCreturnsandamountsfromtax year2018(IRSSOI).TheNewYorknumberofreturnsusesbothNYstateandNYcityEITC programsandlikelydoublecountsthenumberclaims.CAandMNhavenon-standardprograms thatdonotmapintoasinglesubsidyrate.MTimplementeditsprogramfortaxyear2019andhas notreleasedexpenditurereports.SourcesfortableinAppendixB.1. thecountylevel. 12 ThereappearstobesomenegativecorrelationbetweenstateEITCprograms andtheaverageFederalEITCamountsbutpositivecorrelationwiththelaborforceparticipationof mothers. 12 The2000countyleveldistributionofunmarriedmothersinthelaborforceisnotavailable. 58 Figure2.1:EITCPolicyandUseVariation Note:mapsstatesupplementratesoverfouryears,wherepinkindicatesnosupplement,darker bluesindicatemoregeneroussubsidies,andredindicatesanon-standardsupplement;mapscounty levelIRStaxreturndatafortaxyear2017. 2.2.1AcrossStateEITCPolicyCoordination Figure2.2plotspolicyvariationatstatebordersduetostatesupplementsacrossseveraldimensions. Allthreeplotsareplottedin`event-time'ofastateEITCimplementationthathasoccurredafter 2000.Figure(2.2.a)showstheaveragechangeinmaxstatecredit(federalplusstateEITC)when astateimplementsasupplementacrossallstateborders.Onaverage,thischangeis$466ora 9.5%increaseingenerosity,whichisroughlya1-2%increaseinannualgrossearningsforasingle tax-˝lerwithonequalifyingdependentinthemax-creditregion. AsFigure2.1shows,somestatebordershaveonlyonestatesupplement(e.g.,Virginiaand Kentucky)whileothershavesupplementsonbothsides(e.g.,VirginiaandMaryland).Icall borderswithonlyonesupplement`one-sided'andborderswithtwosupplements`two-sided.'In thecaseoftwo-sidedborders,theolderprogramisthe`incumbent'andthenewerprogramisthe `implementing'program.Forthispaper,Ifocusonstatesupplementsintroducedafter2000,soall incumbentshaveprogramsinitiatedbefore2000andimplementingprogramsafter2000. 59 Figure(2.2.b)comparesthestatesupplementratesbetweenstatebordersthatareone-sided versustwo-sidedborders.Theplotshowsthatstatesimplementmoregeneroussubsidieswhen theirneighboralreadyhasastateprogram.Onaverage,implementingstatesmaketheirsupplement 7percentagepointsmoregenerousthanimplementingstateswithoutaneighboringincumbent program. Figure(2.2.c)plotstheincumbentstate'spolicyreactiontotheirneighbor'snewsupplement. Speci˝cally,theplotshowswhethertheincumbent'ssubsidyrateineachperiodisstatistically di˙erentfromtheratetheyearbeforethenewprogramisimplemented.Theresultsuggeststhat incumbentsmaketheirprogramsonaverage2percentagepointsmoregenerousinthe˝veyears aftertheirneighbor'simplementation. 2.2.1.1ImplicationsofCoordination Overall,Figures(2.2.b-c)implythatstateborderswherebothsideshavestatesupplementsmaynot besettingtheirstatesupplementratecompletelyexogenously,whichmaylimitwhatcanbelearned fromexpansionsalongtheseborders. Fortwostates, B 2f 1 Œ 2 g alongagivenbordersegment, 1 ,let A B1C bethestateEITCsupplement rate.TheresultsinFigure2.2tellusthat Cov ¹ A 1 1C ŒA 2 1C º < 0 .Thisisnotobviouslyaconcern. Suppose H B1C isanoutcomeofinterest,determinedbythefollowingequation: H B1C = U B ¸ _ 1C ¸ WA B1C ¸ D B1C Ł (2.1) Ifaneighbor'spolicyisuncorrelatedwithunobservabletrendsintheoutcomevariable,thenthe OLSregressionestimateof W isunbiaseddespitethepolicycoordination: Cov ¹ A 1 1C ŒD 2 1C º = 0 = ) E » ^ W OLS ¼ = WŁ (2.2) However,ifthevariablesarecorrelated,thenthepolicycoordinationwillbiastheestimate: Cov ¹ A 1 1C ŒA 2 1C º < 0 ^ Cov ¹ A 1 1C ŒD 2 1C º < 0 = ) E » ^ W OLS ¼ < W .Examiningthistheoretical relationshipisbeyondthescopeofthischapter,butwouldbeafruitfulfutureproject. 60 Figure2.2:E˙ectofStateSupplementImplementation (a)AverageE˙ectonRealMaxCredit (b)SupplementRatesbyNeighbor'sEITCStatus (c)Neighbor'sReactiontoSupplementIntroduction Note:( a )plotstheaveragechangeinrealmaxcreditacrossallstatesupplementsintroducedafter 2000;( b )plotsregressioncoe˚cientsofstatesupplementratesonevent-timeindicatorsinteracted withneighborincumbencystatuscontrollingforyearFEswithstate-borderclusteredstandard errors;( c )plotsregressioncoe˚cientsoftheincumbentneighbor'ssupplementrateonevent-time indicatorscontrollingforyearFEswithWhitestandarderrors Todealwiththisissueempirically,Iwilllookatthefull-sampleresultsandresultswhereonly onesideoftheborderhasastateEITCprogram.Fortheseborders,becauseonlyonesidehasa statesupplement,thenmechanically Cov ¹ A 1 1C ŒA 2 1C º = 0 as A 2 1C = 0 . 2.3EvaluatingStateEITCSupplements TojustifythelabormarketoutcomesthatIusebelow,Iformalizeasimplemodeloflocation andworkchoicethatexplainshowthetaxpolicyvariationinteractswithlabormarketchoicesto 61 a˙ectstatebudgets. 13 Thechangeinthestatebudgetconstraintduetothebehavioralresponsesto thepolicychangeisawaytoapplyadollaramounttothe`unintendede˙ect'ofthepolicychange andcanbeusedameasureofeconomicwelfarechange(Hendren,2016b;Kleven,2020). Let S bethesetpossiblelocations`counties'intheeconomy,andthecountiesin S canbe partitionedinto " `states,' S = f ( 1 Œ( 2 ŒŁŁŁŒ( " g .Lettherebeaunitmassofindividualsindexed by 8 2 # makingaresidenceandworklocationchoicewiththeoptionofunemployment.Suppose thatindividualshavepreferencessuchthattheprobabilitythatanindividualchoosesaworkand residencepair ¹ >Œ3 º as: Pr ¹¹ o 8 Œ d 8 º = ¹ >Œ3 ºº | {z } : = c >Œ3 = Pr ¹ d 8 = 3 j o 8 = > º Pr ¹ o 8 = > º | {z } : = c 3 j > c > Ł (2.3) Thatis,individualshaveatwo-stagedecisionprocesssuchthatthey˝rstchoosearesidencelocation, > 2S ,andthenaworkchoice 3 2fS[f Unemployment gg basedonsome(potentiallyendogenous) indirectutilityvalue;e.g.,aresidence-locationspeci˝camenitypluspost-taxearnings.Idenote agent 8 'schoicebundleas ¹ o 8 Œ d 8 º . 14 The˝scalexternalityofamarginaltaxreformisequivalenttothebehaviorale˙ectontax revenues(Hendren,2016b;FinkelsteinandHendren,2020;Kleven,2020).Ifstategovernment B usesresidencebasedincometaxation 15 withorigin-destinationspeci˝ctaxrates, ' B = Í > 2 B ' > = Í > 2 B Í 3 2S C > 3 F > 3 c 3 j > c > ,thenthe˝rst-order 16 ˝scalexternalityasaproportionofinitialrevenue 13 ThemodelissimilartoMonteetal.(2018),whodocumentvariationinlocallaborsupply elasticities,andconceptuallysimilartoAgrawalandHoyt(2018a)whodocumentthee˙ectoftax di˙erentialsoncommutingpatterns. 14 SuchpreferencescanbemicrofoundedbasedastochastictasteshifterdrawnfromaGeneralized ExtremeValuedistribution,oneexampleofwhichleadstotheNestedLogitmodel. 15 Ifresidentsspenda˝xedportionofnetincomeacrossgoods(viahomotheticpreferences), thentheincometaxisisomorphictoacompositetaxonlaborincomeandpurchases. 16 Thatis,assumingmultiplicativetermsarenegligible: ^ G ^ H ˇ 0 . 62 is(where ^ G = d G š G ): FE B ' B = Õ > 2 B ' > ' B © « ^ c > |{z} Migration ¸ ' > > ' > ¹ ^ F > > ¸ ^ c > j > º | {z } OwnEmployment ¸ Õ 3 2Sn > ' > 3 ' > ¹ ^ F > 3 ¸ ^ c 3 j > º | {z } Commuting ª ® ® ® ® ® ® ® ® ¬ Ł (2.4) Itcanbeshownthatthe˝scalexternalityisasu˚cientmeasureofthechangeinaggregate welfaredividedbythemarginalcostofpublicfunds( ` )whenevaluatedatutilitariansocialwelfare weights( 6 8 = 1 ): d , š d \ ` j 6 8 = 1 = FE (Hendren,2016b;Kleven,2020).Kleven(2020)notesif itispossibletodirectlyestimatethebehaviorale˙ectontaxliabilities,thenthisquantitycan theoreticallybeestimatedwithoutestimatingspeci˝cresponseelasticities.However,giventhe possibilityofmigrationandcommuting,itisnotobviouswhattheappropriatecontrolgroupwould beforsuchanempiricalexercise. Ultimately,thisstudyonlyestimatesthecausalchangeinrealeconomicvariablesanddoesnot attemptawelfareevaluation.Theestimatedelasticities,reportedbelowinthenextsection,donot capturethelocalheterogeneityofbehavioralresponsesimpliedbythemodel,butdogiveahint towardstheirmagnitudeinordertoassessthe˝scalexternality. 2.4EmpiricalDesigns Iusetwoempiricaldesignsonthesetofcountiesthatareatstateborderswithapolicydi˙erence. The˝rstisastate-border˝xede˙ect(SBFE)designthatremovescommontime-varyingshocks betweeneachbordercountypair.Thesecondisastate-borderregressiondiscontinuity(SBRD) designthatparametricallycontrolsfordistancetothepolicyborder. Thesedesignsallowformetocontrolforlocalmacroeconomictrends.FortheSBFEthese arecounty-pairtrendsandforSBRDthesearestate-bordertrends.Thesespeci˝cationsusethe countiesacrosstheborderasacounterfactualifthestatesdidnotimplementasupplement.The assumptionisthatthesecountiesfacesimilareconomicforcesthatarenotlimitedbystateborders exceptfortheEITCpolicychange.Ifmacroeconomictrendsdospilloveracrossstateborders,then 63 notincludingthebordercontrolswillleadtobiasedestimates. Forallthedesignsbelow,let H bethelogofsomeoutcomevariable,let - becontrols,let A be thestatesupplementrate,andlet ) beanindicatorequaltooneifthestate'sprogramisin-e˙ect. Foralltheregressions,Icontrolforlogpopulation(orlogtaxreturns),logrealstateGDP,county ˝xede˙ects,andeithercounty-pair-year˝xede˙ectsorstate-border-year˝xede˙ectsinteracted withdistancetothestateborder.Inaddition,Iweightallregressionsbycountypopulationin2000. Iexplaineachdesigninmoredetailseparately. 2.4.1MaxStateCreditVariation MyprimaryindependentvariableofinterestisthestateEITCsupplementrate, A BC ,asdiscussed above.Thisvariabledirectlyrepresentsthestategenerosityandisthespeci˝cpolicytoolusedby thestates. Previousstudies 17 haveusedthe`(log)statemaximumcredit'wherethestatemaximumcredit isconstructedasadependent-sizeweightedmaximumcredit,wheretheweightsrepresentthe numberoffamilieswith1,2,or3+dependents.Literally,thesestudiescalculatethisas ˘ BC = 0 Ł 4 ˘ 1 BC ¸ 0 Ł 4 ˘ 2 BC ¸ 0 Ł 2 ˘ 3 ¸ BC ,where ˘ 8 BC isthemaxstatecreditfor 8 dependents.Asmoststates programsusea`topup'formula,each ˘ 8 BC termiscalculatedas ¹ 1 ¸ A BC º ˘ 8 C ,where ˘ 8 C isthe federalmaxcreditfor 8 dependents. 18 Combiningthesetwofacts,therealmaxstatecreditisone plusthestatesupplementratetimesaweightedaverageofthefederalmaxcreditsfordependents: ˘ BC = ¹ 1 ¸ A BC º¹ 0 Ł 4 ˘ 1 C ¸ 0 Ł 4 ˘ 2 C ¸ 0 Ł 2 ˘ 3 ¸ C º . Aregressionof ˘ BC or ln » ˘ BC ¼ onthesupplementrateandyearindicators, f A BC Œˇ C g ,willabsorb allthevariationinthestatemaxcreditvariableandyieldan ' 2 valueof1. 19 Thusthestatemax creditvariableiseconometricallyequivalenttousingthestatesubsidyrateandyearindicators.One cannotseparatelyidentifythee˙ectofthelevelofEITConanoutcomevariablefromcommonyear 17 ThreeprominentexamplesincludeLeigh(2010);Kasy(2017);Bastian(forthcoming). 18 OneexceptiontothisisforWisconsinthathasdependentspeci˝csubsidyrates,soforthis state ˘ 8 BC = ¹ 1 ¸ A 8 BC º ˘ 8 C ;however,thisisnotenoughvariationforidenti˝cationonanationalscale. 19 Forexample,usingthelogmaxstatecredittheregressionistheexactspeci˝cationofthe variable'sde˝nition: ln » ˘ BC ¼ = ln » 1 ¸ A BC ¼¸ ln » ˘ C ¼ . 64 e˙ectscapturedbyyearindicatorvariables;rather,onecanonlyidentifytherelativedi˙erences betweenstateswithinagivenyear.SincenearlyallworkontheEITCincludesyearindicatorsas controlvariables,anypriorworkthatclaimedtoidentifythee˙ectof`dollarsofadditionalEITC' misstatedtheiractual˝nding. Giventheaboveandmyuseofyear-locationindicatorvariables,Idirectlyusethestatesup- plementratestoassessthecausalimpactofthestateEITCprograms.Iinterpretcoe˚cients asthegivenchangeintheoutcomevariableintermsofadditionalpercentagepointinthestate supplement.Thisusagemakestheidentifyingvariationmoretransparentandinterpretationmore reliable. 20 Finally,forstateswithanon-standardorniaand˝ndthefamily- sizeweightedmaximumcreditbasedonthenon-standardsupplementandthendividethisbythe federalmaximumEITCcreditforthee˙ectivestatesupplementrate. 2.4.2StateBorderFixedE˙ect TheSBFEdesignuseseverycountypairwithapolicydi˙erencetogeneralizethecasestudy approach(Dubeetal.,2010).Thedesignresidualizesbyapair-year˝xede˙ectthatisassumedto capturecommonunobservabletrends.Underthatassumptionanduncorrelatednesswiththeerror term,di˙erencescorrelatedtostateEITCpoliciesareinterpretedcausally. Theregressionequationis: H 2?BC = - 2?BC V ¸ W A ln » ˘ BC ¼ ¸ _ 2 ¸ _ ?C ¸ D 2?BC Œ (2.5) where 2 indexescounties, ? forcountypairs, B forstates,and C foryears.Forinference,Icluster standarderrorsatthestate-borderlevel. 20 Ifonewantstointerpretthee˙ectsintermsofdollars,thenonecouldmultiplythecurrentreal federalEITCmaxcreditandmultiplythisby 0 Ł 01 to˝ndthedollarvalueofaonepercentagepoint increaseincreditamount. 65 2.4.3StateBorderRegressionDiscontinuity TheSBRDdesigntakesseriouslytheideaofaspatialdiscontinuityinpolicyatthestateborderby modelingthedi˙erenceinexpectedoutcomeasafunctionof`economicdistance'totheborder. Holmes(1998)providesthesedistancemeasures. Anidealstudywoulduseas˝nealocalgeographyaspossible,suchascensusblocks,totake fulladvantageofusingdistancetotheborderasanidenti˝cationstrategy.Dieterleetal.(2020) notethatcountiesarenotidealforthisanalysissincecountiesareapoliticaljurisdictionratherthan aneconomicmarketareaandcountylandareavariesgreatlybystate. 21 Iuseaglobalpolynomial methodbecausetheimpliedmeasurementerrorfromusingcountiesforcestheuseofaparametric methodratherthananon-parametriclocalmethod(Dieterleetal.,2020). Theregressionequationis: H 2B1C = - 2B1C V ¸ W ˘ ln » ˘ BC ¼ ¸ _ 2 ¸ _ 1C ¸ ˇ 1C " 1 ¸ Õ : \ 0; : 1C ¹ 1 ) BC º < : 2B1 ¸ Õ : \ 1; : 1C ) BC < : 2B1 # ¸ D 2BC Œ (2.6) where 2 indexescounties, B forstates, 1 forstateborders, C foryears,and : fortheorderofthe globalpolynomial.Iconsideronlylinear( : = 1 )andquadratic( : = 2 )termsbutallowthedistance regressionstovarydependingonbeingonthetreatedoruntreatedside. 22 Forinference,Icluster standarderrorsatthestate-borderlevel. 2.5Data ThedatausedintheanalysisarebasedonthecontiguousbordercountiesintheUnitedStates. Thereare3,144countyequivalents(includingDC)intheUSofwhich1,184shareabordersegment withanothercounty,butonly905haveapolicydiscontinuityduetoastateEITCprogramatsome pointintime.Themedianbordercountyhastwocontiguousneighbors,butthereare30counties 21 Theseauthorsusecensusblockemploymentweightedcountycentroids,whilemyanalysis usespopulationweighted. 22 ThisissimilartoDieterleetal.(2020)excepttheyimplementamoredata-drivenapproachby allowingthenumberofpolynomialstovaryforeachstateborder. 66 Figure2.3:BorderCountiesbyTreatmentStatus This˝guremapsthecountiesusedintheempiricalsectionbystatesupplementprogramimplemen- tationgroups,wheredarkercolorsaremorerecentandgreycountiesareeitherinastate'sinterior ornon-continentalstates(AKandHI). with5ormoreneighbors.Iobservethesecounty-pairsfrom2000to2018. 23 Ifocusontheperiod startingin2000toavoidusingvariationfromthe1994OBRAexpansionandwelfarereforminthe late1990s.Figure2.3showsthespeci˝ccountiesusedinthepaperbystatesupplementstart. 24 ThetaxreturndataisfromtheIRSStatisticsofIncome(IRSSOI). 25 Themigrationdataisalso basedontheIRSStatisticsofIncomeCountytoCountyFlows. 26 Thecommutingdataisfromthe CensusLongitudinalEmployer-HouseholdDynamicsOrigin-DestinationEmploymentStatistics Data,whereIaggregatetothecountylevel.Finally,theemploymentandearningsdataarefrom theCensusQuarterlyWorkforceIndicators. Forthemigrationandcommutingdata,Icalculatethenetmigration/commutingpercentasthe di˙erenceofentrantsminusexitersoveraninitiallocalvalue.Speci˝cally,thenetmigrantspercent isentrantsminusexitersdividedbythestartofyearcountyresidents,whilethenetcommuting percentisthedi˙erencebetweenin-commutersandout-commutersdividedbyemployedcounty 23 BecauseIuseacontinuousvariableasthetreatment,logmaxstatecredit,allbordercounties provideidentifyingvariationevenifbothstateshaveanEITCprogram.Insupplementalanalysis whereIusetreatmenttimingforpolicyvariation,I`stack'thestatebordersineventtime,which ensuresonlyonestateistreatedintheestimationwindow. 24 COhadashort-livedprogramfrom1999-2001thatIhaveomitted;SC'sprogramstartedin 2018. 25 Iaccessedthe2000to2010EITCreturnsdatafromtheBrookingsInstituteviaCecileMurray. 26 Theyears1990to2000areadaptedfrompre-formated˝lesfromHauer(2019). 67 residents(equaltotheout-commutersplusnon-commutingworkers). IcollectstateEITCparametersfromthesupplementaryinformationforNBER'sTAXSIM (FeenbergandCoutts,1993). 27 CountypopulationisfromtheCensusPopulationandHousingUnit Estimates,whichestimatescountylevelpopulationbetweencensusyears.StateGrossDomestic Product(GDP)dataisfromtheBureauofEconomicAnalysis'sGrossDomesticProductbyState series. InTable2.2Ipresentsummarystatisticsforthedataused.Column(a)includesallcountiesin thecontinentalUSwhilecolumns(b-d)onlyusethe905contiguousbordercountiesthatIusein theestimation.Countiesthatarenever-treated(c)appeartodi˙errelativelymorefromallcounties incolumn(a)thantheever-treatedcounties(d). Table2.2:SummaryStatistics AllCountiesFullSampleNeverTreatedEverTreated (a)(b)(c)(d) StateEITCProgram37.4%52.0%0.0%77.1% (0.21)(0.39)(0.00)(0.40) StateEITCSupplementRate5.0%7.4%0.0010.9% (0.04)(0.07)(0.00)(0.09) CountyReturns(1000s)43.650.937.357.42 (0.59)(1.08)(1.17)(1.49) CountyPopulation(1000s)98.1108.683.9120.5 (1.27)(1.13)(1.25)(1.56) RealStateGDP(1000s)413.0376.8371.3379.5 (1.81)(3.03)(5.86)(3.50) FedTaxEITCReturns7,7908,5196,8879,304 (116)(208)(239)(286) NetMigrationPercent0.20%0.37%0.14%0.48% (0.10)(0.35)(0.02)(0.51) NetLow+MidWageCommutingPercent16.4%17.9%16.4%18.6% (0.06)(0.23)(0.43)(0.27) Employment1,9692,0631,5872,290 (18.9)(28.5)(32.7)(39.1) AvgMonthlyEarnings1,5741,5901,5791,595 (0.87)(1.63)(2.81)(2.01) Counties3,137905294611 USContiguousCounties,2000-2018.Columnsb-duseborder-countieswithapolicydi˙erence attheborder.NevertreatedcountiesneverenactastateEITCprogram;EverTreatedenactastate EITCduringthesampleperiod. 27 Ihavealsomanuallycheckedthevaluesbygoingtothevariousstatewebsites. 68 2.6Results GiventhepatternsshowninFigure2.2,Ipresentthreesetsofresults.First,Ipresentresults thatuseallpossiblestateborderswithatleastoneyearofapolicydiscontinuity.Second,Ifocus ontheone-sidedstateborderswhereonlyonestatehasaEITCsupplementforthewholesample period.Eachoftheseusevariationinthemaximumcreditavailableinthestatebasedonthestate's subsidyrate. Iusethestatesupplementrateasthetreatmentvariable.Whentheoutcomeisalogvariable, thenthentheestimateisaasemi-elasticityinterpretedas aonepercentagepointincreaseinthe subsidycausesa 100 ¹ e W 1 º percentchangeintheoutcome .Forcontext,recallthattheaverage statesupplementrateis9.5percentofthefederalEITC. Inthethirdsetofresults,Iusevariationinstatepolicytimingratherthanstatesupplementrate toestimatestateEITCe˙ects.Ipresenttheseresultsusingstackedeventstudyestimates,separating resultsbywhethertheborderisone-sidedortwo-sided.Idescribethisapproachingreaterdetail below. 2.6.1AllBorders Table2.3displaystheresultsusingallborders.Thetablepresentseithersemi-elasticities(returns, employment,earnings)orlevelchanges(netmigrationpercent,netcommutingpercent).Recall, onaverageastatesupplementincreasesEITCgenerositybyabout10percentagepointsfroma federalmaxcreditof$4,870in2017,the˝nalyearinthesample. 28 PanelAshowsthataonepercentagepointincreaseinEITCgenerosityinducesbetween » 0 Ł 16 Œ 0 Ł 44 ¼ percentadditionalFederalEITCreturnsforthecountyrelativetocountiesacross thestateborder.Eachsemi-elasticityisstatisticallysigni˝cantlydi˙erentfromzero.Thisresult impliesthatstatesupplementsinducegreatertake-upofthefederalEITCeitherduetogreater 28 InJanuary2020terms,theamountis$5,138.Note,thefederalEITCisadjustedannually forin˛ationbasedontheConsumerPriceIndexbefore2017andnowthePersonalConsumption Expenditureindex. 69 awarenessorincreasingearningstorequire˝lingataxreturn. PanelsBandCdisplayestimatesofaonepercentagepointincreaseinthestatesupplement impliesa W -percentagepointchangeinthenetmigration/commuting.Neithersetofestimates isstatisticallydi˙erentfromzero.Themigrationcoe˚cientestimatesarebetween » 0 Ł 003 Œ 0 Ł 017 ¼ fromameanof0.004.Thecommutingcoe˚cientestimatesarebetween » 0 Ł 54; 0 Ł 23 ¼ froma meanof0.18.Whilethemigrationchangeestimatesseemplausible,takenliterallythecommuting changesimplyhugeeconomice˙ectsgiventhatsupplementsincreasedby10percentagepoints. PanelsDandEdisplayemploymentandearningssemi-elasticities,similartoPanelA.The estimatedemploymentsemi-elasticityisbetween » 0 Ł 26 Œ 0 Ł 07 ¼ ,whichwouldimplythatstate supplementsdecreasethenumberofworkersinacountyrelativetocountiesacrosstheborder. Noneoftheestimatesisstatisticallydi˙erentfromzero.Theestimatedearningselasticityis between » 0 Ł 12 Œ 0 Ł 09 ¼ ,whichwouldimplythatstatesupplementsdecreasetheworkers'earnings inacountyrelativetocountiesacrosstheborder.Theseestimatesareeachstatisticallydi˙erent fromzero.Assumingtheemploymente˙ectisweaklynegative,thenegativeearningse˙ectcould betheresultofworkersreducingtheirhours(anincomee˙ect)orpotentialsubsidycaptureby employers. 29 2.6.2One-SidedBorders Table2.4displaystheresultsusingonlyone-sidedborderswithstateimplementationsafter2000. Thissubsamplemirrorstheeventstudyanalysispresentedinthenextsubsectionbutusesmaximum creditvariationasinTable2.3. Onbalance,theseresultsfailtoprovideevidenceofrecentstateEITCsupplementsa˙ecting labormarketoutcomes.InPanelA,insteadofbeingpositiveandstatisticallydi˙erentfromzero, thenewreturnssemi-elasticityisnear-zerofortheSBFEandnegativefortheSBRD.InPanelB, themigrationchangesaresimilarinmagnitudeasbeforeandarestillstatisticallyindistinguishable 29 Incomee˙ectsduetotheEITCaretypicallyassumedtobesmallornon-existent;incidence e˙ectsoftheEITCareexploredinLeigh(2010);Rothstein(2010);Watson(2020). 70 Table2.3:E˙ectofStateEITCPrograms:AllBorders Model:SBPFESBRDD:LSBRDD:Q (a)(b)(c) PanelA:(Annual) ln » FedEITCReturns ¼ StateSupp.Rate0.150.210.37 (0.05)(0.17)(0.14) Observations34,79018,60618,606 PanelB:(Annual)NetMigrationPercent StateSupp.Rate0.0030.0060.017 (0.005)(0.010)(0.012) Observations34,81218,61218,612 PanelC:(Annual)NetLow+MidWageCommutingPercent StateSupp.Rate-0.28-0.54-0.23 (0.38)(0.39)(0.35) Observations32,87817,57817,578 PanelD:(Quarterly) ln » TotalEmployment:Women,LessHS ¼ StateSupp.Rate-0.08-0.20-0.31 (0.08)(0.16)(0.17) Observations141,12975,23475,234 PanelE:(Quarterly) ln » AvgEarnings:Women,LessHS ¼ StateSupp.Rate-0.11-0.12-0.10 (0.04)(0.03)(0.04) Observations139,51865,39465,394 ClusterStateBorderStateBorderStateBorder Clusteredstandarderrorsinparentheses;78clusters.Regressionsweightedcountypopulationin 2000.Controls:logofcountypopulation(logtotalreturnsinPanelA)andlogofstaterealGDP. fromzero.InPanelC,thecommutingchangesmagnitudesvarybythreeordersofmagnitude dependingonthedesign.InPanelD,theemploymentsemi-elasticitiesarenowallpositiverather thannegative.InPanelE,twooftheearningssemi-elasticitiesarenowalsopositive. Theinconsistencyintheresultsstemsfromtwosources.First,thesubsampleusesfewerstate- bordersandthusmanyfewerobservations.Second,thestatesbordersusedinsubsamplecouldhave di˙erentpropertiesthanstateswitholderprogramsthatcouldre˛ectdi˙erentunderlyingtrends. 71 Table2.4:E˙ectofStateEITCPrograms:One-SidedStateBorders Model:SBPFESBRDD:LSBRDD:Q (a)(b)(c) PanelA:(Annual) ln » FedEITCReturns ¼ StateSupp.Rate0.07-0.07-0.30 (0.12)(0.25)(0.43) Observations11,9746,3666,366 PanelB:(Annual)NetMigrationPercent StateSupp.Rate-0.006-0.0120.005 (0.012)(0.015)(0.054) Observations11,9986,3726,372 PanelC:(Annual)NetLow+MidWageCommutingPercent StateSupp.Rate0.030.151.73 (0.13)(0.26)(0.93) Observations11,1965,9495,949 PanelD:(Quarterly) ln » TotalEmployment:Women,LessHS ¼ StateSupp.Rate0.230.540.13 (0.15)(0.55)(1.37) Observations47,67225,29825,298 PanelE:(Quarterly) ln » AvgEarnings:Women,LessHS ¼ StateSupp.Rate-0.040.210.56 (0.10)(0.26)(0.61) Observations47,07524,94124,941 ClusterStateBorderStateBorderStateBorder Clusteredstandarderrorsinparentheses;27clusters.Regressionsweightedcountypopulationin 2000.Controls:logofcountypopulation(logtotalreturnsinPanelA)andlogofstaterealGDP. 2.6.3StackedEventStudies Toprobethedi˙erencesbetweenTable2.3and2.4,Iperformeventstudyanalysesthatusevariation instateprogramimplementationtiming. Let ˇ B beanindicatorvariableforthestatealongagivenborderthatimplementsastate supplementandlet ) ?B betheyearthatastateEITCprogramisimplementedalongastateborder. 72 Thespeci˝cationsIestimateisthefollowing: H 2?BC = - 2?BC V ¸ Õ E 2 V W E 1 » C ) ?B = E ¼ 1 » ˇ B = 1 ¼¸ _ 2 ¸ _ ?C ¸ D 2?BC (2.7) H 2B1C = - 2B1C V ¸ Õ E 2 V W E 1 » C ) ?B = E ¼ 1 » ˇ B = 1 ¼¸ _ 2 ¸ _ 1C ¸ ˇ 1C h 1 ¸ \ 0 1C ¹ 1 ) BC º < 2B1 ¸ \ 1 1C ) BC < 2B1 i ¸ D 2BC Œ (2.8) where V = f 5 Œ 4 ŒŁŁŁŒ 10 gnf 1 g istheevent-timevalues.Note,fortheSBRDdesignIonlyuse thelinearspeci˝cation.The f W E g termsaretheestimatesofthedynamictreatmente˙ectsofthe policypooledacrosseachstateimplementation. Iamabletosplittheanalysisbyone-andtwo-sidedbordersandtoinspectpre-trendsand anticipatione˙ects.ThepooledresultscorrespondtotheresultsinTable2.3andtheone-sided resultscorrespondtoTable2.4.Almostalltheestimatesarenotstatisticallydi˙erentfromzero, whichagainfailstoprovideevidencethatstatesupplementsa˙ectlabormarketoutcomes.Gen- erally,thepooledandone-sidedsamplepre-treatmentperiodsarecenteredaroundzeroimplying nopre-trends;however,thetwo-sidedsampleresultsappeartohavepre-trendsthatraiseconcerns aboutthetreatmente˙ects. Forthereturnsplots,usingthepooledortwo-sidedresultsindicatepositivetreatmente˙ects,but theone-sidedresultsindicateessentiallynoe˙ect.Theemploymentplotsshowstrongemployment e˙ectsthatgrowovertime.However,unlikeintheotherplots,theone-sidedsampleestimatesdo appeartohavepre-trendsthatcastsdoubtontheresults.Finally,theearningsresultsarenearzero forallspeci˝cations. 2.7Conclusion TheEarnedIncomeTaxCreditisoneofthelargestanti-povertyprogramsintheUnitedStates andisincreasinglysupplementedbythestates.Severalstatesexplicitlyjustifytheirprogramsasan economicdevelopmenttaxexpendituremeanttoincreaselaborforceparticipation.Idocumented variationinstateEITCpoliciesandtestthisclaimusingtwoempiricaldesignsthatusevariationat 73 Figure2.4:StackedEventStudyPlots LogEITCReturns-SBFE LogEITCReturns-SBRD:L LogEmployment,WomenLHS-SBFE LogEmployment,WomenLHS-SBRD:L LogEarnings,WomenLHS-SBFE LogEarnings,WomenLHS-SBRD:L Note:Plotsofeventstudycoe˚cientsforSBFEandSBRDdesignswithstate-borderrobust standarderrorsforthreedi˙erentsamples:pooled,one-sided,andtwo-sided.Thepooleduses allpossiblestateborders,theone-sidedusesonlyborderswherethenewstateprogramisthe˝rst programontheborder,andthetwo-sidedusesonlyborderswherethenewstateprogramisthe secondprogram.Eachcoe˚cientisthedi˙erenceinoutcomevariableforthestateimplementing theprogram. 74 stateborders.Itestfore˙ectsinfederalEITCtakeup,countymigration,countycommuting,and employmentandearningsforwomenwithlessthanahighschooldegree. I˝ndthatestimatesarehighlydependentontheempiricaldesignandsampleused.IfIuse allpossiblestatepoliciesandborders,thenI˝ndthatstateEITCsupplementsincreasetake-upof thefederalEITC,donota˙ectmigrationorcommuting,andeitherdecreaseorhavenoa˙ecton loweducatedwomen'semploymentandearnings.WhenIlimitthesampleto`one-sided'borders whereastatesupplementedwasimplementedafter2000,I˝ndmixedresultsthatallstatistically insigni˝cant. Overall,myresultsimplythatstateEITCexpansionsdonotfunctionaseconomicdevelopment tools.Thus,stateEITCfunctionasananti-povertyprogrambutwithlittle(orno)labormarket distortions.Myevaluationcenteredonthelabormarkete˙ects,soitispossiblethatexpansion increaselocaldemand.Thischannelremainstobeexplored. 75 CHAPTER3 ISTHERENTTOOHIGH:LANDOWNERSHIPANDMONOPOLYPOWER(WITH ORENZIV) 3.1Introduction Propertyrightsgrantlandownersexclusiveuseoverparcelsofland.SinceChamberlin(1933), andasfarbackasAdamSmith,economistshaveconsideredwhetherthisarrangementendows landownerswithmonopolypricingpowers. 1 Apriori ,propertyrightsneednotgeneratemonopoly power,anditisstandardformodelsofrealestatemarketstoassumecompetitionisperfect. 2 Moreover,theempiricalrelevanceofanypotentiallandownermarketpowerand,asaresult,its policyimplicationsarepoorlyunderstood. Thispaperinvestigatestheeconomicimpactofmarketpowerduetolandrights.Weanswer twoquestions:isthispowereconomicallymeaningful,andhowshouldthisalterourunderstanding ofurbanlandusepolicies?Usingdataonmulti-unitresidentialrentalbuildingsinNewYorkCity (NYC),we˝ndthatmonopolymarkupsareonaverageaboutathirdofrentalprices.Weshowhow monopolymarkupsinteractwithzoningregulations,andexaminethepossibilitythatrestrictions onlandownershipconcentrationcanreducerents. Usingamodelthatneststwomonopolypowergeneratingmecerticalandhorizon- tale˝rstexplorethetheoreticalimplicationsofmonopolymarkupsforurban policy.Previousworkhasfocusedalmostexclusivelyonajusti˝cationofrentcontrolbasedon landownermonopolypower(Arnott,1989;ArnottandIgarashi,2000;BasuandEmerson,2003). Ourframeworkallowsustoexplorehowmonopolypricingandalargersetofurbanpoliciesinteract 1 ForSmith,thatthelandownerscouldrentunimprovedlandleadhimtobelievethatrentwas ayprice(Smith,1776).Ricardo(1817)consideredlandadi˙erentiatedfactorof production,sothatrentsre˛ecteddi˙erentialsinmarginalproduct.Marxarguedthatmonopoly landrentscamefromthreesources:qualitydi˙erences,markupsdesignedtolimitaccesstoland, andextractionofrentsfromproducerssellingatmarkups(Evans,1991). 2 SeeBrueckner(1987)forauni˝ed,formalAlnso-Muth-Mills(AMM)modelandGlaeser (2007)forstandardmodellingofcompetitivedevelopers. 76 ingeneralequilibrium. 3 Forinstance,ontheonehand,monopolypowerattenuatestheimpactofup-zoningatup- zonedparcelsthemselves,asrentandquantitychangesreverttomonopolisticratherthane˚cient levels.Ontheotherhand,zoningregulationshaveanadditionalimpactonrentsatotherlocations throughmarkups,andweshowthatwhenthecostfunctionfordevelopingandrentingunitsis nondecreasing,heavierzoningconstraintsinoneparcelalwaysraiserentsatother,unzonedparcels byraisingmarkups. Wealsoexplorethepotentialformunicipalitiestoreducerentsbylimitingtheconcentration oflandownership.RestrictionsonconcentrationhavebeenrecentlyproposedbyBerlinhousing activists(Stone,2019).WeapplytheresultsofNockeandSchutz(2018a),partofagrowing literatureonmulti-productoligopoly(A˙eldtetal.,2013;Ja˙eandWeyl,2013;NockeandSchutz, 2018a),totheimpactofzoningonmonopolymarkups,andshowthatwithnon-decreasingmarginal cost,landownerswithhigherconcentrationalwaysraisemarkups.Intuitively,landownerswith multiplelotscanpotentiallyinternalizetheimpactofoneparcel'spricingdecisiononthatoftheir otherparcels.Whencost-relatedsubstitutione˙ectsbetweenparcelsaresu˚cientlysmall,this canleadtohigherrentsandmarkups.Furthermore,weextendtheresultsofNockeandSchutz (2018b),˝ndingconditionsunderwhichincreasedconcentrationalsogeneratesincreasesinprices forallotherproducts,or,inourcase,parcels. Whilethesetheoreticalchannelsmayexist,aseparatequestion,overwhichtheliteratureis silent,iswhethertheyareempiricallyrelevant.Theextenttowhichlandowners'marketpower a˙ectrentswilldependonthestrengthofcomplementaritiesbetweenrenterandbuildingtypes,as wellasthedegreetowhichconsumersseehousingatsimilarbuildingsassubstitutes.Toanswer thisquestion,weconstructanewbuilding-leveldatasetformulti-unitresidentialbuildingsinNYC. Weobtainbuildingrentalincomefromacombinationofscrapedpublicownercommunications anddeconstructingformulasusedbytheNYCDepartmentofFinance(DOF)forcalculatingtax 3 Diamondetal.(2019)considertheequilibriume˙ectsofrentcontrolsonlandownerentryand exit.Urbanpoliciescouldalsointeractwithmonopolypro˝tsthroughequilibriumentryandexit. Wedonotknowofanypaperthatexploresthisinteraction. 77 assessment.OurmainresultsfocusonManhattanbuildings,althoughweproberobustnessand deriveadditionalpowerwherenecessaryfrombuildingsintheBronx,Brooklyn,andQueens. First,we˝ndthatpatternsinthedataareconsistentwiththepredictionsofourmodel.In particular,we˝ndthatoverasevenyearperiod,a10%increaseinCensustractconcentrationis correlatedwitha1-1.6%increaseinaveragebuildingrents.Therelationshipholdsevenwhenfully accountingfortime-invariantbuildingcharacteristics.Thesecorrelationsarenotcausal,butthey areconsistentwiththeexistenceofmeaningfulmonopolypower. Next,weestimateourmodelinordertoascertainthequantitativescopeofmarkups. 4 The˝rst stepinourmarkupestimationistheestimationofbuilding-levelown-priceelasticityofdemand, accountingforsortingandunobservedbuildingquality.Previoushousingdemandelasticityes- timatesfocusonthehousing-consumptiontrade-o˙and,asaresult,tendto˝ndinelasticresults (AlbouyandEhrlich,2018),which,iftakenliterally,wouldbeinconsistentwithmonopolypric- ing. 5 However,therelevantelasticityforalandowner'spricingdecisionistheown-priceelasticity thataccountsforsubstitution between rivalbuildings.Weestimatethiselasticityand˝ndmedian buildingown-pricedemandelasticityof 3 Ł 3 inourpreferredspeci˝cation. 6 Animportantaspectofourempiricalenvironmentistheubiquityofconstraintsonpricesand quantitiesintheformofrentrestrictionsandzoningregulations. 7 , 8 Inordertouseourestimated 4 Ourestimationmethodisbasedondi˙erentiatedproductdemandestimationdevelopedby Berry,LevinsohnandPakes(1995)andGrigolonandVerboven(2014).Withinurbanhousing demandliterature,ourworkismostcloselyrelatedtoBayer,McMillanandRueben(2004),who estimatehousingdemandandresidentsortingwithinSanFrancisco.SeeKumino˙,Smithand Timmins(2013)foraliteratureoverview. 5 Usinghedonicapproacheswithbuilding-leveldata,GyourkoandVoith(2000)andChenetal. (2011)˝ndelasticitiescompatiblewithmonopolypricing,butonlythelatternotestheconnection withmonopolisticlandowners. 6 Whenweestimatethechangeinaggregaterentaldemandif all buildingrentsincreasedby1%, whichiscloserinspirittopreviousestimates,wethen˝ndaninelasticresultof 0 Ł 14 . 7 NYChastwoformsorrentregulation,rentcontrolandrentstabilization;weusethetermrent stabilizationforallrentregulation.Controlisnowrareasitappliesonlytobuildingsbuiltbefore 1947fortenantsinplacebefore1971.Stabilizationbyfarmorecommonbasedonabuilding having6+unitsandbuiltbefore1974andandmaypassbetweendi˙erenttenants;stabilizedunits' rentannualgrowthsetbyNYCRentGuidelinesBoard. 8 Forzoningconstraints,weaskwhetherabuildingcouldaddoneadditionalminimumsized residentialunitbasedon˛oor-area-ratiosanddensitylimits. 78 parameterstofurtherestimatemarkups,weusedetailedbuildingcharacteristicstoisolatethesetof buildingsinoursamplewhichareneitherrentstabilizednorconstrainedbyzoning. 9 Wecallthis samplepolicy-unconstrained.We˝ndthatinthepolicy-unconstrainedsample,rentsincludean averagemarkupovermarginalcostsof$705permonth,withthemeanandmedianmarkupbeing 30%oftherentinourpreferredspeci˝cation.Thesemarkupsareovermarginalcosts includingamortizedpurchaseandmaintenancecostsandoutsideoptions. Inaddition,ourmodelassumesquantitycanbesetoptimallyforcurrent-perioddemand,a conditionunlikelytobemetinoursettingwhere˝xedcostsofconstructionanddurablehousing stocksmakequantityadjustmentslumpy.Whileweshowthatourmodelisisomorphictoone withseparateddevelopersandlandownerswithrationalexpectations,muchofthehousingstock inoursamplewaslikelyconstructed(andquantityset)atatimewhen21stcenturydemandwas unforeseeable.Accordingly,weisolatethesubsetofthepolicy-unconstrainedsamplewhichwere constructedinthelastdecadeofourdata,andseparatelycalculatemarkupsforthese.We˝nd markupsaresimilarlyonaverage31-32%ofrentforthesebuildings.Inanadditionalspeci˝cation, weestimateelasticitiesandmarkupsusingdatafromtheBronx,Brooklyn,andQueensinaddition toManhattan.We˝ndaveragemarkupsrangebyboroughbetween21-30%fornew,policy- unconstrainedbuildings. Finally,weuseourresultstoassessthequantitativeimpactofup-zoningonmarkups,using thecross-priceelasticitiesgeneratedbyourestimatesinordertoquantifytheimpactofamarginal relaxationofzoningconstraintsonrentsatpolicy-unconstrainedparcels.Asnotedbyourmodel's predictedinteractionbetweenzoningandmarkups,thelargemarkupswe˝ndmayinpartre˛ect thepecuniaryspilloversofthe(many)zoning-constrainedlotsonthepolicy-unconstrainedsample. Indeed,we˝ndtheubiquityofzoningconstraintsappearstohaveanappreciableimpactonrentsat policy-unconstrainedlots.Onaverage,apolicychangeresultingintheconstructionofroughly417 additionalunitsatzoning-constrainedparcelsreducesmarkupsbybetween$6.72and$7.41per unitatpolicy-unconstrainedbuildings,whichimpliesanadditional5-19unitsthroughincreased 9 Wecalculatethat92%ofManhattanrentalbuildingswithfourormoreunitsareeitherzoning constrainedorrentstabilized. 79 pricecompetition.Forcontext,themagnitudeofthisspilloveronrentsatthesigni˝cantlysmaller unconstrainedsampleisover10%ofwhatthemagnitudeofthe(˝rst-order)averagerente˙ecton theup-zonedlotsthemselveswouldbe. 3.2Model We˝rstsetuptheoptimizationroutinesforeachagentinourmodel:landownersendowedwith locationsandchoosingrentalrates,andrentersendowedwithincomeandchoosingresidences.We thende˝neandsolvetheequilibriumintwocases:˝rst,withoutverticaldi˙erentiationinlocation quality,and,second,withouthorizontaldi˙erentiation.Wereviewhow,ineachcase,themodel deliverslandownerpricingpower. 3.2.1Setup ParcelsandLandowners Thespace,acity,iscomprisedofaset A = f 0 0 Œ0 1 Œ0 2 ŒŁŁŁŒ0 ˜ g discreteparcels,whichdi˙eraccordingtotheirunderlyingquality 0 ,drawnwithoutreplacement fromadistribution ˝ 1 ¹ 0 º .Highervaluesof 0 havehigheramenityvaluetorenters.Wereferto 0 asquality"anddi˙erencesin 0 asverticaldi˙erentiationinparcels.Alocation'srealized quality 0 willalsobeusedhenceforthtoindexeachlocationintheset A .Wemakethesimplifying assumptionthat 0 isexogenous,whilenotingthatinthedatabuildingandparcelcharacteristicsare amixofendogenouslychosenandexogenouslygiven.Additionally,weset 0 0 aslivingoutofthe city;i.e,anoutside-option. Eachparcelhasauniquelandowner 5 2 F whomaximizespro˝tsbychoosingtherentlevelat herlocation.Here,wealsoassumelandownerseachownauniqueparcel,althoughwerelaxthis lateron. Landownersprovideamassofrentershousingatapositive,di˙erentiablemarginalcost 2 0 ¹ @ º , where @ isthemassofrentersthelandowneraccommodatesinequilibrium.Totalrevenueisrent A collectedtimes @ .Agivenlandowner 5 'spro˝tsfromparcel 0 are c 0 = A @ 2 0 ¹ @ º .Landowners determinetheconstructedquantityandrentalpriceofunits,andsubtractingmarkupsfromrent 80 backsoutamarginalcostscombiningbothoftheseactivities.Ourestimationwillnotrely onobservingthesecosts.AppendixBshowsthatequilibriumpricesandquantitiesareunchanged whenweseparatethedevelopmentandrentalpriceproblemsandthemarkupiscapitalizedinto thepriceofthebuilding.InSection3.6.3,wediscusshowwenavigatethisassumptioninour empiricalsetting,wherelandownersareconstrainedbypolicyandsupplyissetinadvance. Renters Amass " ofheterogeneousrenters,indexedby 8 2 # ,drawincome-types H from distribution ˝ 2 ¹ H º .Renterutilityisderivedfromconsumptionandlocationamenities.Renters alsodrawidiosyncratictastesforeachlocation, n 8Œ0 ,fromatype-oneextremevaluedistribution ˝ 3 ¹ n º withscaleparameter f n .Utilitymayvaryindependentlybytypeaswell: * 8 ¹ 0 ; H 8 º = ˙ ¹ 0ŒH 8 A ¹ 0 º ŒH 8 º¸ n 8Œ0 Œ (3.1) whereconsumptionisequivalenttoincomeminusrent.Renterschooseamongalllocations 0 to maximizeutilitytakingamenities,rents,andpersonalincomeasgiven. 3.2.2Equilibrium Anequilibriumwillbede˝nedbyascheduleofrentsandquantities f¹ A 0 Œ@ 0 ºg 0 2A thatmaximize landownerpro˝ts,assignrenterstolocations 0 suchthatnorentercanincreaseutilitybychoosing topayrentsatanyotherparcel,andcleartherealestatemarket.Thus,foreachtype H ,theoriginal densityoftypes H isaccountedforacrossalltheirchosenlocations 0 andtheoutsideoption, 6 ¹ H º = Í A @ 0 ¹ H º¸ @ 0 ¹ H º . 10 Wemakeadditionalassumptionsontherenter'spayo˙function ˙ andthedistributionsoftypes tobrie˛yrevieweachsourceoflandownermonopolyinequilibrium. 10 Wedonotconsidercombinationsof ˝ 2 ¹ H º ,costfunctions,and ˝ 1 ¹ 0 º whichresultinthefull massofrenterschoosingtheoutsideoption. 81 3.2.2.1EquilibriumUnderHorizontalDi˙erentiation Forthehorizontaldi˙erentiationcase,wesetthequalityandincomedistributionsasdegenerate; i.e., 0 9 = 0 and H 8 = H .Thisconstructiondeliversstandardmultinomiallogitchoiceprobabilities formarketdemand: ˇ 0 = e ˙ ¹ 0ŒH A ¹ 0 º ŒH ºš f n Í 0 0 2A f e ˙ ¹ 0 0 ŒH A ¹ 0 0 º ŒH ºš f n g " (3.2) Wesolvethesymmetricpricingequilibriumassuminglandownerscompeteinrentsandnotingthat allamenitiesareequivalent,whichyieldsaninverseelasticitymarkuprule: 11 A ¢ ¹ 0 º = <2 ¹ ˇ 0 º ˇ 0 mˇ 0 š mA = ) A ¢ ¹ 0 º <2 ¹ ˇ 0 º A ¢ ¹ 0 º = 1 Y 0 Œ (3.3) where Y 0 istheown-priceelasticity. Theequilibriumrentateachbuildingequalsmarginalcostplusamarkuprelatedtothecurvature ofdemand,whichisafunctionofthemarginalutilityofconsumption,thescaleoftheidiosyncratic tastes,andsubstitutionbehaviorofrenters. 12 Thesolutionimpliesstrictlypositivemarkupsin rents. 13 Toclosethemodel,weapplyamarketclearingconditionthatthetotalnumberofrenters housedinandoutofthecityequalsthetotalnumberofrenters. 3.2.2.2EquilibriumUnderVerticalDi˙erentiation Fortheverticaldi˙erentiationcase,weassumethattherenters'utilityfunctiondisplaysincreasing complementsbetweenrenterincome H andlocationquality 0 andthatidiosyncraticdraws, n 8Œ0 ,are 11 Giventhedegeneratedistributionofamenities,asymmetricsolutiontothelandowner'sprob- lemcanbereasonedverbally.Supposealllandownerswithamenityvalue 0 setrentatsome equilibrium A ¢ ¹ 0 º .Anyindividualdeviationtoahigherrentleadstolessdemandsinceamenities areequivalent,butanydeviationtoalowerrentwouldleadtogreaterdemand. 12 CaplinandNalebu˙(1991)andPerlo˙andSalop(1985)showthatsuchanalwaysequilibrium exists. 13 Aneconomicconsequenceofthemarkupisthatsomerentersdonotenterthoughtheywould ifparcelswerepricedatmarginalcost;i.e., ˇ 0 ¹ A " º ˇ 0 ¹ <2 ¹ ˇ 0 ºº .Thus,thereexistrenters withawillingnesstopayforspacegreaterthantheirimpactonmarginalcost,butarenevertheless pricedoutofthemarket.SeeBajariandBenkard(2003)formoreimplicationsfromthehorizontal discretechoicemodel. 82 allzero.Wenowsuppressindividualsubscripts 8 asalldi˙erencesarebasedon 0 and H .Themodel yieldsverticaloligopolyasinShakedandSutton(1983).Weassumeutilityislog-supermodular inrenterandparceltype: ˙ ¹ 0ŒH AŒH º = ˙ 1 ¹ 0ŒH º ˙ 2 ¹ H A º Œ (3.4) wherefunction ˙ 1 islog-supermodularin 0 and H ,and ˙ 2 isanincreasingfunctionofconsumption (equivalenttoincomeminusrent).Landownerssetrentsaccordingtoindividualwillingnessto pay(WTP).Because ¹ d ˙ 1 š d 0 º ¡ 0 ,it'sclearthatallelseequal,alltypespreferhigher 0 locations, andthereforethat ¹ d A 0 š d 0 º ¡ 0 .Moreover,conditionalonrentsatotherlocations,di˙erenttypes H willhavedi˙erentWTPforagivenparceloftype 0 .WTPoftype H forlocation 0 is ,)% ¹ HŒ0 º = min 8 1 2An 0 ˙ 1 ¹ 0ŒH º ˙ 2 ¹ H A 0 º ˙ 1 ¹ 1ŒH º ˙ 2 ¹ H A 1 º Ł (3.5) Theequilibriumisgivenbyasetofrents A 0 andcuto˙s H 1 ŒŁŁŁŒH # 1 .Betweenanycuto˙ H 0 1 and H 0 ,thewillingnesstopayofindividualsassignedtolocation 0 isheterogeneousandsingle-peaked intype H atsome H 0Œ?40: 2» H 0 1 ŒH 0 ¼ .Inotherwords,increasingcomplementarityactswithin assignmentsofcontinuoustypestothediscretenumberofparcelstocreatevariationinWTP. Thelandownerpricingrulechoosesq,ande˙ectively H 0 1 and H 0 suchthat A 0 <2 0 ¹ @ º = ˝ 2 ¹ H 0 º ˝ 2 ¹ H 0 1 º 6 2 ¹ H 0 º 3H 0 3A 0 6 2 ¹ H 0 1 º 3H 0 1 3A 0 Ł (3.6) Notethat 3H 0 3A 0 0 Œ 3H 0 1 3A 0 ¡ 0 ,andthereforemarkupsarepositive.Aslandownersadjustrent A 0 upwards,theyloserentersontwomargins,thelowest-typeassignedtotheirparcel, H 0 ,who˛eeto thecheapernext-bestoption 0 1 ,andthosenearthetopofthedistributionattheirlocationthat spendmorefortheoption 0 ¸ 1 . Toclosethemodel,thehousingmarketmustclear.Notethatcuto˙sarecontinuous,andfor any H 1 ,if H 1 choosesaparcelinthecityall H¡H 1 doaswell.IfWTPisnegativeforthelowest type H atthelowestlocation 0 ,somemassoftypeswillchoosetheoutsideoption.Aparcelis unoccupiedif H 0 = H 0 1 . 83 3.3PolicyImplications:Theory Inthissection,weassessthee˙ectsofseveralpoliciesinthecontextofmonopolymarkups. First,wediscusstheimpactofzoning.Weshowthatinthehorizontalcase,zoningraisesrents ofparcelsthatare not constrainedbyzoning,evenwhenmarginalcostsareconstant.Second,we discusshow,undernon-decreasingmarginalcosts,concentrationoflandownershipraisesmarkups andrentsatallparcels.Weconcludebydiscussingthescopeforanalysisofmonopolypowerin severalotherurbanpolicies.AppendixC.1presentsproofsofourpropositions. 3.3.1OldPolicies,NewImplications Animmediateimplicationoftheabovemodelisthat,evenintheabsenceofspillovers,apolicyofno zoningisnot˝rst-best.Becauseamonopolistlandownerrestrictsquantity,thequantitydi˙erence betweenzoning-restrictedandanidentical,unrestrictedparcelwithamonopolistlandownerisless thanthedi˙erencebetweenzoning-restrictedparcelsandacompetitivelypricedparcel.Height minimumscouldreducerents. Whathappenswhenzoningconstraintsarenotbindingeverywhere?Totheextentthatzoning constrainsbindataparticularparcel,thequantitymustberestrictedbeyondthemonopoly-optimal quantity,andrentsasaresultmustbehigher.However,inacitywhereonlysomeparcelsare constrainedbyzoningrules,thoseconstraintsalsoimpactrentsatunzonedparcelsbya˙ecting equilibriummonopolypoweratunconstrainedparcels.Inboththeverticalandhorizontalcase,the rentatagivenparcelisinverselyproportionaltorentsatotherparcels.Whenwerestrictourselves tothehorizontalcase,wecanstatethefollowing: Proposition1. Withlogitdemandandnon-decreasingmarginalcost,allelseequal,theimposition ofbindingzoningconstraintsonagivenparcelincreasestherentatallotherparcels,including unzonedparcelsandparcelswherezoningconstraintsdonotbind.Whenmarginalcostisconstant, markupsatthoseparcelsgoupaswell. AppendixC.1presentsaproof.Byraisingrentsatcompetinglocations,bindingzoning constrainshavespillovere˙ectsonrentsatpolicy-unconstrainedlocationsthroughmonopoly 84 pricing.Likewise,relaxingzoningconstraintsatoneparcelbringsdownrentseverywhere.Of course,evenwhenunitsarepricedcompetitively,ifmarginalcostsareincreasing,bylimiting supplyatonelocation,zoningcanimpactrentsandquantitiesatotherlocations.ButProposition 1pointsoutthatmonopolypowerexacerbatesthepricee˙ectsbychangingoptimalmarkups.In otherwords,eveninaworldofconstantmarginalcosts,zoningconstraintsatoneparcelwouldraise rentsatallotherparcelsinthecitybyincreasingmonopolymarkups.Thise˙ectoperatesthrough thecross-priceelasticities,which,inthemultinomiallogitcasecanbesignedandcomparedacross anyequilibria.InSection3.8,weassesstheempiricalmagnitudeofthisforcebyconsideringa marginal,acrosstheboardlooseningofzoningconstraintsinManhattan. 3.3.2NewPolicies,NewImplications Undermonopolypricing,higherrentscangenerateapositivepecuniaryexternalityonother landowners,and,byincreasingdemandanda˙ectingelasticity,monopolymarkupsatoneparcel maypositivelyimpactmarkups,rents,andpro˝tsatotherlocations.Whenlandownersownmultiple parcels,theyinternalizethesepecuniaryexternalities,whichmayresultinhighermarkupsandrents overall.Intuitively,monopolistswithgreatermarketsharemayreducequantitytoagreaterextent inordertomaximizetotalpro˝ts. Ingeneral,however,theimpactofchangesinlandownershipconcentrationisanalogousto mergersinthemulti-productoligopolysetting.Asinthatsetting,wecannotmakestatementson thee˙ectsofconcentrationontheequilibriumwithoutadditionalassumptions.WeextendNocke andSchutz(2018b)togeneratethefollowingproposition: Proposition2. Withlogitdemandandnon-decreasingmarginalcost,allelseequal,landowners withhighermarketsharehavehighermarkupsandrents;anincreaseintheownershipshareof onelandownerwillgenerateincreasesinmarkupsandrentsatallthelandowner'sparcels,and increasesinrentsatallotherparcels. Becausewecannotassumemarginalcostisconstant,weintroduceanevenmore˛exiblecost functionthanthosefoundinNockeandSchutz(2018b,a).That,inturn,requiresanextensionto 85 theresultontherelationshipbetweenownshareandothers'shareonmarkupandrent.Appendix C.1providesaproof. NotethatProposition2isonlyguaranteedtoholdwhenwecanexcludethepossibilitiesofscale economiesandwhentherearenosystematicvariationsinindividualvaluationsbyindividualchar- acteristics;i.e.,nosorting.Intuitively,iflandownerscanraisepro˝tsbyforcingmoreindividuals intooneparcel,generatingscale,oriftheycana˙ectthesortingequilibriumthroughmanipulations totherentsofmultipleparcels,theymay˝nditoptimaltoreduce,ratherthanincreaserentsand markups. Animportantimplicationofthisresultisthatmanipulatingtheownershipstructureofparcels a˙ectsrentsthroughmonopolypricing.Inparticular,underspeci˝cconditions,reducingownership concentrationwillreducerents.InSection3.5,welookforevidenceofscopeforsuchpoliciesin ourNewYorkCitydataset. 3.3.3AdditionalPolicies Wecloseourpolicydiscussionbybrie˛yandinformallydiscussingthepotentialinteractionsof monopolypricingwiththreeotherurbanpolicies:rentregulation,inclusionaryzoning,anduse laws. Wherepreviouslyintroducedintothehousingliterature,theconceptofmonopolypoweramong landownershasbeenusedtoadvocateforrentregulation.Theintuitionisthatreducingrentsin thepresenceofmonopolymarkupscanachievethee˚cientequilibrium.Bycontrast,Diamond etal.(2019),whodonotexploremonopolymarkups,showthatrentcontrolsgenerateanextensive marginimpact.Whileitisbeyondthescopeofthispapertodiscussexitandentry,AppendixB showshowmonopolymarkupsarecapitalizedintolandrentsandcouldimpactsuchdecisions. Inthiscontext,inclusionaryzoningpolicies,whichmandatea˙ordablehousingbeincludedin newdevelopments,canbeconsideredasapolicywhichmovesmonopolyquantitiestoe˚cientlevels similarlytorentcontrols,butwithoutreducingmonopolypro˝tandthereforewithouta˙ectingentry decisions. 86 Finally,wepointoutthatzoninguselawsmayalsooperateonmonopolymargins.Whilewe onlyconsidermarkupsinaresidentialmarket,ifdemandelasticitiesvarybetweenresidentialand commercialmarkets,uselawsmayreducemarkupsbyconstraininglandownerstobuildinless pro˝tablemarketswithmoreelasticdemand. 3.4Data Sources Ourmaindataarederivedfrompublicadministrativebuilding-levelrecords,aswell asscrapeddata,fromseveralNewYorkCitydepartments,includingtheDepartmentsofCity Planning,Finance,andHousingPreservation&Development.Ourprimarydatasetcombinesthe PrimaryLandUseTaxLotOutput(PLUTO)andtheFinalAssessmentRoll(FAR)forallbuildings inNYC,aswellascurrentandhistoricMultipleDwellingsRegistrationandContacts(MDRC) datasets(withprioryearsgraciouslyprovidedtousbytheNYUFurmanCenter). 14 ThePLUTO provideslocation,zoning,andbuildingcharacteristicswhiletheFARprovidesmarketvalues,land values,andbuildingownershipinformation. WemergethesewithdataderivedfromcommunicationsbetweentheDOFandlandowners, scrapedo˙thePropertyTaxPublicAccesswebportal,whichwecalltheNoticeofPropertyValue (NPV)dataset.Itincludesinformationmailedtobuildingownersincludinggrossrevenueandcost estimatesandthenumberofrentstabilizedunits. 15 Weusethe2010DecennialCensustoallocaterentalhouseholdstobuildingstoestimatebuilding vacancies. 16 Todeterminethesizeoftherentalmarket,weusethetotalnumberofNYCrenter householdsthatareinbuildingswithfourormoreunits. 17 14 TheMDRClinksbuildingownerstoshareholdersrevealingcommonownershipacrossbuild- ings. 15 TheNPVdatasetwasoriginallyweb-scrapedbyathird-partyfromtheDOF'sProp- ertyTaxPublicAccesswebportal.Fulldetailsaboutthisprocessareavailableat http://blog.johnkrauss.com/where-is-decontrol/ . 16 Toallocaterentalhouseholds,wemultiplybuildingresidentialunitsbytheblocklevelrental occupancyrate.ThismethodassumesthatvacancyratesareuniformwithinCensusblocks. 17 The2010Censusreportsthenumberofrenterhouseholdsbutnotstrati˝edbybuildingunits, sowescalethe2010Censusvaluebytheratioofrentersin4+unitbuildingstoallrentersfromthe 2010ACS. 87 Sample Ourdataspansfrom2008to2015.Weuseallyearswhenanalyzingownershipconcen- trationbutfocuson2010fordemandestimation. Fordemandestimation,weuseallprivatebuildingsclassi˝edasmulti-familyrentalbuildingsin Manhattanwithfourormoreunits,whereallunitsareresidentialunitsandthereisnomissingdata. Whenweconstructtheinstrumentsbasedonrivalbuildingcharacteristics,detailedinSection3.6.2, weexpandthesampletoincludemixed-use,residentialrentalbuildings.Weexcludemixed-use buildingsintheestimationbecausewecannotseparatebuildingincomeduetoresidentialversus commercialtenantsources. 18 Foranalyzingrentsandownershipconcentration,weuseasubsetofourestimationsamplethat excludesbuildingsthatarezoningconstrainedorrentstabilized,whichwecalltheunconstrained sample. 19 Fortheownershipconcentrationresults,weadditionallydropbuildingswherethelisted buildingownerintheFARdatadidnotmatchtheMDRCdataandbuildingswithlessthansix units. 20 Formoredetails,seeAppendixC.3. Forcomputationandexpositionalpurposes,ourmainanalysisfocusesonbuildingsinMan- hattan.Foradditionalpowerandrobustness,weexpandoursampletoincludebuildingsfrom Brooklyn,theBronx,andQueens;weexcludeStatenIslandduetorelativelysmallnumberof multi-unitrentalbuildings. GeographicUnits WeuseCensustractsasaunitofobservationforownershipconcentrationas wellasfornestsinonespeci˝cationofourelasticityestimation.Thelargenumberoftractsprovides usgreatervariationinthedata.Inaddition,asdiscussedinAppendixC.4,ownershipconcentration ismoreeasilycalculatedatthetractlevel,afeaturewhichwillhelpusinSection3.5.Anobvious downsidetothischoiceisthatmarketsarelikelygeographicallycontinuous.Individualsatthe 18 Inthecontextofourdemandmodeldiscussedlater,wedo not pushmixed-usebuildingstothe `outside'good;instead,wesimplydonotincludethemintheestimation. 19 Speci˝cally,abuildingiszoningconstrainedifthebuildingwouldnotbeallowedtocreatean additionalunitbasedonbuilding˛oor-area-ratiosandminimumunitarearequirements,andisrent stabilizedifmorethan10%ofunitsarerentstabilized. 20 Weareabletomatchover80%ofallbuildingownersacrossyears.Wedropbuildingswith f 4 Œ 5 g unitsduetoNYCassessmentmethodologychangesforthesebuildings. 88 bordersoftractsaremorelikelytosearchatadjacenttractsthaninotherneighborhoods.Thenested logitstructureweadoptwillnotfullycapturethis,norwillourconcentrationmeasures,whichwill likelyattenuateresults.WealsouseanNYCspeci˝cgeography,NeighborhoodTabulationAreas (NTAs),thatisasub-countycollectionofCensustracts. BuildingRentalIncome For80%ofourmulti-yearsample,weusescrapeddatafromcommuni- cationsbetweenthecityandlandownersaboutbuildingincome.Fortherestofoursample,werely onpublicdataonassessmentsrecordsfromtheDOF,whichincludemethodologiesforgenerating assessmentsfrombuildingincome,thatallowsustobackoutincomefromtheassessmentdata. 21 InNYC,rentalbuildingsareassessedbasedontheirincomegeneration.TheDOFcollects annualrevenueandcostinformationforallrentalbuildingsandthenappliesastatisticalformula totranslateannualrevenueinto`marketvalue'(MV)ofthebuildingifitweresold,whichisthe basisofabuilding'staxassessment.Importantly,MVisdeterminedbyasimpleGrossIncome Multiplier(GIM)formula: MarketValue 9 SQFT 9 = GIM 9 AnnualRevenue 9 SQFT 9 Œ (3.7) wheretheGIMisdeterminedbytheDOFbasedonactualsalesinagivenincomedecilerangeand location. 22 TheDOFreportsMVandSQFTforallbuildingsintheFARdataset,andsofor80% ofthesampleweobservebothincomeandMV.Wenon-parametricallyestimatetheGIMtermas afunctionofMV/SQFT,borough,andyearbasedonDOFguidancedocuments. 23 Weassessour procedurebyusingtheestimatedGIMandreportedMVtocalculatea˝ttedincomevalueforthe matchedsample,and˝ndacorrelationof 0 Ł 99 andcoe˚cientofdeterminationof 0 Ł 98 .Formore details,seeAppendixC.5. Oncewehavebuildingincomeforallbuildings,wemustsubsetthedatatosingle-useresidential buildingsduetoourinabilitytodistinguishbetweenresidentialandcommercialincome.Wedivide 21 See nyc.gov/site/finance/taxes/property-assessments.page . 22 E˙ectively,ifabuilding'sMV/SQFTisinthe @ th quantile,thenitsAnnualRentbySQFTis alsointhatquantile,andallbuildingsinagivenquantileandlocationwillhavethesameGIM. 23 Foreachborogh-year,weestimatetheempiricalGIMwithin50quantilebinsofMV/SQFT (whichweobserveforallbuildings)andthenapplythistotheunmatchedbuildings. 89 buildingincomebythenumberofunitsforaverageannualunitrentinabuilding,andagainby twelveforaveragemonthlyrent.Alimitationofthisapproachisthatwerelyonbuildingaverages aswedonotseeindividualunitincome. OtherVariables Welinkbuildingsbasedontheirk-lot(BBL)identi˝cationthat isuniquelyassignedtorealestateparcels,withadditionalveri˝cationbasedonlotcharacteristics. 24 Thebuilding-levelcharacteristicsthatweincludearebuildingage,logmilestothecentral businessdistrict(CBD,whichwede˝neasCityHall),logmilestonearestsubwaystation,years sincethelastmajorbuildingrenovation,averageunitsquare-feet,andwhetherthebuildinghasan elevator.Wealsomeasurethenumberofresidentialbuildings,o˚cebuildings,retailbuildings,and openparksintheCensusblockgroup.Forlocationcontrolsweincludepolynomialsofbuilding latitudeandlongitudecoordinatesandincludelocation˝xede˙ects. 25 Wealsousereportedland valueofparcels,whichisconstructedbytheNYCDOFusingadatabaseofbuildingandvacant parceltransactions. Animportantlimitationofourdataistheinabilitytocontrolforunit-levelcharacteristics.We approachthisissueasanomittedvariablesissue.Inouranalysisofconcentrationchanges,building ˝xede˙ectswillbeanimportantcontrolthat,togetherwithinformationonrenovations,help uscontrolfortheseunobservables.Inourelasticityestimation,unobsevableunitcharacteristics willshowupasbuildingunobservablesandwillbeanimportantmotivationforourinstrumental variableapproach. SummaryStatistics Table3.1presentssummarystatisticsfor2010Manhattanrentalbuildings. Eachcolumnrepresentsacutofthedatathatweuse.Asexplainedabove,the˝rstisusedfor calculatingourinstruments,thesecondisusedinourestimation,thethirdisthesetofpolicy- unconstrainedorwhichwecancalculatemarkups,andthefourthisasubsetofthe policy-unconstrainedbuildingsthatare10yearsoldorlessin2010.Figure3.1plotsthetotal 24 Mostparcelscontainasinglebuilding,butlargeparcelscancontainmultiplebuildingswith openspacebetweenthem.WerefertobuildingsandBBLsinterchangeablythroughout. 25 WeuseCensustractFEsfortheRCLandNeighborhoodTabulationAreaFEsfortheRCNL. 90 numberofhouseholdsandmeanunitrentsbyCensustract.InAppendixC.3weplotadditional spatialdistributions,suchaszoningconstraintsandrentstabilization. Table3.1:SummaryStats: 2010ManhattanRentalBuildings IVSampleEstimationSampleUnconstrainedSampleNew,Unc.Sample TotalMarketShare 26.5%11.7%0.7%0.1% Res.UnitsperBuilding 25.321.120.546.3 HouseholdsperBuilding 24.920.019.443.4 VacancyRate 5.4%5.5%5.7%5.8% PercentMixed-Use 47%0%0%0% PercentRentStabilized 63%60%0%0% PercentZoningConstrained 77%80%0%0% MedianMonthlyRent * $1,309$2,071$2,247 MedianRentbyMedianIncome * 30%48%52% MedianMonthlyLandValueperUnit $2,989$2,520$5,314$2,381 YearsSinceConstruction 9495874 YearsSinceRenovation 4848354 log(DistanceCBD) 1.341.581.451.32 log(DistanceSubway) -1.94-1.89-1.96-1.72 AvgUnitSqft 7697521,135.111,339 Buildings 17,8289,48456653 Note: ThetablereportssummarystatisticsforourmainsamplesusingManhattanbuildingswith fourormoreresidentialunits.The˝rstcolumn,IVSample,includesmixed-usebuildings.The secondcolumn,EstimationSample,includesbuildingswithonlyresidentialunits.Thethird column,UnconstrainedSample,includesbuildingswithnorent-stabilizedunitsandwhichareable toaddanadditionalunitaccordingtozoningregulations.TheNew,UnconstrainedSample(last column)ishtesubsetoftheUnconstrainedSamplewhichwereconstructedbetween2001-2010. BuildingdatafromPLUTO,NPV,andFAR˝les.Marketshareisthesumoftotalhouseholds inallbuildingsbylargebuildingtotalrenterpopulationinNYC.Householdsareallocatedto buildingsbasedonbuildingunitsand2010DecennialCensusandAmericanCommunitySurvey. Thevacancyrateisoneminusthetotalhouseholdsinbuildingdividedbytotalbuildingunits.A buildingismixed-useifthebuildinghaspositivecommercialarea.Abuildingisconsideredrent stabilizedifmorethan10%ofunitsarerentstabilized.Abuildingiszoningconstrainedifthe buildingwouldnotbeallowedtocreateanadditionalunitbasedonbuilding˛oor-area-ratiosand minimumunitarearequirements.Monthlyrentalincomeisbuildingincomedividedbytotalunits dividedby12.Medianincomein2010forNYCis$50,711.Monthlylandvalueperunitis[Land Value/(12xResidentialUnits)].Yearssinceconstructionandrenovationequal2010minusthe constructionyearandmostrecentmajorrenovationyear.Geodesicdistancesareinlogmilesbased onbuilding(lat,lon)coordinates.AvgUnitSqftistotalbuildingareadividedbytotalunits.(*) Rentdataisonlyavailableforsingleusebuildings 91 Figure3.1:Distributionof2010ManhattanRenters&Rents Note: The˝guredisplaysthegeographicdistributionofhouseholdsandrentintheManhattan data.ThemapontheleftplotstotalrenterhouseholdsbyCensustractin2010.Themaponthe rightdisplaysthemeanmonthlyunitrentbyCensustractin2010.MissingvaluesareCensus tractswherewehaveinsu˚cientdata,inpartduetotheexclusionofmixed-usebuildings.Red tractsindicatehigherhouseholdsandrentsrespectively,usingalogscale.DatafromPLUTO, FAR,NPV,and2010Census. 3.5ConcentrationandRentsinNewYorkCity Wenowexaminethecorrelationinthedatabetweenownershipconcentrationandrents.We notethatresultsinthissectionarenotcausallyidenti˝ed.Nonetheless,we˝nd,reassuringlyandin linewithpredictionsofProposition2,thatincreasesinconcentrationarecorrelatedwithincreases inrents. ToexaminewhetherthedataareconsistentwiththepredictionsofProposition2,we˝rst constructownershipsharesattheCensustractlevelfrom2008to2015.Section3.4summarizes thetradeo˙softract-levelanalysis,aswellasourconstructionoftract-levelownershipdata,in tandemwithAppendixC.4.AsnotedinSection3.4,wecalculateconcentration,whichwillbea Her˝ndahl-HirschmanIndex(HHI),o˙ofthefullsampleofbuildingsineachyearbutforrents,our outcomevariable,werestrictoursampleheretounconstrainedbuildingswithmatchedownership information.Notethatoursampledi˙ersfromourestimationsampleinTable3.1becausewepool 92 eightyearsofdataandonlyusebuildingswithsixormoreunitsineachyear. 26 Summarystatistics forthissampleareavailableinTableC.1inAppendixC.3.Webeginwithourmaingeography, Manhattan,andthenextendthesampletoequivalentbuildingsinthewholeofNewYorkCityto improvepower. Usingourconstructionsofownership,wecalculatetract-levelconcentration.Let A 5Œ6ŒC be thesetofbuildingsownedbylandowner 5 intract 6 intimeperiod C ,andlet F 6ŒC bethesetof landownersinthattractandtime.Wethuscalculatelandownermarketsharesas: B 5 6ŒC : = Í 9 2A 5Œ6ŒC ˇ 9ŒC Í 5 0 2 F 6ŒC Í 9 2A 5 0 Œ6ŒC ˇ 9ŒC Ł (3.8) Figure3.2,plotstract-levelHHImeasuresforManhattan,whereHHIisthesumofsquaredowners' shares, HHI 6ŒC : = Í 5 0 2 F 6ŒC B 5 0 6ŒC 2 . TomorecloselymatchthepredictionsofProposition2,whichlinksownershipconcentration elsewheretorents,weconstructamodi˝edve-outHHIindex.Foreachlandowner 5 ,we recalculatethemarketshareofarivallandowner, ,as: ~ B 5Œ6ŒC : = Í 9 2A Œ6ŒC ˇ 9 Í 5 0 2 F : 5 6ŒC Í 9 2A 5 0 Œ6ŒC ˇ 9 Œ (3.9) where F : 5 6ŒC isthesetofrivalstolandowner 5 ,andthencalculatetheleave-outHHIforlandowner 5 asthesumoftheserivallandowners'squaredshares: HHI 5 ¹ 9 º Œ6ŒC : = Í 2 F : 5 6ŒC ~ B 5Œ6ŒC 2 . 27 Wethentestthebasicpredictionthatrentincreasesinconcentration.Ourmainspeci˝cation estimates ln » A 9Œ6ŒC ¼ = U 0 ¸ U 1 ln » HHI 5 ¹ 9 º Œ6ŒC ¼¸ U 2 - 9Œ6ŒC ¸ n 9Œ6ŒC Œ (3.10) where A 9Œ6ŒC istheaverageunitrentofbuilding 9 intract 6 attime C , HHI 5 ¹ 9 º Œ6ŒC isdescribedabove, and U 2 isavectorofcoe˚cientsoncontrols - 9Œ6ŒC .Wealsoinclude ln » B 5 ¹ 9 º 6ŒC ¼ insomespeci˝cations 26 InSection3.7ourresultsuserentalincomeforbuildingswithfouror˝veunits.Theseare obtainedusingDOFassessmentprocedureslinkingreportedmarketvaluestorentalincome.We cannotusetheseherebecauseofassessmentprocedureschangesoverthecourseofthispanelfor thisgroup. 27 InAppendixC.4,weproberobustnessusingthemorestandardconstructionofHHIandshares inEquation(3.8). 93 Figure3.2:DistributionofOwnershipConcentrationinManhattan Note: The˝gureplotsthetract-levelownershipconcentrationindex HHI 6ŒC in2008(leftmap)and 2015(rightmap)onlogscales.Redsindicatemoreconcentration.FTCHorizontalMerger Guidelinesconsidervaluesabove0.25tobehighlyconcentrated.Sampleisallresidential buildingswith4+unitsinManhattan.DatafromPLUTO,MDRC. 94 toseparatelytestfortheimpactofowners'sharesonrentsattheirownbuildings.Notethatwhile weusegeneralsubscripts f 9Œ6ŒC g for - 9Œ6ŒC ,inspeci˝cspeci˝cationssomecontrolswillbetime variant,e.g.,whenusingbuilding˝xede˙ects. Column(1)ofTable3.2Panel(A)estimatesthespeci˝cationinEquation(3.9)forManhattan buildingsusingyear˝xede˙ects,buildingage,squareofbuildingage,thelogofdistanceto nearestsubwayandthelogofdistancetotheCBD,averagesquarefeetoflivingspaceperunit,and yearssincelastrenovation.Theinclusionofyear˝xede˙ectstreatsthedataasarepeatedcross section,andsu˙ersfromclearunobservedvariablebias.Werefrainfrominterpretingthesmall andinsigni˝cantresultingcoe˚cienton HHI 5Œ6ŒC . InColumn(2)ofPanel(A),weaddtract˝xede˙ects.Here,identifyingvariationischanges overthecourseofthepanelatthetractlevel,removingunobservedtime-invarianttract-level variation.A10%increaseintractconcentrationindexisassociatedwitha1.6%increaseinrents. Thesigni˝cantcoe˚cientisconsistentwithProposition2:buildingsintractswhereownership elsewhereinthetractisconcentratingexperiencelargerincreasesinrents. Column(3)ofPanel(A),ourmoststringentspeci˝cation,furtherimposesbuilding˝xede˙ects. Here,buildingtime-consistentcontrolsdrop,thoughyearssincerenovationisanimportantcontrol thatremains.Becauseofthedi˚cultyinobservingkeybuildingcharacteristics,thisspeci˝cation ensuresthatofColumn(2)isnotidenti˝edo˙ofunobserveddi˙erencesinbuildingquality.The coe˚cientispositivebutinsigni˝cantamotivationforourinclusionofmoredatainPanel(B) below. Finally,Columns(4)-(6)introducecontrolsforbuildingowners'ownshareofthetractasa control.AccordingtoProposition2,weexpectownerswithgrowingsharesandthusmarketpower toincreaserents.AnimportantconditioninthePropositionisthatcostsbenon-decreasing,which wouldbeviolatediftherewerescaleeconomiesinownership.Acrossspeci˝cations,thecoe˚cient issmallbutnoisyandinconclusive. Becauseourmoststringentspeci˝cationsappeartolackpowerinColumns(3)and(6),we expandoursampletoincludethreemoreboroughs:theBronx,Brooklyn,andQueens(withtoo 95 fewobservationspertractinStatenIsland,wedonotincludeitinoursample).Here,coe˚cients aregenerallyinthesamedirection,andinparticular,thecoe˚cientsontractHHIinColumns (3)and(6)arenowpositive,signi˝cant,andeconomicallymeaningful,witha10%increasein concentrationagainassociatedwitharoughly1%increaseinrents. Animportantcaveatinthisanalysisistheinabilitytoobservechangingtractconditionsthat arecorrelatedwithbothrentsandownershipconcentration.Tractswithimprovingoverallneigh- borhoodqualitiesmayexperiencerisingrentsandrisingownershipconcentrationintandem.We thereforecautionagainstinterpretingthesecoe˚cientscausally,butinsteadtakereassurancefrom thestylizedfactthatincreasesinconcentrationarecorrelatedwithincreasesinrents.Weusethis stylizedfactasmotivationforouridenti˝edestimationresults. 3.6EstimatingElasticitiesandMarkups Toempiricallyassessthemonopolyforcesdescribedabove,weestimatethebuilding-level demandelasticityforManhattanrentalbuildingsin2010.Wefollowtheliteratureempirically estimatingdi˙erentiatedproductmodelswithconsumerheterogeneitybasedBerryetal.(1995) (BLP)andthecitingliterature. 28 Below,wedescribeourempiricalmodelandidenti˝cation strategy. 3.6.1RenterDemandEconometricModel Asinourtheoreticalmodel,theurbanrentalmarketismadeupofallindividualswhowillchooseto liveinarentalproperty. 29 Inourmainspeci˝cation,wedi˙erentiatethechoicesetgeographically, suchthatweconsiderallrentalpropertiesinManhattanas`inside'goodsandallrentalproperties intheotherboroughsaspartofan`outside'good. 30 WethenproberobustnessusingNYCdata 28 Inparticular,wefollowthemethodologicaladviceinDubéetal.(2012);KnittelandMetaxoglou (2014);GandhiandHoude(2018);ConlonandGortmaker(2020). 29 Ourmarketde˝nitionmaybebetterstatedas large rentalpropertiesasweonlyconsiderrental propertieswithfourormoreunits. 30 ThisisanalogousofcomparingutilityfromaManhattanpropertytotheaveragenon-Manhattan propertyforeachindividualrenter. 96 fromfourboroughsasseparatemarkets,wheretheoutsidegoodsaresmallerbuildingsinthesame borough. Weestimatetwoversionsofourmodel.ClosesttoourexpositioninSection3.2,weestimate arandomcoe˚cientslogit(RCL)model.Second,weestimatearandomcoe˚cient nested logit (RCNL)modelwherenestsareCensustracts,whichbynecessityremoveourmoststringentlocation vel˝xedtocollinearitywithourde˝nitionofbuildingnests.The RCLmodelissimplertoestimateandallowsgreaterlocationcontrols;however,theRCNLmodel allowsforwithin-nestpreferencecorrelationwithnearbybuildingsattheexpenseoflessrobust locationcontrols. Weassumethatrenter 8 'sutilityfromchoosingunit 9 iscomposedofacommonvertical di˙erentiationcomponent, ` ,andidiosyncratichorizontalcomponents, f kŒn g : * 89 = ` 9 ¸ k 89 ¸ n 89 : = X 9 ¸ - 9 V | {z } ` 9 ¸ U H 8 A 9 ¸ Õ 2 ˛ 2 f W E 8 G 9 g | {z } k 89 ¸ n 89 Ł (3.11) Equation(3.11)parameterizesutilityasafunctionofrenterincome, H ,observedcovariatesand rent, f -ŒA g ,ascalarunobservableamenity, X ,andcovariate-speci˝ctasteshifters, E .Foreaseof notation,weexpressthejointdistributionofrenterincomesandtastes, \ = ¹ HŒ f E gº ,conditional onobservedvariables, ¹ -ŒA º ,as ˙ ¹ \ º ,whichwewillde˝neempiricallywhenwedescribeour estimationroutine. Forourempiricalspeci˝cations,buildingcovariatesin - includeaconstant,age,yearssince lastrenovation,logdistancetoCBD,logdistancetonearestsubway,avgerageunitsquarefeet,and thelocationcontrolsmentionedinSection3.4,includingCensustractFEsfortheRCLandNTA FEsfortheRCNLmodels. 31 Wecalculateabuilding'smarketdemand, ˇ 9 ,astheaggregationofindividualrenterdemands, 3 89 .Undertheassumptionthat n 89 isdistributedType1ExtremeValue,theRCLmodelimpliesan 31 Forthe ˛ 2 subsetofcovariateswithrandomcoe˚cients,weuseaconstant,age,yearssince renovation,logdistancetoCBD,logdistancetonearestsubway,andavg.unitsquarefeet. 97 individualrenter'sbuildingdemandiscalculatedas: 3 89 = e ¹ ` 9 ¸ k 89 º Í : 2A e ¹ ` : ¸ k 8: º Ł (3.12) Similarly,undertheassumptionthat n 89 = ~ n 8Œ ¹ 9 º ¸¹ 1 d º ~ n 89 ,where ~ n 89 isdistributedType1 ExtremeValue,theRCNLmodelimplies: 3 89 = 3 89 j ¹ 9 º 3 8Œ ¹ 9 º = e ¹¹ ` 9 ¸ k 89 ºš¹ 1 d ºº Í : 2 ¹ 9 º e ¹¹ ` : ¸ k 8: ºš¹ 1 d ºº Í : 2 ¹ 9 º e ¹ ` : ¸ k 8: º Í 2H Í : 2 e ¹ ` : ¸ k 8: º Œ (3.13) where 3 89 j isthewithin-nestbuildingdemandand 3 8Œ isthenestdemand.Therandomvariable ~ n 8Œ introducestastevariationacrossnestsand d governspreferencecorrelationswithinnests. 32 3.6.2Identi˝cationandInstruments Therearetwoendogenousvariablesforeveryobservation:marketshareandrent. 33 Ourestimation strategyallowsustoidentifydemandparameterswhilebeingagnostictothesupplysideofthe market.Whileweobservesomebuildingamenitiesdirectly,rentsarelikelycorrelatedwith unobservedamenities, X 9 .Broadly,theseunobervablesmayeitherbeaboutbuildings'amenities orareaamenitiesnotinourdata.Toidentify U ,werequireaninstrument / ¹ A º thatshiftsrent butisunrelatedtotheseamenities.Toidentifythe W coe˚cients,werequireinstrumentsthat shiftthesubstitutionpatternsbetweenproducts, / ¹ G º .Withinstruments, / = ¹ -Œ/ ¹ G º Œ/ ¹ A º º ,the identifyingmomentconditionis E » X ¹ -ŒAŒB ; \ ºj / ¼ = 0 Œ (3.14) whichleadstoouruseof E » / 0 X ¼ astheempiricalmomentwewishtominimize. 32 Theparameterisde˝nedovertheinterval d 2» 0 Œ 1 º ,where d = 0 collapsestotheRCLmodel and d = 1 isinconsistentwithutilitymaximization.Ther.v. ~ n 8Œ isintegratedout,butcouldbe includedattheexpenseofincreasingthenumberofnon-linearparameters. 33 Weassumethatthebuilding-levelcharacteristicsareexogenousandcanadditionallyserveas instruments.Forarigorousdiscussionofidenti˝cation,seeBerryandHaile(2014,2016). 98 Weconstruct / ¹ G º usingfunctionsofrivalbuildingcharacteristics.Whencreatingtherivalset ¹ 9 º ,weexcluderivalswithina1kmradiusofagivenbuilding,basedonBayeretal.(2004)and Bayeretal.(2007) 34 FortheRCNLmodel,wealsocreate`localrivals'whoareinthesametract (i.e.,nest)butnotinthesameblockgroup.WeuseDi˙erentiationInstrumentsbased onGandhiandHoude(2018).Thesearea˝niteorderbasisfunctionapproximationoftheoptimal instrumentsinthesenseofAmemiya(1977)andChamberlain(1987).Foragivencovariate for building 9 withrivals ¹ 9 º ,eachinstrumentisde˝nedas: / DQ 9 = Õ : 2f ¹ 9 ºg ¹ G : G 9 º 2 Ł (3.15) For / ¹ A º ,weusethelandvalueofthebuildingparcel;i.e.,themarketvalueofvacantlandwhere thebuildingislocated,whichcapturestheopportunitycostofthelandownerforrentingthespace out.Theexclusionrestrictionisviolatedifconstructedlandvaluefromsalesaroundthecityare correlatedwithunobservableamenitiesatthebuilding-level,conditionalonbuildingobservables andlocationcontrols.Whileactuallandvalueingeneralmaybecorrelatedwithnearbybuilding characteristics,ourmeasureisconstructedbyNYCDOFusingsalesofsimilarparcelswhichare notnecessarilyclose.Furthermore,wecontroldirectlyforlocationobservables(whichinclude tract˝xede˙ectsinourRCLogitspeci˝cation),andassuchtheresidualmeasureshouldnotbe systematicallycorrelatedwithlocalbuilding-levelunobservableresidentialamenities.Appendix C.7describesfurtherdetailsoninstrumentconstructionandotheraspectsofestimation. Armstrong(2016)discussestheasymptoticsofdi˙erentiatedproductestimationwhenthere arefewmarketsandmanyproductsandprovidessu˚cientconditionssuchthatmarkupconverges toaconstant.Ifmarkupsconvergetoaconstant`faster'thantheinstrumentalvariablesestimator, thenthelatterisinconsistentbecausethereisnotvariationinmarkupstouse. Weaddresswiththisissueinthreeways.First,ourRCNLspeci˝cationfollowsArmstrong (2016)bysplittingproductsintonests.Armstrong(2016)showsinthissettingthatnestse˙ectively boundthenumberofrivalproductswithininanest,soneitherwithin-nestshares, ˇ 9 j ¹ 9 º ,nor 34 Theauthorsuseringsof˝veandthreemiles,respectivelyfortheirinstrumentconstruction usinghomesintheSanFranciscobayarea. 99 markupsconvergetoaconstantevenifthetotalnumberofproductsinthefullmarketgoesto in˝nity. 35 Second,weuseamarginalcostshifterin / ¹ A º thatisvalideveniftheconditionsof Armstrong(2016)hold,asthatvariationisnotduetomarkups.Third,weperformstatistical testsforunder-identi˝cationoftheinstrumentsonthemodelimpliedmarkups(Armstrong, 2014),andwealsocalculatearobust˝rststageFstatisticfromalinearregressionoftheendogenous rentsontheinstrumentvector ¹ / ¹ G º Œ/ ¹ A º º ,advocatedinArmstrong(2016). 3.6.3EstimatingMarkupsinthePresenceofSupply-SideRestrictions Whileourelasticityestimationisagnostictothesupplysideofthemarket,toderivemarkupsfrom estimateddemandelasticities,wemustaccountforhowlandownerssetrentsandquantitiesinour setting.Inparticular,ourmodelassumedlandownersare(policy-)unconstrainedintheirability tosetrentsbyadjustingsupply.Twofeaturesofoursettingareparticularlyproblematicforthis assumption:rentandquantityconstraints(throughrentstabilizationandzoning),andconstraints onquantityadjustmentsdueto˝xedredevelopmentcostsandthedurabilityofthehousingstock. Inparticular,constraintsonrentintheformofrentcontrolandrentstabilization,andconstraints onsupplyintheformofzoningrestrictionsmeanthattheobservedpricingandquantitybehaviorof aconstrainedlandownerwillnotbere˛ectiveofoptimallychosenpricesandquantities.Inaddition, themarkupsinourmodeldonotaccountforlumpyredevelopmentorthedurabilityofthehousing stock.AppendixC.2showshowourmodelcanbeextendedtoamodelwithseparateddeveloper andlandownerquantityandpricedecisions,butclari˝esthatmonopolistquantities,andthusthe abilitytoderivemarkupsfromthepriceelasticity,areonlyachievedwhendeveloperscorrectly anticipatethedemandfacedbylandowners.Inreality,˝xedcostsmaydelayredevelopmentand thedurabilityofthehousingstockmeansthatcurrentquantitiesmaynotre˛ectcurrentdemand. Weapproachtheselimitationsbysubsettingourdatatwice.First,ourmainresultsderive markupsonlyforpolicy-unconstrainedparcels,whichcouldraiserentsandadjustquantitiesun- encumberedbyzoningconstraintsorrentregulation.Second,weseparatelyexaminethe53 35 Themediannumberofbuildingspernestis32,theaverageis43,andthemaximumis195. 100 policy-unconstrainedbuildingsthatwerebuiltinthelast10yearsofour2010data,wherede- veloperswillhavebeenmorelikelytohavecorrectlyanticipatedcontemporarydemandandset monopolist-optimalquantities,accordingtoAppendixC.2. Withthoserestrictionsinmind,weturntoourmarkupcalculation. 3.6.4ElasticitiesandMarkupCalculations Usingestimatedparameters, \ ,wecancalculatebuilding-levelelasticitiesandmarkupsthatwill informourunderstandingofmonopolypowerintheManhattanmarket.Wecalculatethebuilding- leveldemandelasticitiesusingtheanalyticalderivativesofthedemandfunctions,andwecalculate thepercentmarkupassuminglandownerssolveaBertrandpricecompetitiongame: Y 9 = mˇ 9 mA 9 A 9 ˇ 9 = 8 > > > >< > > > > : h ¯ 8 U H 8 3 89 ¹ 1 3 89 º d ˙ ¹ \ º i A 9 ˇ 9 ifRCL h ¯ 8 U š H 8 1 d 3 89 1 d3 89 j ¹ 9 º ¹ 1 d º 3 89 d ˙ ¹ \ º i A 9 ˇ 9 ifRCNL (3.16) Lerner 9 = A 9 <2 9 A 9 = 1 Y 9 (3.17) Again,weuseBertrandpricingonlyforinterpretationbutnotestimation. Mosthousingdemandliteratureestimatesinelasticdemandseeminglyincompatiblewith monopolypricing(Chenetal.,2011;Albouyetal.,2016).Wereconcilethisbythefactthat therelevantelasticityforlandownersistheown-priceelasticity, Y 9 ,ratherthantheregate elasticity,thechangeintotalhousingconsumedwithachangein(aggregate)rents.Toconnectour settingtoprevioushousingdemandestimates,wecalculatetheaggregateelasticitywhichprovides theresponsivenessofrenterstoa1%increaseinrentforall`inside'buildings(BerryandJia,2010; ConlonandGortmaker,2019): Y Agg = Õ : 2A ˇ 9 ¹f A : ¸ A : g : 2J º ˇ 9 1% Ł (3.18) Foreshadowingresults,wewill˝ndbothmonopoly-consistentelasticities Y 9 aswellasliterature- consistentinealisticaggregateelasticity Y Agg . 101 3.6.5EstimationRoutine Herewebrie˛ydescribeourestimationalgorithm.Weareguidedbymethodologicalreviews (Nevo,2000;KnittelandMetaxoglou,2014;ConlonandGortmaker,2020)andpointinterested readerstoAppendicesC.6,C.7,andC.8foradditionaldetails. Weestimatetheeconometricmodelusingmarket-levelvariablesonbuildingchoiceshares, rents,andcharacteristics, f ˇ 9 ŒA 9 Œ- 9 g .Wesimulate ' rentersbydrawing ¹ H 8 Œ ® E 8 º tocalculatethe individualdemands,andthenusepseudoMonteCarlointegrationtocalculatemarketdemand. 36 Estimationhasfoursteps,whichareiterateduntilparametersconverge. 37 First ,anon- linearinversionstep˝ndsmeanproductutility, ` ,givenaninitialsetofnon-linearparameters, i = ¹ UŒWŒd º . 38 Second ,weuselinearGMMtoestimatemeanutilityparameters, V ,which identifytheunobservedmeanutilitycharacteristic, X . Third ,weuseanon-linearminimization routinetoestimatethenon-linearparametersusingthemomentcondition E » / 0 X ¼ . Fourth ,we updatetheweightmatrixusingtheresidualsfromStep3,andrepeatuntiltheparametervector converges, k i B ¸ 1 i B kˇ 0 . 3.7EstimationResults Inthissection,wereportourmainresultsforManhattanandasarobustnesscheckasimilar modelusingManhattan,theBronx,Brooklyn,andQueensasfourseparatemarkets. 3.7.1ResultsusingManhattan Table3.3presentsourmainempiricalresultsforManhattan.Weestimateutilityparametersbased onourempiricalmodel,thencalculatebuilding-levelelasticities.Fortheunconstrainedsubset 36 WeuseHaltonsequencestoapproximateuniformrandomdraws.Incomeissimulatedbyusing alognormaldistributionwithmeanandvariancebasedontheACS2010˝le. 37 In˝nitesamplesthe2-Stepparametersdependontheinitialweightmatrixandcanbesubject togreatermisspeci˝cationerrors,leadingustouseanIteratedGMMapproach(HansenandLee, 2019). 38 Fortheinversion,weuseatoleranceof k ` A ¸ 1 9 ` A 9 k 1 10 12 .SeeAppendixC.6formore details. 102 ofoursampleaswellasthesubsample,wethencalculatethemarkupshareofrent.We presentboththeLogitandNestedLogitmodels,bothestimatedviaIGMMandusing Di˙erentiationInstruments,asdescribedinSection3.6.2.Ofourestimatedparameters,weonly presentourestimatesof f UŒd g andtheirheteroskedasticyrobuststandarderrors.UsingEquation (3.16)wecalculatetheown-priceelasticity,Equation(3.17)themarkupshareornerindex, andEquation(3.18)theaggregateelasticity. The˝rstfourrowsofTable3.3reportourestimatesofmodelparameters U and d ,withstandard errorsinparentheses.Ourestimatesoftherentcoe˚cient, ^ U ,aresimilarinmagnitudebetweenthe modelswithroughlyequalstandarderrors.Ourestimate ^ d isclosebutstatisticallydi˙erentfrom zeroimplyingonlyslightlygreaterwithin-nestcorrelationrelativetotheRCLmodel.Forthefull sample,weestimatemedianown-priceelasticitiesof 2 Ł 99 and 3 Ł 16 forLogitandNestedLogit speci˝cations,respectively.WecalculatebutdonotinterprettheLernerindexforthissample. Themodelimpliedbuilding-levelown-priceelasticitiesareallelastic,whichisconsistentwith monopolypricing. Fortheunconstrainedbuildings,the˝rstsubsetforwhichwewill˝ndmeaningfulmarkup results,we˝ndelasticitiesof 3 Ł 40 and 3 Ł 30 ,respectively.Weexpecttheseunconstrained landownershavethemostcontrolovertheirrentscomparedtolandownerswithrent-stabilized unitsorpressedagainstzoningconstraints.Forthesecondsubset,unconstrainedbuildings builtbetween2000-2010,we˝ndelasticitiesof 3 Ł 48 and 3 Ł 31 . We˝ndthatthemedianmarkupshareoftotalrent,theLernerindex,isbetween32-33%of totalrentforthefullsample,withaslightlygreatermean(33-35%).Fortheunconstrainedsamples themedianandmeanmarkupsharesarebetween29%and31%.Amongthenewconstructions subsetofunconstrained,meansandmediansrangefrom29-32%.Overall,wereunitspricedat themarginalcostre˛ectiveoftheproductionandmaintenanceofbuildings,wewouldexpectrents tobeabout70%oftheircurrentlevels.Figure3.3plotsthefulldistributionoftheown-price elasticitiesandLernerIndexbybuildingforallthreesamplesandboththeRCandRCNLmodels. Allthreesamplesofthenestedlogitmodel,drawninthinnerlines,arelessdispersed.Figure3.4 103 plotsthemeanown-priceelasticityandthedollarvalueofmarkupsinmonthlyrentbyCensustract forthefullsampleonly. Again,wenotethatourresultsdi˙erfromtheliteratureontheelasticityofhousingdemand. Ourelasticityofinterestisconceptuallydi˙erentthanthattargetedbythatliterature,whichseeksto measurethesubstitutionbetweenquantityofhousingandconsumption.Inthatliterature,housing demandistypicallyfoundtobeinelastic.Whenweestimatetheaggregateelasticityinourdata, whichismoreakintotheparameterestimatedinthepriorhousingdemandliterature,we˝nd similarlyinelasticdemandwithanelasticityisbetween ¹ 0 Ł 14 Œ 0 Ł 16 º .Thisestimateisslightly lowerthantheconsensusrangeinthepriorliterature: ¹ 0 Ł 64 Œ 0 Ł 3 º (Albouyetal.,2016).This maybeduetoadi˙erencesinsetting(Manhattanrentalmarkets)orinmethodologyasouroutside goodincludesotherhousingchoicesinNYCratherthanpureconsumption. 3.7.2ResultsforManhattan,theBronx,Brooklyn,andQueens Inthissubsection,wereportresultsusingallfourNYCboroughsforwhichwehaveadequatedata, usingeachasaseparatemarket.OurestimationbroadlyfollowsthatforManhattanwithsome necessarychanges.First,forcomputationalreasons,werun2-stepratherthaniteratedGMM. Second,withfourmarkets,wede˝netheoutsideoptionassmaller1-3unitNYCbuildings.As withManhattan,werunbothRCandRCNLmodels.AppendixC.9providesmoredetailsonthis robustnesscheckandreportssummarystatisticsbyborough. Table3.4reportsthemodels'parameterestimatesandTable3.5reportsborough-levelelasticities andmarkups.Againnearlyallbuildingelasticitiesareestimatedasbeingconsistentwithmonopoly pricing.AverageelasticitiesandmarkupsforManhattanareinlinewiththosereportedinSection 3.7.1.Markupsinotherboroughsvarybetween20-30%. 3.8Up-Zoning'sSpilloverE˙ectsThroughMonopolyPower Inthissection,weuseourdataandtheresultsofourmodeltoquantifythepotentiale˙ects looseningzoningrestriction.Inoursetting,additionalcompetitionfromup-zoningputsdownward 104 Figure3.3:DistributionofResults (a)Own-PriceElasticity (b)MarkupasaPercentofRent Note: The˝gureplotsthekerneldensityplotofown-priceelasticities(Panel(a))andmarkups (Panel(b),LernerIndex),formainresultsusingManhattanbuildings.Thinlinesplotresults fromRandomCoe˚cientNestedLogitmodel.ThickerlinesplotresultsfromRandomCoe˚cient model.Orangedashedandredlong-dashedlinesplotelasticitiesandmarkupsforthefullsample. Purpleshort-dashedandnavydot-dashedlinesplotresultsfortheunconstrainedsample.Green andblacksolidlinesplotresultsforthenewandunconstrainedsample.ResultsbasedonTable3.3. ThefullsampleiscomprisedofallManhattansingle-useresidentialbuildingswithfourormore units.Theunconstrainedsampleiscomprisedofallbuildingsinthefullsamplethatarenotzoning constrainedandwhereunitsarenotrentstabilized.Thenewandunconstrainedsampleisthesubset oftheunconstrainedsampleforwhichbuildingsare10yearsoldorless.TheverticallineinPanel (a)indicateselasticitiesgreaterthan-1,whichwouldbeincompatiblewithmonopolisticpricing. RCLandRCNLmodelsandestimationaredescribedinthetext. pressureontherentsofpolicy-unconstrainedbuildings.Bycontrast,werepolicy-unconstrained buildingstobepricedatmarginalcost(e.g.,iftherewasnomarkupinrent),thenwewouldnot expectalooseningofzoningconstraintsin other buildingstoa˙ectrentsofalreadyunconstrained buildings,exceptingchangesinmarginalcost. Toillustrateandquantifytherente˙ectofup-zoningconstrainedbuildingsonpolicy-unconstrained buildings,weusethemodel-estimatedelasticitiestoexaminethee˙ectofamarginalchangein zoningintheformofa1%across-the-boardreductioninzoningquantityconstraints.Theprice e˙ectthatweestimateisthechangeinmonopolymarkupsforthe566unconstrainedbuildings givenamarginalreductioninzoningconstraintsforthesetof3,226zoning-constrained,non-rent 105 Figure3.4:ResultsforManhattan (a)Own-PriceElasticity (b)MonthlyMarkupinRent Note: The˝gureplotsCensustractlevelaverageown-priceelasticitiesinPanel(a)andmonthly markups(LernerIndex)inPanel(b)fortheRCLmodel(left)andtheRCNLmodel(right).Reds indicatehigherown-priceelasticitiesandmarkupsonalogscale.Resultsbasedarebasedonthe FullSampleestimationpresentedinTable3.3,whichuseall2010Manhattansingle-useresidential buildingswithfourormoreunits.MissingvaluesareCensustractswherewehaveinsu˚cient data,inpartduetotheexclusionofmixed-usebuildings.RCLandRCNLmodelsandestimation aredescribedinthetext. regulatedresidentialbuildings. 39 Weconsideramarginalchangeinconstraintsratherthanafullcounterfactualwithchangesin actualnumbersofwholeunitsforspeci˝cbuildings.Forexample,aone-unitchangefor˝ve-unit buildingsisa20%changeindemand,andsuchnon-marginalchangeswouldrequirere-solving themonopolistproblem.Wealsoassumemarginalcostisconstantatunconstrainedbuildings. Increasesinmarginalcostswoulddampenthepositivequantityandnegativepricee˙ectswe˝nd. 39 Weexcluderentstabilizedbuildingswhereestimatedown-priceelasticitiesmaynotre˛ect rentsofadditionalunitsonthemargin. 106 Inlightoftheseconstraintsonourexercise,weviewthisexerciseasanillustrationoftheinteractions betweenzoningconstraintsandmonopolyrentsratherthanapolicyevaluation. Weimplementtheexerciseasfollows. First ,weusetheestimatedown-priceelasticitiesto calculatethepercentchangeinrentsrequiredtoincreasethemarketshareofallzoning-constrained buildingsby1%, f % A cf : g : 2Z . Second ,wetotallydi˙erentiatethemonopolypricingrulewith respecttoallrentsandsolveforagivenunconstrainedbuilding'srentchange, f % A cf 9 g 9 2U . Third , wemanipulatethesolutionforanelasticityrepresentationthatyields: % A cf 9 = Õ : 2fZg 8 > >< > > : o 9 : % A cf : Y 9 o 9 9 9 > >= > > ; Œ (3.19) where Y istheown-priceelasticityand o 9 : = mY 9 mA : A : Y 9 .SeeAppendixC.10foracompletederivation. Wealsocalculatethechangeindemandforunconstrainedbuildingsfromthepriceandquantity changeatconstrainedbuildings: % ˇ cf 9 = Y 9 % A cf 9 .Thistellsusthe˝rstordere˙ectsofthe increasedcompetitionforresidencesontheoverallquantityofspaceprovided.Notethatweexclude cross-priceelasticitiesbetweenpolicy-unconstrainedbuildings,aswellashigher-ordere˙ectson allconstrainedplots.Totheextentthatthesearenegative,ourestimatesarealowerboundonthe result. Table3.6presentsourresults.We˝ndthattheRCLogitandRCNestedLogityieldroughly similarresultsinaggregate.A1%looseningofzoningconstraintsforrivalbuildingsleadstoa meanmarkup decrease of$7.41and$6.72perunitfortheRCLandRCNLmodels,respectively,on unconstrainedbuildings.Theseareover10%ofthe˝rst-orderpricee˙ectsonthedirectly-impacted units.We˝ndsmallmeanelasticitiesof 0 Ł 017 and 0 Ł 012 ,respectively.Looseningthezoning constraintsby1%wouldyieldadirectincreaseofabout417householdsandthespillovere˙ects fromincreasedcompetitionwouldadd19and5 additional householdsthroughlowerrentsforthe theRCLandRCNLmodels,respectively0.16%and0.04%increaseattheunconstrainedplots. Altogether,weinterprettheseresultsasadditionalrationalesforeasingresidentialzoning restrictions.Withoutmonopolypower,onlychangesinmarginalcostwoulda˙ectrent.Theprice e˙ectwecalculaterepresents additional downwardpressureonrentsthatarisespurelythrough 107 themonopolyforcesinthemodel.Inaddition,theseresultsimplythatatleastpartofthelarge equilibriummarkupsonunconstrainedparcelswe˝ndinourestimationmaybearesultofspillovers from(thenumerous)zoning-constrainedparcels. 3.9Conclusion Whileprevioushousingandurbanliteratureshaveconsideredthescopeformonopolypower, webelievewearethe˝rsttoquantifyitsimportanceinurbanrentalmarkets,˝ndingthatitsscope appearseconomicallysigni˝cantandpolicyrelevant.We˝ndthata10%increaseinCensustract levelownershipconcentrationcorrelatestoroughlya1%increaseinbuildingrents,andthatin Manhattanmarkupsaccountfor30%ofrents. Second,weexplorethelinkbetweenmonopolypricingandurbanpolicies,speci˝callyzoning constraints.Weshowthetheoreticallinkbetweenzoningconstraintsandmonopolymarkupsand quantifytherelationshipinourestimation,˝ndingmodestbutappreciablespillovere˙ects. Lastly,wecautionthatanimportantaspectoftheresidentialrealestatemarketbeyondthescope ofthispaperisthedecisionoflandownerstoenterandexitthemarket.Wehavehighlightedthe existenceofmonopolypricingpowerandthecomplexinteractionbetweenthatandurbanpolicies. However,monopolypro˝tsfromrenting,andthusurbanpoliciesa˙ectingthosepro˝ts,impact entryandexitdecisions.Policieswhichimpactthosemarkupswilllikelyimpactthesizeofthe rentalmarket. 108 Table3.2:TheRelationshipBetweenOwnershipConcentrationandRent (1)(2)(3)(4)(5)(6) ln » Averager 9Œ6ŒC ] Panel(A):Manhattan ln » HHI 5 ¹ 9 º Œ6ŒC ¼ -0.0120.1610.0750.0090.1620.075 (0.032)(0.080)(0.076)(0.038)(0.076)(0.076) ln » B 5 ¹ 9 º 6ŒC ¼ -0.0280.002-0.013 (0.026)(0.025)(0.027) YearFEsYYYYYY TractFEsNYNNYN BuildingFEsNNYNNY Observations2,5192,5042,3932,5192,5042,393 ' 2 0.290.630.750.290.630.75 Panel(B):Bronx,Brooklyn,Manhattan,Queens ln » HHI 5 ¹ 9 º Œ6ŒC ¼ 0.0470.1220.1020.0430.1280.095 (0.016)(0.056)(0.037)(0.018)(0.053)(0.037) ln » B 5 ¹ 9 º 6ŒC ¼ 0.0060.006-0.027 (0.013)(0.012)(0.014) Borough-YearFEsYNNYNN TractandYearFEsNYNNYN BuildingandYearFEsNNYNNY Observations13,65113,57612,74313,65113,57612,743 ' 2 0.400.640.770.400.640.77 Note :Thetablereportstheresultsfromregressionsoflogofbuildingaverageunitmonthly rentonthelogofthe`leave-out'HHIindex,calculatedatthebuildinglevelbyleavingoutthe buildingowner'sunits.Regressionsareatthebuilding-yearlevelandareweightedbybuilding units.Columns(4)-(6)addlogofbuildingowner'smarketshareasacontrol.Thesamplein Panel(A)areallmatched,unconstrainedbuildingsinManhattan;Panel(B)expandsthesampleto allmatched,unconstrainedbuildingsinNYC.Columns(1)and(3)inPanel(A)useyear/Panel (B)borough-year˝xede˙ects,runningarepeatedcross-section.Columns(2)and(4)include tractandyear˝xede˙ects,runningapanelatthetractlevel.Columns(3)and(6),ourmost stringentspeci˝cations,includebuildingandyear˝xede˙ects,exploringvariationintract-level concentrationwhilecontrollingforbuilding-level,time-invariantdi˙erences.Buildingcontrolsfor allcolumnsincludebuildingage,agesquared,yearssincerenovation,indicatorifbuildinghasan elevator;forcolumns(1,2,4,5)logdistancetoCBDandlogdistancetoclosestsubway(omittedin columns(3,6)duetobuildingFEs.Standarderrorsinparenthesesareclusteredtwowaysbytract andyear. 109 Table3.3:MainEstimationResults:Manhattan RCLogitRCNestedLogit U -43.79-34.80 (11.66)(11.96) d 0.065 (0.037) FullSample Mean Y 9 -2.95-3.09 Median Y 9 -2.99-3.16 MeanLerner 9 35%33% MedianLerner 9 33%32% Percent Y 9 1 100%100% Y Agg -0.16-0.14 # 9,4849,484 Policy-UnconstrainedSample Mean Y 9 -3.36-3.31 Median Y 9 -3.40-3.30 MeanLerner 9 31%30% MedianLerner 9 29%30% # 566566 New,Policy-UnconstrainedSample Mean Y 9 -3.35-3.29 Median Y 9 -3.48-3.31 MeanLerner 9 32%31% MedianLerner 9 29%30% # 5353 BLPFStat42.724.9 LinearFStat94.249.9 GMMObj10.336.3 Note: ThetabledisplaysresultsfromtheRandomCoe˚cientLogit(RCL)andRandomCoe˚- cientNestedLogit(RCNL)modelsusingdataonManhattanmulti-unit(fourormore)residential buildings.NestsforRCNLareCensustracts.Thecoe˚cient U correspondstothemarginal utilityofconsumptionand d governswithin-nestpreferencecorrelations.Bothmodelsinclude randomcoe˚cientsareonaconstant,age,logdistancetoCBD,logdistancetonearestsubway, avgunitsqft.RCLusesCensustract˝xede˙ects(FEs),andRCNLusesNYCNTAFEsplus additionallocationcontrols:measuresresidentialbuildings,commercialbuildings,andparksin Censusblock-groupandpolynomialsoflatitudeandlongitudecoordinates.Bothmodelsestimated usingGMManduseDi˙erentiationInstrumentsbasedonGandhiandHoude(2018), asdescribedinSection3.6.2.Theown-priceelasticityis Y 9 ,theLernerindexis 1 š Y 9 ,andthe aggregatepriceelasticity, Y Agg ,isbasedonBerryandJia(2010).Buildingsare`unconstrained'if not rentstabilizedand not zoning-constrained;newbuildingswerebuiltafter2000.TheRobustF statisticsarefromonregressionsofbuildingrentonbuildingcharacteristics,locationcontrols,and instruments.TheBLP-Fstatistictestsidenti˝cationofdi˙erentiationIVsfortheRCmodelandis basedonArmstrong(2014).Standarderrorsinparenthesesarerobusttoheteroskedasticity. 110 Table3.4:ModelParameterEstimatesforFourNYCBoroughs RCLogitRCNestedLogit U -27.80-23.74 (13.97)(4.23) d 0.069 (0.043) BLPFStat88.032.4 LinearFStat111.6121.9 Note: ThetablepresentsresultsfortheRandomCoe˚cientLogit(RCLogit,RCL)andRandom Coe˚cientNestedLogit(RCNestedLogit,RCNL)estimationsusingManhattan,theBronx, Queens,andBrooklynasfourseparatemarkets.Thecoe˚cient U correspondstothemarginal utilityofconsumptionand d governswithin-nestpreferencecorrelations.Bothmodelsinclude randomcoe˚cientsareonaconstant,age,logdistancetoCBD,logdistancetonearestsubway, averageunitsquarefeet,andbuildingcontrolsdescribedinthetext.TheRCLmodelusesCensus Tract˝xede˙ects(FEs)andtheRCNLusesNYCNTAFEsandadditionallocationcontrols describedinthetext.BothmodelsuseraticDi˙erentiationInstrumentsbasedonGandhi andHoude(2018),asdescribedinSection3.6.2.BothmodelsareestimatedusingTwo-Step E˚cientGMMduetocomputationconstraints.TheRobustFstatisticsarefromonregressionsof buildingrentonbuildingcharacteristics,locationcontrols,andinstruments.TheBLP-Fstatistic testsidenti˝cationofdi˙erentiationIVsfortheRCmodelandisbasedonArmstrong(2014). Standarderrorsrobusttoheteroskedasticityareinparentheses. 111 Table3.5:EstimationResults:FourNYCBoroughs ManhattanTheBronxBrooklynQueens (1)(2)(3)(4)(5)(6)(7)(8) RCLRCNLRCLRCNLRCLRCNLRCLRCNL FullSample Mean Y 9 -3.67-3.41-5.10-4.67-4.40-4.08-3.49-3.28 Median Y 9 -3.76-3.54-5.17-4.75-4.50-4.17-3.54-3.33 MeanLerner 9 28%30%20%21%23%25%29%31% MedianLerner 9 27%28%19%21%22%24%29%30% Percent Y 9 1 99.9%99.9%99.9%99.9%99.9%99.9%99.9%99.9% # 9,4849,4847,1287,12826,13626,13610,57310,573 Policy-UnconstrainedSample Mean Y 9 -3.75-3.32-4.94-4.60-4.27-3.98-3.51-3.32 Median Y 9 -3.77-3.36-4.99-4.67-4.39-4.07-3.55-3.36 MeanLerner 9 27%30%20%22%24%25%29%26% MedianLerner 9 27%30%20%21%23%25%28%25% # 5665664084083,4573,457784784 New,Policy-UnconstrainedSample Mean Y 9 -3.54-3.35-4.80-4.44-4.01-3.78-3.54-3.35 Median Y 9 -3.58-3.38-4.92-4.59-4.05-3.78-3.58-3.38 MeanLerner 9 28%30%21%23%26%27%28%30% MedianLerner 9 28%30%20%22%25%26%28%30% # 53533232261261159159 Note: ThetablepresentsresultsfortheRandomCoe˚cientLogit(RCLogit,RCL)andRandom Coe˚cientNestedLogit(RCNestedLogit,RCNL)estimationsusingManhattan,theBronx, Queens,andBrooklynasfourseparatemarkets.Bothmodelsincluderandomcoe˚cientsareona constant,age,logdistancetoCBD,logdistancetonearestsubway,avgerageunitsquarefeet,and buildingcontrolsdescribedinthetext.TheRCLmodelusesCensusTract˝xede˙ects(FEs)and theRCNLusesNYCNTAFEsandadditionallocationcontrolsdescribedinthetext.Bothmodels useDi˙erentiationInstrumentsbasedonGandhiandHoude(2018),asdescribedin Section3.6.2.BothmodelsareestimatedusingTwo-StepE˚cientGMMduetocomputation constraints. Y 9 istheown-priceelasticityandtheLernerindexis 1 š Y 9 .Samplede˝nitions follow,byborough,thoseinTable3.3;buildingsare`unconstrained'if not rentstabilizedand not zoning-constrained;newbuildingswerebuiltafter2000. 112 Table3.6:SpilloverE˙ectsfromUp-ZoningManhattanBuildings RCLRCNL DirectPriceE˙ectofLooserZoning: E h d A cf : i -$59.64-$58.55 SpilloverMarkupE˙ectofLooserZoning: E h d A cf 9 j d <2 9 = 0 i -$7.41-$6.72 ImpliedSpilloverZoningElasticity: E " d A cf 9 A 9 š d ˇ cf : ˇ : # -0.017-0.012 NetIncreaseinHouseholds DirectandSpillover436421 SpilloverOnly195 Note: Thetablereportsthee˙ectsofup-zoningzoningconstrainedbuildingsthatarenotrent stabilizedbyamarginalamount;i.e.,a1%increaseinallowablequantity,whichcorrespondsto atotaladditionof417wholeunits.ResultsarepresentedseparatelyfortheRandomCoe˚cient Logit(RCL)andRandomCoe˚cientNestedLogit(RCNL)modelsdescribedinthetext. E h d A cf : i isthe˝rst-orderaverageannualpricee˙ectonbuildings : intheset Z of3,226directlyimpacted buildings. E h d A cf 9 j d <2 9 = 0 i istheaveragee˙ectonannualrentsonthezoningunconstrained buildings 9 intheset U of566non-zoningconstrained,non-rentregulatedbuildings,assuming constantmarginalcosts.Thisnumberdoesnotincludecross-pricee˙ectsbetweenbuildings 9 2U orotherhigherordere˙ects.Theimpliedspilloverelasticityistheaveragepercentchangeinannual rentsatbuildings 9 2U givena1%increaseinmaximumquantityallowedatbuildings : 2Z . Formoredetails,seeAppendixC.10. 113 APPENDICES 114 APPENDIXA APPENDIXTOCHAPTERONE A.1TheoryAppendix Inthisappendix,Idescribeadditionaltheoreticaldetailsofthemodelinthemaintextaswellas considertwotheoreticalextensions.First,Ipresenttheparametersforthenumericalcomparative staticsfromFigure1.3anddescribehowwelfareiscalculatedwithinthemodel.Second,Ipresent theequilibriumconditionsthatleadtothethemanytypemodelthatisusedintheempirical exercises.Addingadditionaltypesoflaborinthiscontextisrelativelysimpleduetothesymmetry ofthemodelingassumptions.Next,Ireturntothetwoskillmodelbutnowthehighskillworkeris abletoswitchbetweensectors.Thisextensionisessentiallyasimpli˝edversionofSaez(2002)with endogenouswages.Finally,inthetwoskillmodel,Iallowfortwoconsumptiongoodsproducing industriesthatemploybothhighandlowskillworkers.Thisextensionessentially`stacks'the equilibriumconditionsusedinthesingleindustrymodelinthemaintext. A.1.1IncidenceValueComparison Here,Icomparethegrosswageincidencefromaonepercenttaxchange 1 betweenPEandGEand acrosslabormarketelasticities.Iuseequation1.15forthePEincidenceandIuseequation1.17 fortheGEincidence.Themaintakeawayisthattheincidencee˙ectmagnitudedependsprimarily onthelaborsubstitutionelasticity, d ,andthecostshareofthesubsidizedmarket, B ! 0 . InTableA.1,Ipresentincidencevaluesforvariousparameterpairings.Iusethefollowing baselineparameters: Y ! 0 Œ 0 = Y ! 0 Œ 1 = 0 Ł 75 , Y ! 1 Œ 0 = Y ! 1 Œ 1 = 0 Ł 6 ,and Y = 1 ,basedonRothstein(2010), EissaandHoynes(2004),andGoolsbee(1998),respectively.FortheelasticityofsubstitutionIuse d 2f 0 Ł 3 Œ 1 Œ 2 g ,basedonRothstein(2010),myempiricalanalysispresentedlater( d = 2 ),and 1 ThatisIplot ^ F 0 š¹ \ 0 Œ 1 ^ g º ,sothattheseresultsarenota˙ectedbytheshareofeligibleworkers withinaskilllevel. 115 anintermediatevalue.Iset B ! = 0 Ł 66 basedontheapproximate1990slaborshareofinputcosts. Iset B ! 0 = 0 Ł 125 and B ! 1 = 0 Ł 66 B ! 0 ,basedonthe1992MarchCPSandmyowncalculations. Forthe˝rsttwopanelsIassumethatonlythelowwagemarketissubsidized ^ g 1 Œ 1 š ^ g 0 Œ 1 = 0 ,but inthethirdpanelIallowforasmallersubsidyonthehighwageworkers, ^ g 1 Œ 1 š ^ g 0 Œ 1 ¡ 0 . TableA.1:Summary: PercentChangeinGrossWageforLowWageMarket from 1% SubsidyIncrease PartialEquilibriumGeneralEquilibrium UsingBaselineSupplyElasticities d = 0 Ł 3 -0.714-0.645 d = 1 -0.429-0.390 d = 2 -0.273-0.252 OtherElasticitieswith d = 2 Y ! 0 = 1 Ł 0 -0.333-0.269 Y ! 1 = 0 Ł 3 -0.273-0.254 Y ! 1 = 0 Ł 9 -0.273-0.251 Y = 2 -0.273-0.249 Allowing ^ g 1 Œ 1 ¡ 0 with d = 2 ^ g 1 Œ 1 ^ g 0 Œ 1 = 0 Ł 1 -0.273-0.240 ^ g 1 Œ 1 ^ g 0 Œ 1 = 0 Ł 2 -0.273-0.228 Baseline: Y ! 0 = 0 Ł 75 ŒY ! 1 = 0 Ł 6 ŒY = 1 Œ ^ g 1 Œ 1 ^ g 0 Œ 1 = 0 .Incidenceresultscomputedat B ! 0 = 0 Ł 125 ŒB ! = 0 Ł 66 . TableA.1showsthatthegeneralequilibriumincidencealwaysattenuatesthePEincidence, especiallyasmarketsizegrows.Theresultshighlightthatthelaborsubstitutionelasticityappears todictatethemagnitudeoftheincidencee˙ect.Usingthevalue d = 0 Ł 3 fromRothstein(2010) impliesaPEincidenceof 0 Ł 71% whilea d = 2 impliesonlya 0 Ł 25% changeingrosswages. Figure1.3isagraphicalrepresentationofTableA.1.Iplotthepartialandgeneralequilibrium incidenceofthegrosswageatdi˙erentlaborcostshares( B ! 0 2» 0 Œ 1 ¼ )anddi˙erentsubstitution elasticities.The˛atlinesarethePEincidenceandtheupwardslopinglinesaretheGEincidence. ThegraphicalrepresentationshowsthatasmoreworkersaresubsidizedtheGEincidencee˙ects canquicklydivergefromthePEe˙ects. 116 A.1.2Welfare Here,Idescribethemeasureofwelfareinthemodelandchangesduetotaxpolicy. Forthissection,Iadjustthenotation.Let 8 2N indexeachspeci˝cworker: 8 = ¹ 4 8 Œ2 8 Œa 8 º .Let eachworkerhavesomenon-laborincome, < 8 .Leteachworkerownsomeshareofthe˝rmsinthe economy, e 8 2» 0 Œ 1 ¼ ,suchthat Í 8 2N e 8 = 1 . A.1.2.1Welfare Totalwelfareintheeconomyisthesumofutilitygiventheoptimaldecisionsbyworkersand˝rms. IntermsofChetty(2009),withanaddedcapitalrevenueequation, 2 themodelisthefollowing: Utility : * ¹ -Œ! ; a º = - ¸ a ! (A.1) TaxFunction : ) 8 ¹ F!Œ< º = ¹ F ¸ g 8 º ! 1 8 ¹ 1 ! º = 8 (A.2) CapitalRevenue : ' = ¹ 9 ¹ A b 9 º : 9 d 9 (A.3) BudgetSet : - ¸ ) 8 ¹ F!Œ< º F! < 0 (A.4) Thus,aggregatewelfarewithaUtilitarianSWFisaggregateconsumptionplustheutilitycostof laborforthosethatwork: , = ¹ 8 a 8 d 8 ¸ ¹ 8 ¹ ) 8 º d 8 (A.5) = ¹ 8 ¹ ¹ F 8 ! 8 ) 8 º¸ a 8 ¹ ! 8 º¸ e 8 ' º d 8 ¸ ¹ 8 ¹ ) 8 º d 8 (A.6) = ¹ 8 ¹ ¹ F 8 ! 8 º¸¹ a 8 ! 8 º¸ e 8 ' º d 8 Ł (A.7) A.1.2.2WelfareChanges Thechangeinwelfarefortheeconomyisdeterminedbytotallydi˙erentiatingtheaggregatewelfare measure.Ifollowthemethodsspeci˝edinChetty(2009)andKleven(2018).Thatis,Itotally 2 Recallthateachworkerhassome e a 2¹ 0 Œ 1 º shareofcapitalrevenueaspartofunearned incomethatistakenasgiveninthelaborsupplychoice. 117 di˙erentiateequationA.6holdingunemploymentbene˝tsconstantbutadjustingthelumpsumtax to˝nancethesubsidyincrease(andrecallthat g 8 = d g 8 = 0 if ¹ 4 8 Œ2 8 º < ¹ 0 Œ 1 º ): d , GE = ¹ 8 ¹ d F 8 ¸ d g 8 º ! 8 ¸¹ F 8 ¸ g 8 1 8 º d ! 8 ¸ ma 8 m! 8 d ! 8 ¸ e 8 d ' d = 8 d 8 ¸ ¹ 8 ¹ d g 8 ! 8 ¹ g 8 1 8 º d ! 8 ¸ d = 8 º d 8 (A.8) = ¹ 8 ¹ ¹ d F 8 º ! 8 ¸ e 8 d ' º d 8 ¸ ¹ 8 ¹ ¹ g 8 1 8 º d ! 8 º d 8 (A.9) = ¹ 8 ¹ ¹ g 8 1 8 º d ! 8 º d 8 = ¹ 8 ¹ g 8 1 8 º Y ! 8 ¹ d F 8 ¸ d g 8 º d 8 (A.10) = ¹ 8 ¹ g 8 1 8 º Y ! 8 ¹¹ 1 ¸ W 8 º d g 8 ¸ 8 º d 8 Ł (A.11) FromequationA.8toA.9,Iusetheenvelopeconditiontoremove ma 8 m! 8 ;fromA.9toA.10,I usethezeropro˝tconditiontoshowthat d ' = ¯ 8 ¹ ¹ d F 8 º ! 8 º d 8 ;andfromA.10toA.11,Iusethe incidenceresulttocharacterizetheexterintermsofelasticities(Hendren,2016a; Kleven,2018).Thewelfaremeasure'snegativesignbecausethebehavioral˝scalexternalityimplies thatthegovernmentispayingmoresubsidiesduetotheextensivemarginresponse.However,if d ! 8 ¡ 0 ,thenthegovernmentisalsopayinglessinunemploymentbene˝ts,asempiricallyshown inBastianandMichelmore(2018). Theabovesupposesthatlumpsumtaxationisused,sothefactthatwagesriseforotherworkers isnotpartofthe˝scalexternality;i.e.,thefactthatgreaterearningslessentheneedtochange thelumpsumtax.Ifinsteadanincometaxwasused(withindividualrate C 8 ),thenthechangein welfareisthefollowing: d , GE = ¹ 8 ¹ C 8 F 8 d ! 8 º d 8 = ¹ 8 C 8 F 8 Y ! 8 ¹¹ 1 ¸ W 8 º d g 8 ¸ 8 º d 8 Ł (A.12) Seethathighwageworkersnowcontributethefollowingtermtothewelfarechange: C ˛ F ˛ ˛ ¡ 0 . Becausetaxrevenuesincreaseforthehighwagegroup,thegovernment'sbudgetconstraintisfurther loosenedwhichlessensthenegative˝scalexternality.Thewelfarechangeinthiscasecannotbe theoreticallysigned,sothewelfareimpactbecomesanempiricaltoquestion. 118 A.1.3ModelwithManyWorkerTypes Here,Iallowforeachlabortypetohaveaheterogeneoustaxchange,andthenIsolvetheequations inthesamemannerasbeforeusingsubstitutionaftertotallydi˙erentiating.Letworkertypesbe indexedby 4 2f 0 Œ 1 Œ 2 ŒŁŁŁŒˆ g = E . 3 Iusethefollowingequilibriumsystem(suppressinglaborsupplyarguments): LaborClearing ! 4Œ 0 ¸ ! 4Œ 1 ! ~ 4Œ 0 ¸ ! ~ 4Œ 1 = F 4 š \ 4 F ~ 4 š \ ~ 4 d 8 ~ 4 2En 4 (A.13) FactorClearing Í 4 ! 4 ( ¹ A º = F š U A š 1 U 1 (A.14) ZeroPro˝ts % = 2 ¹ f F 4 g 4 2E ŒA º : = 1 (A.15) Theincidenceissolvedusingbytakingthetotalderivativetolinearizethesystemandtheneither iterativesubstitutionorCramer'sruletosolveforthefactorpricechangesasafunctionofthetax change.Byadjustingthelaborclearingcondition(equationA.13),Icansolveforanyspeci˝c market'sincidence. Thegeneralequilibriumincidencefortype 0 laboris: ^ F GE 0 = Y ! ¹ 0 Œ 1 º \ 0 Œ 1 ^ g 0 Y ! 0 d ¸ Í 4 B 4 Y ! ¹ 4Œ 1 º \ 4Œ 1 ^ g 4 Y ! 4 d ! ¹ Y ! 0 d º 1 ¸ Í 4 B 4 Y ! 4 d (A.16) = ¹ W 0 ¸ 0 º ^ g 0 ¸ 0 ¹f g 4 g 4 2En 4 = 0 º (A.17) where = Y ¸ 1 B ¸ 1 ¸ d B ! Ł (A.18) Generally,onecannotsigntheexpressionwithoutknowingthedirectionofeach f g 3 g 3 .This issimilartoAgrawalandHoyt(2018b)inthecontextoftaxingmultipleconsumergoods.For example,iftheowntaxchangeislargebutallothertaxchangesaresmall,thenverylikelythe partialequilibriumtermwilldominate,sotheexpressionisnegative.However,iftheowntax changeissmallbutallotherarelargeandpositive,thenthegeneralequilibriumspilloverswill dominate,sotheexpressionispositive. 3 Inthecalibratedmodel, jEj = 72 basedonage,education,andmaritalstatusofwomen. 119 Again,thisshowsthatgenerallytherewillbe two ˝rstordertermswithrespecttothetaxchange. Onlyifthegeneralequilibriumspillovertermissmallwill F GE ˇ F PE .Note,withmultipletax changes,itisnolongersu˚cienttosupposethat B 0 ˇ 0 fortheGEtermstodisappear.Rather,one needstoassumethattheaveragecostshareweightedtaxchangeisequaltozero: E » B 4 \ 4Œ 1 ^ g 4 ¼ˇ 0 . A.1.4ModelwithMarketSwitching Here,IreturnthreefactormodelbutIallowthehighwageworkers, 4 = 1 ,toswitchbetween markets.Additionally,Iallowforadi˙erentialtaxchangeinbothlabormarkets. ThissetupissimilartothemodelusedinSaez(2002),onlysimpli˝edtofeweremployment groups.Thisallows 4 = 1 workerstosubstitutebetweenunemployment,lowwagework,andhigh wagework.Workerswith 4 = 0 areonlyabletoadjustbetweenunemploymentandlowwagework. Forexample,intheEITCcontext,supposethathighwagemothersseethenetlow-wagesector wageincreaserelativetohigh-wagework,andifthisworkerismarginallyattachedtohighwage work,thenthereshewillswitchtolowwagework.Alternatively,ifa 4 = 1 workerwithoutchildren originallychoselow-wagework,thenthepotentialrealwagedecreaserelativetothehigh-wage sectorwillcausethisworkertochoosehighwagework. Inthisframeworknotationcangetmessybecauseworkersofthesame ¹ 4Œ2 º canearndi˙erent wages,soIneedtotrackbothworkertypeandworkerlaborchoiceforfourdi˙erenttypesof workersandthreesectors.Thisisnotconceptuallydi˚cult,butmessy.Iassumethat 4 = 1 workersarepaidequalto 4 = 0 iftheyparticipateinthelow-wagesector.Onefoundationforthis isthatlow-wageworkinvolvessomesettasksthatcannotbene˝tfromhigh-wageworker'sskills, soworkersofboth 4 typeswillhavethesamemarginalproduct. 4 Letthelaborsupplyofatype ¹ 4Œ2 º workerbedenotedas ! 4 6Œ2 ,where 6 2f 0 Œ 1 g designates loworhighwagelaborgroup.Let Y ! 4Œ6Œ2 betheextensivelaborsupplyelasticity,andfortype 4 = 1 workerslet j 6 ! 6 0 2 bethecrosswageelasticitywithrespecttosectorchoiceforworkers.Thelatter 4 Note,thisrulesoutpricingpowerby˝rmstocreateaseparatingequilibriumamongworker types. 120 elasticityisonlyconcernedwithincumbentworkerswhopotentiallyswitchsectors.Isuppressthe groupconditionaldemographicshares, \ 4 6Œ2 ,toeasenotation. Thisimpliesthefollowingequilibriumsystem(suppressinglaborsupplyarguments): LaborClearing ! 0 0 Œ 0 ¸ ! 1 0 Œ 0 ¸ ! 0 0 Œ 1 ¸ ! 1 0 Œ 1 ! 1 1 Œ 0 ¸ ! 1 1 Œ 1 = F 0 š \ 0 Œ 1 F 1 š \ 1 Œ 1 d (A.19) FactorClearing ! 0 0 Œ 0 ¸ ! 1 0 Œ 0 ¸ ! 0 0 Œ 1 ¸ ! 1 0 Œ 1 ( ¹ A º = F š U A š 1 U 1 (A.20) ZeroPro˝ts % = 2 ¹ F 0 ŒF 1 ŒA º : = 1 (A.21) Thegeneralequilibriumincidenceforthismodelis: ^ F GE 0 = ¹ Y ! 0 Œ 1 ~ j 1 Œ 0 1 º ^ g 0 ¹ Y ! 0 ~ j 1 Œ 0 d º ¸ Í 3 B 3 ^ g 3 ¹ Y ! 3Œ 1 ~ j : 3Œ3 1 º ¹ Y ! 3 ~ j : 3Œ3 d º !! 1 ¸ Í 3 B 3 ¸ ~ j : 3Œ3 1 ¹ Y ! 3 ~ j : 3Œ3 d º ! (A.22) = ¹ p 0 ¸ 0 ¸X 0 º ^ g 0 ¸ 0 ¹ ^ g 2 º¸ X 0 ¹ ^ g 2 º (A.23) where Y ! 3Œ 1 and ~ j 6Œ6 0 2 incorporatetherelevantshareofworkersbasedon \ 4 6Œ2 .Asbefore, = Y ¸ 1 B ¸ 1 ¸ d B ! . Themaindi˙erenceisthatthesupplyelasticitiesaremorecomplicated,intuitively,because workerscanmakemorechoicesandsupplyisnotinelasticbetweenmarkets.Therearenow ˝ve ˝rstordertermsintheincidenceanalysis,eachcapturingadi˙erentsupplyresponsestowages. Thisshowsanadditionalconsequenceofpartialequilibriumanalysis.Ifworkerhavetheability toswitchbetweensectors,thenapartialequilibriumanalysiswillholdthesupplyoftheother markets˝xed.Thisomitsimportantequilibriumresponsestosubsidiesevenforthemarketbeing studied. 121 A.1.5TwoSectorModel A.1.5.1Model Lettherebetwo˝nalgoods, f -Œ. g ,forsaleatmarketprices, f ? G Œ? H g ,producedusingthree factors, f !Œ˛Œ g ,thatareeachelasticallysuppliedgivenfactorprices, f F G ŒF H ŒE G ŒE H ŒA G ŒA H g . Ireferto ! aslow-skilllabor, ˛ ashigh-skilllabor,and ascapital(oranyotherfactorwhich iselasticallysupplied), F aslow-skillwages, E ashigh-skillwages,and A ascapitalrents.Letall agentsthatcansupply ! or ˛ service(labor)becalled`workers'regardlessoftheirlaborforce participation;e.g.,alow-skillworkereitherparticipatesinthelaborforceordoesnotparticipate. Production+Capital Let - = ˙ ¹ - º ¹ 6 G ¹ ! G Œ˛ G º Œ G º and . = ˙ ¹ . º ¹ 6 H ¹ ! H Œ˛ H º Œ H º ,where ˙ ¹º arebothCRSpro- ductionfunctionswithaCESsubfunctionthataggregatesthetwolabortypes.ForproductionI use ˙ = ¹ ! 1 ¸ d d ¸ ˛ 1 ¸ d d º U d 1 ¸ d ¹ 1 U º Œ (A.24) whichisanestedCESproductionfunctionthatsatis˝estheassumption.Pro˝tforanindustry 9 is de˝nedas c 9 = ? 9 - 9 F 9 ! 9 E 9 ˛ 9 A 9 9 ,andinequilibrium c 9 = 0 . Let besuppliedaccordingtothefunction ( ¹ A G ŒA H º ,wherethesuppliersofcapitalconsider thetwosectorsperfectsubstitutes.Forexample,if A G ¡A H ,then G = ( ¹ A º and H = 0 .Thus,in anyequilibriumwherebothgoodsareproduced, A G = A H ,andwemayonlyreferto A . Utility Lettype B workerutilitybe D B = * B ¹ -Œ.Œ! G Œ! H Œ! > º ,where ! > = L ! G ! H isleisuretime. Letutilitybeseparablesothat D B = ˘ B ¹ -Œ. º¸ = ¹ ! G Œ! H Œ! > º .Further,let ˘ B ¹ -Œ. º = 2 ¹ - š . º . , sothatutilityishomotheticforgoods.Sinceutilityisquasi-linearwithrespecttoaggregate consumption,thelaborsupplywillnotdependonrelativeoutputpricesthiscanberelaxed. 122 Importantly,thedisutilityoflabordependsonthetypeoflabor.Dependingonthefunction form(andstochasticassumptions),thisimpliesthattwotypesofworkersmaymakeheterogeneous laborsupplydecisionsgiventhesamemarketprices.Thiscanbemicro-foundedbyassumingthat workersdrawatriple( f n G Œn H Œn > g )fromsomedistribution,thensolvethefollowingproblem: max GŒHŒ> f + ¢ ¹ G º¸ n G Œ+ ¢ ¹ H º¸ n H Œ+ ¢ ¹ > º¸ n > g Œ (A.25) where + ¢ ¹º istheoptimalconsumptionchoicegivenalaborsupplydecisionandprices.This yieldstheprobabilitythataworkerwillworkintherespectivesectors: p B 9 .Thisapproachisvery commoninthelaborsupplyliteratureaswellasinSaez(2002). Foranindividual,thiscanbeinterpretedastheamountoflaborsupplydevotedtoeachsector, where Í 9 p B 9 = 1 .Or,onecanassumethateachworkertrulychoosesonlyonesectorbutthatthe aggregateemploymentismatchedexactly: ! = # p . BudgetConstraint+Subsidy Theworkerbudgetconstraintis ? G - ¸ ? H . T B ¹ F G ! G ŒF H ! H Œ! > º .Let T B ¹º = ¹ F G ¸ g B º ! B G ¸ F B H ! B H ¸ 1 B ! B > ) B ,where g B isalaborsubsidyforsector - , 1 B inanunemploymentbene˝t,and ) B isalumpsumtaxonallworkersregardlessoflaborsupply.Giventhatutilityonlydependson leisure,thenetreturntosupplyinglaborinthetwosectorsimpliesthatinanyequilibriumwith bothgoodsbeingproduced, ¹ F B G ¸ g B º = F B H . Topayforthesubsidytosector - andunemployment,thegovernmentmustsetthelump- sumtaxestocoverthiscostinequilibrium.Letthegovernmentbudgetconstraintbe ) ! ¸ ) ˛ = g ! ! G ¸ 1 ! ! > ¸ g ˛ ˛ G 1 ˛ ˛ > . 123 A.1.5.2Equilibrium Thefollowingaretheequilibriumconditions: XLaborMarketClearing: ! ( G ¹ F G ¸ g ! ŒF H Œ1 ! º ˛ ( G ¹ E G ¸ g ˛ ŒE H Œ1 ˛ º k G ¹ F G š E G º = 0 (A.26) XFactorMarketClearing: ! ( G ¹ F G ¸ g ! ŒF H Œ1 ! º ( G ¹ A º k G ¹ F G š E G º G ¹ F G š A º = 0 (A.27) XZeroPro˝ts: ? G 2 G ¹ F G ŒE G ŒA º = 0 (A.28) YLaborMarketClearing: ! ( H ¹ F H ŒF G ¸ g ! Œ1 ! º ˛ ( H ¹ E H ŒE G ¸ g ˛ Œ1 ˛ º k H ¹ F H š E H º = 0 (A.29) YFactorMarketClearing: ! ( H ¹ F H ŒF G ¸ g ! Œ1 ! º ( H ¹ A º k H ¹ F H š E H º H ¹ F H š A º = 0 (A.30) YZeroPro˝ts: ? H 2 H ¹ F G ŒE G ŒA º = 0 (A.31) Themodelhassevenendogenousprices f F G ŒF H ŒE G ŒE H Œ? G Œ? H ŒA g andtherearesixequations, soInormalize ? H = 1 . 5 Thissystemisessentiallythesameasinthemaintext,butwithanextra outputsectorandadditionalprices. A.1.5.3SolvingforWageIncidence Inthissection,Iwillsolvethemodelforincidencetermsbylinearizingthesystemintermsof di˙erentialchangesinthesubsidy. Let g ˛ = 0 and d 1 B = 0 . Inmatrixform,theequilibriumsystem ^ I = a ^ g is: 2 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 4 Y ! G d G ¹ Y ˛ G d G º j ! G j ˛ G 00 Y ! G ¸ 1 ¹ 1 ¸ d G º B ˛ G 1 B G ¹ 1 ¸ d G º B ˛ G 1 B G j ! G 00 ¹ Y G ¸ 1 º j ! H j ˛ H Y ! H d H ¹ Y ˛ H d H º 00 j ! H Y ! H ¸ 1 ¹ 1 ¸ d H º B ˛ H 1 B H ¹ 1 ¸ d H º B ˛ H 1 B H 0 ¹ Y H ¸ 1 º B ! G B ˛ G 001 B G 00 B ! H B ˛ H 0 B H 3 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 5 2 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 4 ^ F G ^ E G ^ F H ^ E H ^ ? ^ A 3 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 5 = 2 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 4 Y ! G ^ g Y ! G ^ g j ! G ^ g j ! G ^ g 0 0 3 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 5 5 Theendogenousquantities, f ! 9 Œ˛ 9 Œ 9 Œ-Œ. g ,alldependontheendogenousprices. 124 A.1.5.4Two`Tricks'forSolving If I = 1 ,thenbyCramer'sRule: Cramer'sRule: I 8 = det ¹ j 1 º det ¹ º (A.32) LaplaceExpansion: = Í 9 1 8Œ9 det ¹ ¹ 9 º º det ¹ º (A.33) = Í 9 1 8Œ9 0 8Œ9 0 8Œ9 det ¹ ¹ 9 º º det ¹ º (A.34) MatrixDerivative: = Í 9 1 8Œ9 0 8Œ9 0 8Œ9 m det ¹ º m0 8Œ9 det ¹ º (A.35) : = Õ 9 1 8Œ9 0 8Œ9 W 0 8Œ9 Œ (A.36) where W 0 8Œ9 = m det ¹ º m0 8Œ9 0 8Œ9 det ¹ º istheelasticityofthedeterminantwithrespecttothematrixelement. Thisparameterisgeometricallyinterpretableasthepercentchangeintheareaofthen- dimensionalparallelogramformedbythesystemofequationsfroma 1% elementalchange. Economically,theclosestinterpretationisthat W summarizesthee˙ectoftheexogenousvari- ation ¹ 1 º throughthesystemofequations ¹ º fromeachequilibriumchannel(theotherelements of I ). 125 Additionally,usingsomealgebra: I 8 = Í 9 1 8Œ9 0 8Œ9 0 8Œ9 det ¹ ¹ 9 º º det ¹ º (A.37) = Í 9 1 8Œ9 0 8Œ9 0 8Œ9 det ¹ ¹ 9 º º Í 9 0 8Œ9 det ¹ ¹ 9 º º (A.38) = Õ 9 1 8Œ9 0 8Œ9 0 8Œ9 det ¹ ¹ 9 º º Í 9 0 8Œ9 det ¹ ¹ 9 º º (A.39) = 1 8Œ8 0 8Œ8 ¸ 2 6 6 6 6 4 Õ 9 n 8 1 8Œ9 0 8Œ9 1 8Œ8 0 8Œ8 0 8Œ9 det ¹ ¹ 9 º º Í 9 0 8Œ9 det ¹ ¹ 9 º º 3 7 7 7 7 5 (A.40) = 1 8Œ8 0 8Œ8 ¸ 2 6 6 6 6 4 Õ 9 n 8 1 8Œ9 0 8Œ9 1 8Œ8 0 8Œ8 W 0 8Œ9 3 7 7 7 7 5 (A.41) A.1.5.5LowWageXSectorIncidence ItcanbeshowusingCramer'sRule,LaplaceCofactorExpansion,andsomealgebrathat ^ F ! G ^ g = Y ! G Y ! G d G | {z } PartialEquilibrium ¸ W 0 2 Œ 1 © « ¹ 1 ¸ d G º¹ 1 B ˛ G 1 B G º Y ! G ¸ 1 ¹ 1 ¸ d G º B ˛ G 1 B G ª ® ® ® ® ¬ ¸ W 0 3 Œ 1 ¸ W 0 4 Œ 1 d G Y ! G d G | {z } SpilloverTerms (A.42) A.2DataDescriptionandSummaryStatistics Inthisappendix,Iprovideadditionaldescriptionsandsummarystatisticinformationforthe datausedintheempiricalsections.Broadly,IusetheCurrentPopulationSurveyfrom1986to 2010(Floodetal.,2018)andthe1990USCensus5%sample,(Rugglesetal.,2018).Iadditionally usetheUrbanInstitute'sTransferandIncomeModel,whichrequiresthefollowingdisclosure: InformationpresentedhereisderivedinpartfromtheTransferIncomeModel,Version3 (TRIM3)andassociateddatabases.TRIM3requiresuserstoinputassumptionsand/or interpretationsabouteconomicbehaviorandtherulesgoverningfederalprograms. 126 Therefore,theconclusionspresentedhereareattributableonlytotheauthorsofthis report. A.2.1OutgoingRotationGroupSamples TheORGsamplescomefromtheCurrentPopulationSurvey.ACPSrespondenthouseholdis surveyedintwowavesforfourmonthseachwithaneightmonthbreak.Onmonthsfourand eight,thesurveyorsasktherespondentadditionallabormarketquestions,suchasusualhoursand weeklyearnings.Themonth-in-sampleisstaggeredacrossrespondents,soaboutone-fourthofany monthlysampleisinanORG. IusetheORGsamplesforlabormarketquantities:wagesandlaborsupply. 6 IntableA.2,I providetheunderlyingsampleofwomenintheCPSORGthatareaggregatedforthemainanalysis. Asdescribedinthemaintext,Icalculatehourlywagesbydividing usualweeklyearnings by usualhoursworkedatmainjob .Idiscardcalculatedwagesfromworkerswithimputed earningsand/orhours.Idiscardobservationswheretherespondentsaystheirusualhoursvary, workersreportinglessthanonehourperweek,workersworkerswithimpliedreal$1990wagesless than$0.50orgreaterthan$150.00,and˝nallyiftheworkerisoutofthelaborforce and reports beinginschoolfulltimeovertwo-thirdsoftheirCPSobservations. 7 IntableA.3,Idisplaythenumberofdemographiccellsbymarriageandeducationgroupthat areusedintheincidencecalculations.Ionlyincludemarket-state-yearcellsthathaveaminimumof ˝veworkerswithchildren and ˝veworkerswithoutchildren.Thiscausesmetohaveanunbalanced panelofcells,butensuresthatthemarketaveragesarecalculatedusingareasonablenumberof workers.Thetableitselfalsohighlightsdemographicchangesovertime.Ascanbeseen,with populationgrowth,thetotalnumberofcellsgoesfrom14.2thousandto20.3thousand.Wecan alsoseeeducationattainmentincreasing,asthereisadecreaseinworkerswithoutahighschool 6 ThemajorissueinusingtheORGsampleisthatcannotitdoesnothaveenoughinformation topredictEITCusage,whichisbasedonpreviousyearincomeandlivingarrangements. 7 Additionally,Idropworkerswhoareingrouphousing,whohavenoidenti˝edheadofhouse, whoareinhouseholdswithgreaterthantenmembers(asitistoohardtoformtaxunits),whoare inthearmedforces,andwhoaremarriedwithabsentorseparatedspouses. 127 TableA.2:MarketStateYearObservationsforEstimationSample 1989-19941995-2000Di˙erence MeanSDMeanSDDif C Age38.9812.2439.9111.990.93***(39.21) Married0.630.480.620.49-0.01***(-14.19) White0.830.370.820.38-0.01***(-19.13) Black0.120.320.130.340.01***(9.69) LessHS0.150.360.130.33-0.02***(-35.49) HighSchool0.390.490.340.47-0.06***(-59.15) SomeCollege0.320.470.300.46-0.02***(-22.04) BA+0.140.350.240.430.10***(130.04) QualifyingChild0.480.500.470.50-0.01***(-14.21) AgeofYoungest7.746.077.935.950.19***(11.18) LFP0.680.460.710.460.02***(23.43) EPOP0.640.480.687.000.03***(32.98) UsualHoursTotal37.6010.4838.0010.230.39***(8.11) UsualHoursMain36.689.9037.289.700.61***(25.53) RealH.Wage8.844.8312.476.643.62***(188.06) RealWage10.736.0315.719.055.98***(234.76) RealWeeklyEarnings431.63276.53629.24420.29197.61***(207.12) Observations706,747612,4631,319,210 Alldatafrom1989-2000CPSMORGsamples,onlywomenages20-65,accessedfromIPUMS.Alldemo- graphic,employmentvariablesweightedbyCPSBasicWeight,realwageandearningsbyEarningsWeight Hours.Realwagesandearingsin˛atedto2018dollarsbyBLSCPIResearchSeries.Realwagebasedon weeklyearningsdividedbyusualhoursformainjob.Qualifyingchildbasedonchildage,schoolstatus,and familystructure. degreetothosewithacollegedegree.Interestingly,thereisanincreaseinunmarriedwomenwith somecollegebutadecreaseformarriedwomen,asthislattergroupshiftstowardsattainingtheir collegedegree. A.2.1.1AssignmentofChildreninORG WedonotobservewhoclaimsEITCqualifyingchildrenistheCPS,sochildrenmustbeassigned bytheresearcheraccordingtosome( adhoc )rules.Iassignchildrenbasedonwhoseemsthemost likelyprimarycare-giverinthesocialroleofaparent.Whilenotperfect,Iheavilyusethefactthat childrentypicallyfollowtheirprimarycare-giverintherecordlayout,inadditiontofamilyunitand relationshippointervariables.Formostcases,thisissimpleandthereisnoambiguity;however, 128 TableA.3:MarketStateYearObservationsforEstimationSample LessHSHSSomeCollegeBAPlusTotal YearUnmarriedMarriedUnmarriedMarriedUnmarriedMarriedUnmarriedMarried UnmarriedMarried 199024628257271438666046172 1,2501,828 199125825253673842865846176 1,2681,824 1992268240496680378572166500 1,3081,992 1993210216512684418584158510 1,2981,994 1994186182506634430572142494 1,2641,882 1995182180494602444590176522 1,2961,894 1996158162496580454542152514 1,2601,798 1997156140494550454536160532 1,2641,758 1998144138490544458556190530 1,2821,768 1999154116506546484562218556 1,3621,780 2000156126520532470566204550 1,3501,774 Total2,1182,0345,6226,8044,8046,3981,6585,056 14,20220,292 Alldatafrom1993MarchCPS,WomenfromTaxUnits,Wagein$1993.AllvariablesweightedbyCPS MarchSupplementWt Hours. householdlivingarrangementscanbecomplex.Themainconsequenceofmyallocationrulescan bestatedintwoexamples. First,considerahouseholdwitha40yearoldheadofhouse(HoH),a16yearoldchildofHoH, anda1yearoldgrandchildofHoHwhoisdirectlyrelatedtothechild.Iassignthegrandchildto thechildratherthantotheHoH.AnotherresearchermayassignbothtotheHoH.Second,consider ahouseholdwitha40yearoldHoHanda20yearoldnon-relative(sonotafoster oradoptivechild)whoisunmarriedandinschool.Idonotassignthenon-relativetotheHoH; although,anotherresearchermay. IPUMSconstructsfamilyrelationshipinformation,suchasnumberofownchildren( nchild ), basedonantheirde˝nitionofafamily.Theirgoalisacombinationofaccuracy and scalability formanymillionsofobservations.However,I˝ndthatthisde˝nitionisdoesnotsuitmypurpose ofmatchingchildrentotheirmostlikelycare-giver.WhenCensusfamilyidentifyingvariablesare available(primarilyintheASECsamples,discussedbelow),Iamableto˝ndmanyexamplesof childassignmentthatarenotintuitive.Nevertheless,usingtheIPUMSfamilyde˝nitionsresultis thesamequalitativeresultswithminimalquantitativedi˙erences. 129 A.2.2AnnualSocialandEconomicSamples IusetheASECsamplesfromtheCurrentPopulationSurveytoperformthesimulationexercises: 1993-1995fortheOBRAexpansion,2008-2010fortheARRAexpansion.TheASECsamplesis basedontheMarchCPSandanoversamplingfromothermonthstoincreasedataquality.March ischosentocoincidewithtax-˝lingseason,thesurveyorsaskadditionalquestionsaboutincome, insurance,andotherissuesfromthepreviousyear.Toreducesamplingerrors,thesurveyorsinclude additionalhouseholdsfortheASECfromFebruaryandApril(startingin2002)andoversample Hispanichouseholds(startingin1976)(Floodetal.,2018). IusetheASECsamplesforincidencecalculationsbecausethepossibilityofcalculatingEITC usagegiventheincomeandfamilyvariables.However,thewageinformationisnotasgoodas theORGsample,sincewagesmustbeimputedusingpreviousyearannualearningsandwork informationratherthanweeklyearnings. Ipresentsummarystatisticsontheincidencesamplesofwomenfortaxyear1992inTableA.6 andfor2008inTableA.5. 8 Asdescribedinthemaintext,Icalculatehourlywagesbydividing annualearningslastyear (alltypes)bytheproduct usualhoursworkedatmainjob lastyear times weeksworkedlastyear .Theincidencesampleisrestrictedtowomenages 16to65.Idropwomenwhoarefullorparttimestudents and havenotparticipatedinthelabor forceforoveroneyearandwomenwhohavenegativetaxunitself-employmentearnings. 9 Becausethelabormarketvariablesarebasedonannualinformation,Iclassifyanindividualasa `worker'ifshesatis˝esthefollowing:atleast40hrsofworklastyear,anaverageofatleast8hrsper week,mustearnatleast$100peryear(in$1990dollars),andmusthaveanimpliedwageofatleast $0.50(in$1990dollars).Thisessentiallyrelabelsextremepart-timeworkersas`non-workers.' ThemostnotablefeatureofthedataisthattheEITCisheavilyconcentratedintheunmarried 8 Note,fortheempiricalexerciseinSection1.8,Ialsousethe1993ASEC,butthesample ismarginallydi˙erentduetosimulatingtheWelfareprogrammeasures.Thereise˙ectivelyno impactonthesummarystatisticsinTableA.6. 9 Additionally,Idropworkerswhoareingrouphousing,whohavenoidenti˝edheadofhouse, whoareinhouseholdswithgreaterthantenmembers(asitistoohardtoformtaxunits),whoare inthearmedforces,andwhoaremarriedwithabsentbutnon-separatedspouses. 130 womenwithchildrensegment,butthissegmentisalsothesmallestinlaborcosttermsandlabor supplyterm.Thisimpliesthatsincetheirmarketshareisreasonablysmall,thattheGEe˙ectsare likelytobeclosertothePEincidence,allelseequal. TableA.4:SummaryStatisticsforSimulationIncidenceSample TaxYear1992 AgeAnykidsMarriedGetEic UnmarriedWomen33.000.000.000.00 MarriedWomen47.620.001.000.00 UnmarriedMothers34.291.000.000.50 MarriedMothers36.901.001.000.18 LessHSHSOnlyLessBABA+ UnmarriedWomen0.260.260.300.18 MarriedWomen0.150.410.230.21 UnmarriedMothers0.230.390.270.10 MarriedMothers0.120.380.280.22 WorkerWageShareofWorkersCostShare UnmarriedWomen0.7210.140.320.20 MarriedWomen0.6711.180.240.18 UnmarriedMothers0.689.790.100.07 MarriedMothers0.7010.860.350.23 Alldatafrom1993MarchCPS,WomenfromTaxUnits,Wagein$1992.Demographicvariablesweighted byCPSMarchSupplementWt,WagebySupplementWt UsualHoursLastYear. A.2.2.1AssignmentofChildreninASEC Asdiscussedabove,theassignmentofEITCqualifyingchildrenisuptotheresearcher.Iuse CensuscodedfamilyunitID,householdrecordnumbers,andrelationshippointerstolinkEITC eligiblechildrento(mostlikely)parents.Again,forcreatingtaxunits,theCensusde˝nitionis closerinspirittowhatresearchersareaimingtocaptureratherthanIPUMSde˝nitions. A.2.2.2SampleDi˙erencesbetweenRothstein(2010) Thereisprimarydi˙erencebetweenmyASECsampleandthatofRothstein(2010),whouses nearlythesamecriterialabormarketcriteria.Rothsteindropsfromtheinitialsampleanyperson whoisnotlabeledastheheadofafamilyunit.Thisisroughly36%oftheinitialsample,13% 131 TableA.5:SummaryStatisticsforSimulationIncidenceSample TaxYear2009 AgeAnykidsMarriedGetEic UnmarriedWomen34.160.000.000.05 MarriedWomen50.200.001.000.04 UnmarriedMothers35.981.000.000.55 MarriedMothers39.541.001.000.20 LessHSHSOnlyLessBABA+ UnmarriedWomen0.230.230.310.23 MarriedWomen0.080.330.280.31 UnmarriedMothers0.170.320.350.16 MarriedMothers0.100.250.280.37 WorkerWageShareofWorkersCostShare UnmarriedWomen0.6518.130.330.19 MarriedWomen0.6920.190.250.17 UnmarriedMothers0.7616.750.120.07 MarriedMothers0.7121.490.310.21 Alldatafrom2009MarchCPS,WomenfromTaxUnits,Wagein$2008.Demographicvariablesweighted byCPSMarchSupplementWt,WagebySupplementWt UsualHoursLastYear. oftheinitial18oroldersample,and6%oftheinitial25oroldersample,whowouldnotbe dependents(sampleproportionsareunweighted).Theseindividualshaveroughly$4000lessin wageandsalaryincome(conditionalonage,education,race,maritalstatus,andgender)meaning theyaremorelikelytoqualifyfortheEITCbasedonincome. 10 Thee˙ectofthisisthatinRothstein'sanalysisthereareonly three womenundertheageof 24withoutchildren.Suchasamplemakessenseintheempiricalliteratureinordertoperform di˙erence-in-di˙erenceestimation(thisisbecausetheneedforparalleltrendspushesonetoremove theseyoungworkers).However,itisnotobviousthatitshouldbedoneintheincidencecalculation, whichismostlytheoreticalsimulationexercise.BecauseIbelievemanyoftheseworkersare within-marketrivalsofunmarriedwomenwithchildren,Iincludetheminmysimulations.This increasesthewomeninthesamplebyroughlysixthousandindividualsandchangestheaverage ageofunmarriedwomenwithoutchildrenfrom 41 to 33 . Additionally,RothsteinessentiallyassignsallindividualswhopotentiallyqualifyasEITCde- 10 Theyarealsoyounger,morelikelytohaveahighschooldegreeorless,lesslikelytobewhite, morelikelytobemen,andmuchlesslikelytobeorhavebeenmarried. 132 pendents(basedonageandeducationenrollment)totheheadofhousehold.Intheend,Rothstein assignsabouttwothousandmoreworkersatleastoneEITCdependentsthanmyprocedure(thatis hisprocedureyieldsmoreworkerswithaqualifyingdependentthanmysampleprocedure). ThetwochangesImakemoreworkersinthesampleandfewerEITCclaimantsshould mitigate theincidencee˙ects. A.2.31990USCensus5%Sample Iusethe1990USCensus5%Sample(Rugglesetal.,2018)tocreatethesimulatedtaxinstruments. TableA.6:SummaryStatisticsforSimulationIncidenceSample 1990Census AgeAnykidsMarriedGetEic UnmarriedWomen32.680.000.000.00 MarriedWomen47.290.001.000.00 UnmarriedMothers35.151.000.000.49 MarriedMothers36.431.001.000.15 LessHSHSOnlyLessBABA+ UnmarriedWomen0.300.240.280.12 MarriedWomen0.200.360.250.13 UnmarriedMothers0.260.340.310.07 MarriedMothers0.160.340.300.14 WorkerWageShareofWorkersCostShare UnmarriedWomen0.759.290.330.21 MarriedWomen0.6610.260.230.18 UnmarriedMothers0.739.100.090.06 MarriedMothers0.709.700.340.22 Alldatafrom1990USCensus,5%SampleMarchCPS,WomenfromTaxUnits,Wagein$1989.Demo- graphicvariablesweightedbyCensussampleweight,Wagebysampleweight UsualHoursLastYear. A.3EmpiricalTaxInstruments A.3.1Identi˝cationofElasticities Toidentifythelaborsupplyandlaborsubstitutionelasticities,therearetwosetsofexclusion restrictions.The˝rstsetareusedforthesupplyelasticitiesandthesecondforthesubstitution 133 elasticity.Theincidencemodelresultsimplyanidenti˝cationstrategy.Directchangesintheown EITCATR, g ,shiftsupplythatallowsmetoidentifythelaborsubstitutionelasticitythatgoverns labordemand.GEspillovere˙ectsshiftdemandcurvesthatallowsmetoidentifythelaborsupply elasticities.Below,IformalizethisusingargumentsfromWatson(2020). Considerthefollowingsimultaneousequationsmodel[SEM]: ; ˇ 8C = U 0 ¸ U 1 F 8C ¸ D ˇ 8C ; ( 8C = V 0 ¸ V 1 F 8C ¸ V 1 g 8C ¸ D ( 8C ; ( 8C = ; ˇ 8C Ł (A.43) Thisimpliesthefollowing˝rststageandreduceformequations: F 8C = U 0 V 0 V 1 U 1 ¸ V 1 V 1 U 1 g 8C ¸ D ˇ 8C D ( 8C V 1 U 1 : = c 0 ¸ c 1 g 8C ¸ E F 8C Œ (A.44) ; 8C = U 0 V 1 U 1 V 0 V 1 U 1 ¸ U 1 V 1 V 1 U 1 g 8C ¸ V 1 D ˇ 8C U 1 D ( 8C V 1 U 1 : = ` 0 ¸ ` 1 g 8C ¸ E ! 8C Œ (A.45) whereallvariablesareinlogsand ln »¹ 1 ¸ g º¼ˇ g .Iassumethatlabordemanddependson thegross-wagewhilelaborsupplydependsonthenet-wage,andIsuppressanydependenceon covariates, - . Now,Iusethetheoreticalresultsfromthemaintextimplythefollowingwageincidence equation: d F 8C |{z} WageChangeinData = W 1 d g 8C ¸ 8C | {z } IncidenceInducedChange ¸ W 0 ¸ h 8C | {z } UnobsWageChange Œ (A.46) where 4BC isatheoreticalmeasurementoftheGEspillovere˙ect. CombiningtheSEMwiththeincidenceequation,thefollowingequivalencemustholdinthe postperiod: W 0 ¸ h 8C ¸ W 8 d g 8C ¸ 8C | {z } Incidence+Unobs = d F |{z} Data = U 0 V 0 V 1 U 1 ¸ V 1 V 1 U 1 d g 8C ¸ d D ˇ 8C d D ( 8C V 1 U 1 | {z } SEM Ł (A.47) Oneobviouswaytoreconcilethetwoequationsisthefollowing: h 8C = 1 V 1 U 1 d D ( 8C 8C = 1 V 1 U 1 d D ˇ 8C W 0 = U 0 V 0 V 1 U 1 W 1 = V 1 V 1 U 1 Ł (A.48) 134 Theaboveimpliesthatif Cov ¹ gŒ/ º < 0 ,then Cov ¹ gŒD ˇ º < 0 ,so g istechnicallyaninvalid instrumentintheSEMabove.However,usingtheRFequation,theowntaxchangeandspillovers canbeusedintandemtoestimatetheelasticities: m; m = V 1 V 1 U 1 mD ˇ m/ & mF m = 1 V 1 U 1 mD ˇ m = ) m; š m mF š m = V 1 Ł (A.49) Itisstraight-forwardtoshow: mF m = m » F ¸ g ¼ m and m; š mD ( mF š mD ( = U 1 .Additionally,Icanallow fororthogonaldemandunobservablechanges: h 8C = D ( 8C ¸ D ˇŒ 2 8C ,where Cov ¹ g 8C ŒD ˇŒ 2 8C º = 0 and Cov ¹ 8C ŒD ˇŒ 2 8C º = 0 . ThemainconclusionofWatson(2020)isthatthecontextofthelabormarketSEM,wecan usethetaxreformtreatmentasasupplyshifterandameasureofspilloversasademandshifter Let ¤ H G betheresidualfromfromaregressionof H on G . Proposition3. If g isexogenouswiththeaboveSEM,then d Cov ¹ ¤ ; g Œ ¤ / g º d Cov ¹¤ F g Œ ¤ / g º ! ? V 1 and d Cov ¹ ¤ ; / Œ ¤ g / º d Cov ¹¤ F / Œ ¤ g / º ! ? U 1 ,where `exogenous'meansthat Cov ¹ gŒD ( º = 0 . Thus,toidentify V 1 ,Ineedameasureofthedemandspillovers,whichproxyfordemandshifters, andtoconditionontheowntaxrateasaproxyforsupplyshifters.Theexclusionrestrictionisthat theEITCtaxreformanditsspilloversareuncorrelatedtounobservabledi˙erencesinlaborsupply (conditionalonthemodelcontrols): E h g 42BC D ( 4 0 2BC j - i = 0 Œ 8 4Œ4 0 2E Ł (A.50) ThisassumptionwouldbeviolatediftheEITCpolicychangesacrossdemographicgroups andstate-yearswerechosenbecausethepolicymakersknewcertaingroupsweremorelikelyto systemicallychangetheirlaborsupply.BecausetheOBRAexpansionwasdoneatthenational level(federalEITCrulesareuniformacrossstates),thiswouldrequirethatpolicymakerswereable topreciselydesignthenationalchangetotakeadvantageofsub-statetrends.Moreplausibleisthat statepolicymakersstrategicallyimplementedstate-EITCreforms. 11 However,priorstudies˝nd 11 Ninestateshadastateprogramby1995andeighteenby2000. 135 thatstateEITCintroductionsandpolicychangesappearplausiblyexogenoustolocaleconomic conditions(Leigh,2010;Buhlmannetal.,2018). Alternatively,iftherearesocialprogramreformsthatarecorrelatedwithEITCreforms,thenI willmisattributetotheEITCwagee˙ectsthatareactualtodueotherprogramchanges.Themost obviousexampleisPRWORAthatreplacedAidtoFamilieswithDependentChildren(AFDC) withTemporaryAssistanceforNeedyFamilies(TANF)in1996.Thisreformastheculmination ofstate-ledwelfarereforme˙ortsstartinginthelate1980s...implementedundertheheading ofwelfarewaivers,permissionsfromthefederalgovernmentallowingstatestoexperimentwith theirwelfareprogramsKlevenToaccountforthispossibility,Iinteractanindicatorfor havingchildrenwithindicatorsforimplementationofstate`welfarewaivers'. 12 GiventhatIinclude state-yearFEs,thesevariableswillcontrolforanyvariationinEITCATRs,wages,andsupplythat areduetodi˙erentiale˙ectsofwelfarereformsbyparentalstatus. Toidentifythesubstitutionelasticity,Irelyonasimilarargumentasfor U 1 intheaboveSEM. InowneedtoconditiononthespilloversandusethedirectEITCchangeasasupplyinstrument: E g 4BC g 0 BC D ˇ ¹ 4Œ 0 º ŒBC j -Œ 4BC = 0 Ł (A.51) Thatis,therelativetaxchangebetweenskillsisuncorrelatedwiththerelativedemandunobservables conditionaloncovariatesandspillovers. ThisassumptionwouldbeviolatediftheEITCwasimplementedinawaythatwascomple- mentarytounderlyingskillbiasedtechnicalchangewhere˝rmsweredemandingmorelowskill laborjustastheEITCwasexpandinglaborsupply.Totheextentthatthisoccurred,Iinteract1990 wagedecileswithyearindicatorstocaptureanywagetrendsacrossstatesandskills. A.3.2Construction TherearetwowaysofusingEITCpolicyvariationasaninstrumentformarketvariables.First, onecanusetheEITCpolicyparametersdirectly,suchasmaximumEITCbene˝tgivennumberof 12 TheseareprovidedbyKleven(2019)inonlinereplicationmaterialaccessedontheauthor's personalwebsite. 136 childrenwhichvariesatthestate-yearlevel(Leigh,2010;Kasy,2017;BastianandMichelmore, 2018).Thisvariableisverysimpletoimplementbutisconstantacrossalllabormarketsinastate. Thesecondmethodisusingasimulatedtaxinstrument,similartoGruberandSaez(2002); Rothstein(2008),foreachdemographicgroupacrossstates. 13 HereIdescribetheconstructionof theEITCaveragetaxrateindetail.IadditionallycalculateIVsusingtheshareofamarketwith positiveEITCandthechangeinEITCbasedontaxcodechangesinananalogousway. Usinga˝xeddistributionofworkercharacteristicsfromthe1990Census,Icalculateaverage taxratesduetotheEITCovermultipleyearsofpolicychanges.By˝xingthedistributionof workers,endogenouschangesinATRsduetochangesinlabormarketvariablesarepurged.This constructionallowstheinstrumenttovaryatthelabormarket-state-yearlevel. Tocalculatethis,IneedtoestimatethetrueEITCbene˝tsandthecounterfactualEITCbene˝ts iftheworkerdidnotwork.IcalculatethetrueEITCbene˝ts, ˆ act 8 ,byusingTAXSIMontheactual data,where ˆ isthefederalandstateEITCbene˝t.Tocalculatethecounterfactualbene˝ts, ˆ cf 8 ,Iset theworker'slaborearningsequaltozerobutleavingallelseequalandrerunTAXSIM. 14 Finally, IcalculatetheEITCAverageTaxRateasthedi˙erenceintheactualminusthecounterfactual bene˝tsoverearnedincome: g EITC 8 = ˆ 8 ¹ ! = ! 8 º ˆ 8 ¹ ! = 0 º F 8 8 Ł (A.52) Iusethemarketlevelsampleweightedmeantocalculate g 42BC . Asstatedabove,Iusethe1990Censustocalculatethetaxinstrument.Ireplicatethedatafor eachtaxyearandsendthedatatoInternetTAXSIM.Toavoidissuesof`bracket-creep',Iin˛ate monetaryvaluesbytheBLSCPIAllItemsResearchSeriesbutdonotchangeanyotherquantity. TheaboveonlycalculatedtheEITCATRforaspeci˝clabormarket, g 42BC .However,thetotal incidencealsodependsonaweightedsumoftaxchangesin other labormarketswithinastate-year, 13 Leigh(2010)andBastianandMichelmore(2018)bothalsousethistypeofapproachsecondary analysis. 14 Inmarriedcoupletaxunits,thecounterfactualiswithrespecttothewife'slaborsupply decision.Iassumethehusband'searnedincomeremainsunchanged. 137 42 ¹f g 4Œ2 0 g 4Œ2 0 2D º .Thus,Ineedanempiricalcounterpartforthe 42BC terms,butthisdependson theparametersthatIwishtoestimateseeequationA.16. Iapproximatethefunctionbycreatingtwodi˙erent`leave-out'averagesofthetaxchange acrosslabormarketsmatchedtoagivenmarket.Undertheassumptionthat: 42BC = ˛ f g 4 0 2BC g 42 0 2D ˇ a 1 g 6 1 ¹ 4 º Œ2BC ¸ a 2 g 6 2 ¹ 4 º Œ2BC ¸ a 42BC Œ (A.53) forobserved ¹ g 6 1 ¹ 4 º Œ2BC Œ g 6 2 ¹ 4 º Œ2BC º ,thenIcanusetheseobservedvariablesasapproximationsto thetruespillover. The˝rstmatch-groupisbasedonagegroupsandthesecondmatchgroupisbasedoneducation groups.Icreatetheleave-outaveragesbyexcludingthespeci˝cmarket-segmentwhencreating theaverages.Forexample,if ¹ ~ 4Œ2 º ismarriedwomenwithsomecollegebetweenagesof25and 30,then g 6 1 ¹ ~ 4 º Œ2BC equalstheaverageEITCATRforwomenwithsomecollegepooledacrossage groupsexcludingthespeci˝cgroup, g 6 2 ¹ ~ 4 º Œ2BC equalstheaverageEITCATRforwomenbetween agesof25and30pooledacrosseducationgroupsalsoexcludingthespeci˝cgroup. Recall,becauseIincludetheownEITCATRasacontrolvariableinboththe˝rststageand structuralequation,thevariationintheseleave-averagesisbyconstructionorthogonaltodirect EITCvariation. Asstatedabove,IusetheEITCATRandtwoothersimulatedEITCstatisticsasinstruments: theshareofworkersreceivingEITCbene˝tsandthemeanchangeinexpectedrealEITCamounts. BelowIspecifytheIVsusedinthemainresults.InAppendixA.4,Ishowthattheelasticity estimatesarerobusttovariouscombinationsoftheinstruments. A.3.2.1LaborSupplyInstruments Foreverygroup ~ 3 = ¹ 4Œ2 º ,Ihaveninemarketlevelsimulatedinstrumentsforwages: 1. theEITCATR: f g ATR ~ 3BC g 2. theportionof ~ 3 workerswithpositiveEITC: f I Sh ~ 3BC g 3. themeanchangeinETICamountfor ~ 3 : f I dE ~ 3BC g 138 4,5. twoEITCATRapproximationaverages: f g 6 ¹º ¹ ~ 3 º BC g 6,7. twopositiveEITCapproximationaverages: f I Sh 6 1 ¹ ~ 3 º BC Œ I Sh 6 2 ¹ ~ 3 º BC g 8,9. twomeanchangesinexpectedrealEITCamountsapproximationaverages: f I dE 6 1 ¹ ~ 3 º BC Œ I dE 6 2 ¹ ~ 3 º BC g . Basedontheidenti˝cationargumentsabove,Iconditiononthedemographicspeci˝csimulated EITCATR,sharewithEITC,andaveragechangeinEITC: f g 42BC ŒI sf 42BC ŒI dE 42BC g . A.3.2.2LaborSubstitutionInstruments Thelaborsubstitutionelasticitydependsontherelativewage, ln » F 4BC š F 4 0 BC ¼ .Mymainspec- i˝cationusesajustidenti˝edmodelusingthe`relativeEITCATRs'toinstrumentforrelative wages: g ¹ ~ 4Œ4 0 º BC = g ~ 4BC g 4 0 BC Ł (A.54) IalsoconstructrelativeshareofEITCclaimantsandtherelativechangeinrealEITCamountsto estimateanoveridenti˝edmodel.Forthesubstitutionelasticity,Ionlyusetheeducationbased averagesbecause,whenIcreatetherelativevariablesfortheregressions,Imatchworkersbasedon agesotheage-groupleave-outaveragesareabsorbedintoother˝xede˙ects. A.3.3ComparisonwithTraditionalApproaches Here,IquicklydescribetheissuesusingmoretraditionalapproachesintheEITCliteratureto estimatingrelevantparameterswhenallowingworkerheterogeneityandgeneralequilibriume˙ects. A.3.3.1LaborSupplyDi˙erenceinDi˙erence Previousauthorshaveestimatedlaborsupplyresponsesusingdi˙erence-in-di˙erencestyleas- sumptionsforunmarriedwomenwithandwithoutchildrenseeEissaandLiebman(1996);Hotz etal.(2002)foranearlyexampleandareviewoftheempiricalliteraturelistofexamples.This assumptionsupposesthattheseworkersfacesimilarmarketforces,suchasbeingperfectlysub- stitutableconditionalonageandeducation(andexperience),sothatinanarrowwindowaround 139 EITCexpansionstheonlychangebetweentheseworkersisthedi˙erenceinEITCpolicye˙ects. Suchassumptionsleadtoexpectingtrendsbeforethereformandusingthepost-reform dynamicsofwomenwithoutchildrentoformacounterfactualbaselineforwomenwithchildren. Toseetheimplicationsoftheseassumptions,considerthefollowingmodel,where g 4Œ2ŒC = 0 if C = 0 and g 4Œ2ŒC = 0 if 2 = 0 : E » ; ( 42C ¼ = V 0 ¸ V 4Œ2 ¹ F 4ŒC ¸ g 4Œ2ŒC º¸ _ 4 (A.55) = ) E » ; ( 42Œ 1 ¼ E » ; ( 42Œ 0 ¼ = V 4Œ2 ¹ F 4Œ 1 F 4Œ 0 ¸ g 4Œ2Œ 1 g 4Œ2Œ 0 º (A.56) = ) E » ; ( 4Œ 1 Œ 1 ¼ E » ; ( 4Œ 1 Œ 0 ¼ E » ; ( 4Œ 0 Œ 1 ¼ E » ; ( 4Œ 0 Œ 0 ¼ = ¹ F 4Œ 1 F 4Œ 0 º | {z } IncidenceE˙ects ¹ V 4Œ 1 V 4Œ 0 º | {z } ElasticityDi˙erences ¸ V 4Œ 1 g 4Œ2Œ 1 | {z } ATET Ł (A.57) Ifoneassumesthatwagesare˝xed, ¹ F 4Œ 1 F 4Œ 0 º = 0 ,thentheDiDestimatestheATETwith noadditionalassumptionsaboutbehavioralresponsestowages.Ifoneallowsforwagechanges(via exogenouschangesorincidencee˙ects),thenoneneedstoassumethatthewageresponsiveness ofworkerswithandwithoutchildrenisequivalent;i.e., ¹ V 4Œ 1 V 4Œ 0 º = 0 .Thislatterrestrictionis testableinthedatawithanappropriateempiricalstrategy. Withouteitherassumption,thentheDiDestimateoftheATETisbiasesinanunknown directionunlessoneknowstheparameters f V 4Œ 1 ŒV 4Œ 0 g ,inwhichcaseestimationisnotnecessary. MyapproachallowsforheterogeneouslaborsupplyelasticitiesanduseswageandEITCvariation acrossstatesanddemographicgroupstoestimatetheelasticities. A.3.3.2LogWageDi˙erenceinDi˙erence TheempiricalliteratureontheEITChasnotfocusedmuchonwagee˙ects,duetotypically assuming˝xedwages.Leigh(2010)regresseslogwagesattheindividuallevelonthemaximum stateEITCamount,butdoesnotreportincidenceparametersdirectly. Toseehowthis˝tswiththeincidencemodel,supposeweobservewagesandtaxratesfor skilllevel 4 acrossstates B andyears C .Theincidenceresultsimplythefollowingequation,where 140 g 4BC = 4BC = 0 if C = 0 : E » F 4BC ¼ = W 0 ¸ W 4 g 4BC ¸ _ B ¸ 4BC (A.58) = ) E » F 4B 1 ¼ E » F 4B 0 ¼ = W 4 g 4B 1 ¸ 4B 1 (A.59) = )¹ E » F 4 11 ¼ E » F 4 10 ¼º¹ E » F 4 01 ¼ E » F 4 0 ¼º W 4 ¹ g 4 11 g 4 01 º¸ 4 11 4 01 | {z } GEBias Ł (A.60) UnlessonecancontrolforGEspilloversorknowswhentheyarenegligible,then,evenwithin askillgroup,spilloverscreateaGEbias.Ifwecompareacrossskillgroups, 4 2f 0 Œ 1 g ,inthe samestatewhereweknow g 4BC = 0 for 4 = 0 ,thenwestillgetGEbiasunlessskillgroup 4 = 0 has noexposuretoskillgroup 4 = 1 : W 1 g 1 BC ¸ 1 B 1 0 B 1 .However,ifskillgroup 4 = 0 hasnoGE exposure,thenwecannottrustthatthisisavalidcontrolgroup.MyapproachdealswiththisGE biasbyaddingstructuralassumptionsaboutlabordemandandestimatinglabormarketelasticities thatcomposetheGEspilloversbasedontheincidencemodel. A.4AdditionalEstimationResults InTableA.7,Iprovideadditionalelasticityestimatesforlaborsupply.Thesespeci˝cations di˙eron˝vedimensions:method,weighting,sample,IVs,anddependentvariable.Thetable displaystheKPrkWaldF,aclusterrobustCragg-Donaldstatisticfor˝rststagestrength,the numberofobservations,andsimpleaveragesoftheestimateselasticities. Alargerelasticityforunmarriedwomenwithchildren(`treated'workers)impliesthatthatthe spillovere˙ectwillbelargeronthe`untreated'workers.Alargerelasticityforuntreatedworkers impliesthatspilloverswillbelargeronthetreatedworkers. The˝rstline,model0,isthebaselineestimatesusedinthemaintext:Iusetwo-stepe˚cient GMM,weightedbythenumberofwageobservationsinacell,usingcellswithatleast˝ve observations,usingthebaselinesetofsimulatedtaxinstruments,asdiscussedinAppendixA.3.1. Therestofmodels1-14varysomeaspectoftheempiricalspeci˝cation.Models1,2use moreobservationsintheestimationsbyallowingsparsercells,whichmakestheelasticitiesmore 141 inelastic.Model3estimatestheelasticitiesusingtwo-stageleastsquaresmethod,whichtends tomaketheestimatesmoreelastic.Models4,5useinversewagevarianceweightingandno- weightsrespectively,whichtendtomaketheempiricalinstrumentstrengthweakerandthuslarger elasticities. 15 Inmodels6-9,Iusedi˙erentsubsetsofelasticities,whichdoesnothavealargee˙ectonthe estimatedelasticitiesbutdoesa˙ectinstrumentstrength.BecauseIaminteractingtheendogenous variablewithdemographicindicators,thisissimilartoestimatinganon-linearmodel,soinmodels 10,11Iuseacontrolfunctionapproach.Model10usesalinearcontrolfunction(˝rststageresidual) approachwhilemodel11usesacubicpolynomialofthecontrolfunction,butbothestimatesare e˙ectivelythesame. Models12-15estimatetheelasticitiesinseparateregressionsbasedonparentalandmarriage statusbutusingthesameregressionspeci˝cation.Theestimatesforwomenwithchildrenare similartobaseline,buttheestimatesforwomenwithoutchildrenaremuchlesselastic.Model16 estimatestheOLSrelationshipand˝ndsnearzeroofnegativelaborsupplyelasticities,potentially duetothesimultaneitybiasthatleadstousetheinstrumentalvariablesmethod. Finally,Models17-20usethe(log)totalnumberofworkersinthelaborforceasthedependent variable.Thismeasureismorecoarsethanthehours-per-workervariablethatIusebutispotentially subjecttolessmeasurementerror.Becausethehoursbasedelasticitiesincludetheextensiveand anypotentialintensivemargine˙ects,thesupplybasedelasticitiesaresmaller.Seethat: d 8 8 = d 8 8 ¸ 8 d 8 ¸ d 8 d 8 (A.61) = ) Y ! = ` ¸ h ¸ b Ł (A.62) Panel(C)inthetableshowsestimatesof h whiletheparameterusedinthemaintextandPanels (A)and(B)are Y ! . InTableA.8,Idisplayalternativeestimationsforthelaborsubstitutionparameter.These 15 Inversewagevarianceweightingwouldbeappropriatewithmeasurementerrorinwages (Borjasetal.,2012)whileunweightedtreatssparsercellsequallyascellswithmanyobservations, whichcausebiasifthereismoremeasurementerrorinsmallercells. 142 TableA.7:AdditionalElasticitySpeci˝cations AveragewithinDemographicGroups Model Method Weighting Sample IVs Obs KPrk FStat Total Unmarried NoChildren Unmarried w/Children Married NoChildren Married w/Children (A) LogTotalHoursperPerson:BaselineElasticitiesusedinMainResults 0 GMM WageObs 5,5 All 47339 40 0.74 0.84 1.04 0.50 0.57 (B) LogTotalHoursperPerson 1 GMM WageObs 0,0 All 67,182 29 0.62 0.76 0.88 0.42 0.42 2 GMM WageObs 3,3 All 57,379 33 0.71 0.79 0.99 0.50 0.55 3 2sls WageObs 5,5 All 47,339 40 0.64 1.03 0.94 0.23 0.36 4 GMM InvWsd 5,5 All 47,339 16 1.00 1.16 1.23 0.93 0.66 5 GMM Unwt 5,5 All 47,381 16 0.79 0.92 0.99 0.68 0.60 6 GMM WageObs 5,5 Age 47,339 12 0.65 0.84 1.06 0.33 0.38 7 GMM WageObs 5,5 Edu 47,339 25 0.78 0.87 1.08 0.52 0.64 8 GMM WageObs 5,5 ATR 47,339 8 0.81 1.19 1.12 0.51 0.43 9 GMM WageObs 5,5 Lite 47,339 21 0.56 0.82 1.00 0.12 0.32 10 CFLinear WageObs 5,5 All 47,339 40 0.68 0.75 0.79 0.65 0.53 11 CFPoly WageObs 5,5 All 47,339 40 0.69 0.76 0.80 0.66 0.54 12 GMM WageObs K0,M0 All 13,433 14 0.28 0.28 13 GMM WageObs K0,M1 All 13,623 18 0.58 0.58 14 GMM WageObs K1,M0 All 7,768 8 0.65 0.65 15 GMM WageObs K1,M1 All 12,515 16 0.54 0.54 16 OLS WageObs 5,5 47,339 0.10 0.16 0.21 0.05 -0.05 (C) LogTotalLaborSupply 17 GMM WageObs 5,5 All 47,339 40 0.46 0.55 0.7 0.21 0.37 18 GMM WageObs 0,0 All 67,178 29 0.53 0.69 0.72 0.3 0.4 19 GMM WageObs 3,3 All 57,379 33 0.5 0.63 0.72 0.26 0.41 20 GMM InvWsd 5,5 All 47,339 16 0.67 0.8 0.9 0.41 0.56 21 GMM Unwt 5,5 All 47,428 16 0.62 0.71 0.76 0.53 0.48 22 OLS WageObs 5,5 47,339 0.03 0.07 0.11 -0.02 -0.04 Unmarriedwomennotinschoolfulltimebetweentheageof20-55;CPSORGsamples1990-2000. AllregressionssamecontrolsasTable1.2themaintext.Iconsidercombinationsofestimation methods(GMM,2SLS,OLS,Controlfunctions),weighting(bynumberofwageobservations, inverselogwagevariance,unweighted),di˙erentsampleselections( ¹ # 0 Œ # 1 º refersto # 0 observa- tionsindemographic-state-yearcelland # 1 wageobservationsinaskill-state-yearcell;(K#,M#) referstobeingaparent(K1)ornot(K0)andbeingmarried(M1)ornot(M0)),andofinstruments (Age/EduusesonlyspilloverIVsbasedonAge/Edu,TaxonlyusesEITCATRIVs,Liteusesonly EITCATRandSharew/EITCIVsseeSectionA.3.1). 143 speci˝cationsdi˙eron˝vedimensions:method/FEs,weighting,sample,IVs,anddependent variable.ThetablealsodisplaysthenumberofobservationsandtheKPrkWaldF,aclusterrobust Cragg-Donaldstatistic. Broadly,theoveridenti˝edmodelshavelower˝rststagestatisticsandtheestimatestendto besmallerinmagnitude(towardszero).Additionally,theEmploymentbasedestimatesof d tend tobelargerthantheHoursperWorkerspeci˝cation.Thiscouldbefortworeasons.Giventhat d = d ln » ! 1 š ! 0 ¼š d ln » F 1 š F 0 ¼ ,eitherthenumeratorislargerorthedenominatorissmaller. Approximatelyandusinganequilibriumrelationshipwiththesupplyfunctions,wecanwrite thisas d ˇ ` 1 ¸ h 1 ¸ b 1 ` 0 ¸ h 0 ¸ b 0 .If ` 1 ¸ h 1 ¸ b 1 ` 0 ¸ h 0 ¸ b 0 h 1 h 0 ,thenthisimpliesthattherelativehoursresponse islowerforthelowerskillworkersthanthehigherskillworkers.Anotherpossibilityisthatnew entrantlowskillworkersworkfewerhoursthantheincumbentworkers,so b 0 0 . Aspointedoutinthemaintext,thechoiceofFEshasa˝rstordere˙ectontheestimated elasticity.Thebaselinespeci˝cationincludesa˝xede˙ectthatistheinteractionofeducationand agegroupindicatorvariableswithyearindicators, d 4C ,whichisdi˙erentthanthelaborsupply speci˝cationthatincludesa˝xede˙ectforeducation,age,marriagestatus,andparentalstatus indicatorinteractionswithoutyear. 16 Iaddtheyearinteractionsbasedontheassumedparametric relationship: ! C ! C = F C š o C F C š o C ! d = ) ln » ! C š ! C ¼ = d ln » F C š F C ¼ ln » o C š o C ¼ Ł (A.63) Idropthemarriageinteractionbecausethisabsorbstoomuchvariation. Toseehowthesechoicesa˙ecttheestimates,models5-8usealternativeFEs.Models5,7use theinteractionofeducation,agegroup,andmarriageindicators,andtheestimateseemssimilar tothemainspeci˝cationexcepttheempiricalinstrumentstrengthhasgonedownbyanorderof magnitude.Models6,8interacttheabovewithyearindicators,andthisappearstoraiseinstrument strength(althoughstilllessthanbaseline)buttheestimatesmakelesssense.Forexample,model 6hasapositivesubstitutionelasticity(statisticallyindistinguishablefromzero);although,model8 16 Droppingparentalstatusisdonebecausethesubstitutionelasticityisestimatedatthe`skill' levelratherthandemographiclevel. 144 isnegativeyetaboutafourthaslargeinmagnitude.Giventhatthe˝rststageFstatisticgoesdown, IinterpretthisastheFEsabsorbingneededvariationintheinstrument. TableA.8:AdditionalElasticitySpeci˝cations AveragewithinDemographicGroups Model Method Weighting Sample IVs Obs KPrk d d FStat HoursperWorker Employment (A) BaselineinMainResults 0 2sls WageObs 5 JI-ATR 19,501 67.26 -1.81 -1.75 (B) JustIdenti˝ed 1 2sls WageObs 0 JI-ATR 29,604 63.66 -2.15 -2.00 2 2sls WageObs 3 JI-ATR 25,773 63.61 -2.08 -1.93 3 2sls InvWsd 5 JI-ATR 19,501 47.91 -1.57 -1.40 4 2sls Unwt 5 JI-ATR 19,501 58.03 -1.00 -0.71 5 2sls,FEs1 WageObs 5 JI-ATR 19,501 6.54 -2.15 -3.41 6 2sls,FEs2 WageObs 5 JI-ATR 19,501 21.89 0.15 -0.52 7 2sls,FEs1 WageObs 3 JI-ATR 29,604 5.81 -4.29 -5.34 8 2sls,FEs2 WageObs 3 JI-ATR 29,604 24.05 -0.55 -1.06 9 2sls WageObs 5 JI-Pos 19,501 3.09 -1.83 -2.11 (C) OverIdenti˝ed 10 GMM WageObs 5 OvID 19,501 13.76 -1.57 -1.85 11 2sls WageObs 5 OvID 19,501 13.76 -1.67 -2.06 12 GMM WageObs 0 OvID 29,604 13.93 -2.30 -2.47 13 GMM WageObs 3 OvID 25,773 13.46 -2.18 -2.35 14 GMM InvWsd 5 OvID 19,501 6.86 -1.54 -1.99 15 GMM Unwt 5 OvID 19,501 8.74 -0.61 -0.54 (D) OLSandAlternateVariableConstructions 16 OLS WageObs 5 19,501 0.06 0.01 17 2sls,alt1 WageObs 5 JI-ATR 19,903 59.23 -1.81 -1.73 18 2sls,alt2 WageObs 5 JI-ATR 12,288 88.8 -2.24 -2.20 19 2sls,alt3 WageObs 5 JI-ATR 17,182 81.05 -1.97 -1.97 20 2sls,alt4 WageObs 5 JI-ATR 5,239 61.23 -3.24 -3.19 Unmarriedwomennotinschoolfulltimebetweentheageof20-55;CPSORGsamples1990-2000. AllregressionssamecontrolsasTable1.3themaintext.Iconsidercombinationsofestimation methods(GMM,2SLS,OLS;˝xede˙ectsandvariableconstructions),weighting(bynumber ofwageobservations,inverselogwagevariance,unweighted),di˙erentsampleselections( ¹ # º referstominimumvalueofthemeannumberofskill-state-yearobservationsforthenumerator anddenominatorgroup),andofinstruments(JustIdenti˝esusingrelativeEITCATRsorSharew/ EITCorOveridenti˝edseeSectionA.3.1). 145 A.4.1Di˙erenceinDi˙erenceRegressions Tocomplementthemodelimpliedlaborsupplye˙ects,Iestimateasimpledi˙erenceindi˙erence speci˝cation.Iusethe1990-1996ASECsamplesfortheOBRAexpansionandthe2006-2012 samplesfortheARRAexpansion.Iregressanindicatorforlaborforceparticipationduringthe previousyearonanpostindicator(1994-1996and2010-2012)timesaparentalstatusindicator. Iincludestate-yearindicatorsanddemographicgroupindicatorsthatinteractage,education, marriage,parentalstatus.Iuserobuststandarderrorsclusteredatthedemographicgroupleveland weighttheregressionsusingtheASECsupplementweights. IntypicalEITCDiDstudies,onecomparesunmarriedwomenwithnoqualifyingchildren tothosewithqualifyingchildren(EissaandLiebman,1996;EissaandHoynes,2004;Bastian, forthcoming).Onerationaleforthisisthatunmarriedworkerswhodonotworkde˝nitelydonot receiveEITCbene˝tsandtheseworkersarethoughttoworkinsimilarlabormarkets.Aslong asthereisnootherparentalspeci˝ctime-varyinglabormarketchangesaroundEITCexpansions, thenthisshouldestimatetheaveragetreatmente˙ectonthetreatedwhichisameasureofthedirect laborsupplye˙ectsoftheEITC.BecausetheARRAexpansionwasmostgenerousspeci˝cally forworkerswiththreeormorequalifyingchild,Iincludetwoadditionalspeci˝cations.Incolumn (3),Icompareworkerswithnoqualifyingchildrentoworkerswiththreequalifyingchildren.In column(4),Icompareworkerswithoneortwoqualifyingchildrentoworkerswiththreequalifying children. TableA.9:EITCDi˙erence-in-Di˙erenceResults OBRA ARRA (1) (2)(3)(4) Post ParentStatus 0.039 0.010-0.006-0.011 (0.010) (0.007)(0.014)(0.013) Sub-Sample - - ˘ 2f 0 Œ 3 g ˘ 2f 1 Œ 2 Œ 3 g Obs 78,549 119,08282,82643,379 Clusters 64 646432 Unmarriedwomennotinschoolfulltimebetweentheageof20-55.AlldatafromMarchCPS,ASEC samples,1990-1996&2006-2012.Allregressionsincludestate-yearindicatorsanddemographicgroup indicators,asinthemaintext. 146 A.5AdditionalIncidenceResults A.5.1IndividualLevelE˙ectsof1993Expansion InTableA.10Ireportindividuallevelresultsratherthanaggregateasinthemaintext.These resultsshowhowanindividual'sEITCamountisa˙ectedbyincidenceandbehavioralresponses. ThechangeintheEITCisthenaivechangethatholdsalllaborsupplyandwagesconstant.In Panel(A),unmarriedmothersgetroughly $417 inexpandedEITCbutloseroughlyafourthof thatamountduetowageincidence.Forunmarriedmothers,wagespilloversarelessimportant,at roughly 21% ofthewagee˙ect,primarilybecausethedirecte˙ectsdominate.Formarriedmothers spilloversare 152% ofthewagee˙ect,whileforwomenwithoutchildrenspilloversareonly 8 Ł 4% ofthewagee˙ect. TableA.10:IncidenceResults:IndividualE˙ectsof1993Expansion EDU F! Ch EITC d F PE ! d F GE ! ¹ d F GE d F PE º ! d F GE ! d PE ! 1 d F PE ! Ch EITC d F GE ! Ch EITC (a)(b)(c)(d)(e)(f)(g)(h) (A)UnmarriedMothers LessHS10,059417-117-1142.40-3.4%-28.6%-29.3% HS17,637314-75-704.70-7.6%-13.2%-14.2% SomeCol18,259260-46-414.90-13.6%-9.7%-10.8% BA+30,93699-12-39.30-81.6%-0.3%-1.0% Total19,055273-60-545.20-20.8%-11.7%-12.7% (B)MarriedMothers LessHS10,796.2162-2.500.102.6042.9%-0.0%-0.4% HS15,367.4561.405.504.1075.4%0.2%0.1% SomeCol19,334.3355.3010.505.20118.7%0.4%0.2% BA+31,027.4103.4012.809.40317.1%0.1%0.0% Total20,513.8452.808.605.80152.0%0.2%0.0% (C)WomenwithoutChildren LessHS11,196.220-44-422.60-8.6%-8.4%-8.6% HS16,967.19-26-224.4065.1%-1.1%-1.2% SomeCol18,859.64-20-154.9045.3%-0.7%-0.8% BA+30,888.32-5.303.809.10-94.6%-0.0%-0.0% Total20,880.47-20-155.708.4%-1.3%-1.4% Allitemsareaverageacrossworkers,weightedbyhours sampleweights.Alldatafrom1994 MarchCPS,WomenfromTaxUnitsBaselinelaborsupplyelasticitiesintable1.2and d = 1 Ł 8 . 147 A.5.2EITCvsNIT InTableA.11,IpresentanEITCvsNegativeIncomeTax(NIT)simulationresultsusingthelabor supplyelasticitiesfromTable1.2.Thisexercisecomparesthemainspeci˝cationofRothstein (2010),aspresentedinTable5,withthegeneralequilibriume˙ectsthispaperdescribes. Inthetablebelow,the`Rothstein'speci˝cationreplicatesthe˝rstcolumnofTable5ofRothstein (2010)usingmyincidencesample(wheredi˙erencesaredescribedinAppendixA.2).Forthese columns,Iuseahomogeneouslaborsupplyelasticityof Y ! = 0 Ł 75 andthelaborsubstitution elasticity d = 0 Ł 3 .ThevaluescloselycorrespondtothevaluesinRothstein.Forexample,I calculatealabore˙ectof $0 Ł 13 fortheEITCand $0 Ł 18 fortheNITwhileRothsteincalculates $0 Ł 09 and $0 Ł 16 ,respectively. Thenextsetofcolumns(D-G)usetheestimatedlaborsupplyelasticitiesfromTable1.2but usethesame d = 0 Ł 3 .Theheterogeneouslaborsupplyelasticitychangesthelaborsupplyshocks, whichampli˝esandattenuatesdi˙erentlabormarkete˙ects.Forexample,theEITCwagee˙ects are $0 Ł 42 incolumn(B)butareonly $0 Ł 29 incolumn(D). Thelastsetofcolumns(H-K)usetheestimatedlaborsupplyelasticitiesandsubstitution elasticityfromTable1.2, d = 1 Ł 8 .Thishasapronouncede˙ectonthePElabormarkete˙ects butlessontheGEe˙ects.Forexample,theEITCwagee˙ectsare $0 Ł 42 incolumn(B)butare nowonly $0 Ł 12 incolumn(H)butforcolumns(F)and(J)thee˙ectsmuchcloserat $0 Ł 04 and $0 Ł 03 . OnenoteworthypointisthatifRothsteinhadusedageneralequilibriumanalysis,then,com- paringthedi˙erencesincolumns(D,E)to(F,G),theEITCwouldhavefaredfarbetter.First,note thatRothsteinprimarilyusednetearningsandtransferswith˝xedtaxestocomparetheprograms. Ihaveprovidedtheadditionalcolumnsofnetearningsthatallowtaxestochange(givena˝xed averagetaxrate)andthechangeinwelfareassumingtheexpansionsarerevenueneutral. EvaluatingtheprogramsbasedonRothstein'scriteria,inPEtheEITCdoesworseonboth measures,butinGEthemeasuresgiveamixedsignal.Usingthenetearningsallowingfortax changes,faresbetterinbothPEandGE.ThenetearningsfortheEITCarealwayspositivewhileare 148 TableA.11:IncidenceResults: AggregateE˙ects:AllWomen Rothstein(2010)Replication&Extension Rothstein d = 0 Ł 3 d = 2 Ł 00 GE GE Dollars EITC NIT EITC NIT EITC NIT EITC NIT EITC NIT (B)(C) (D)(E)(F)(G) (H)(I)(J)(K) Intended 1.000.56 1.000.561.000.56 1.000.561.000.56 Labor 0.13-0.18 0.09-0.120.24-0.35 0.22-0.300.27-0.37 Wage -0.420.60 -0.290.42-0.040.06 -0.120.17-0.040.05 GrossEarnings -0.300.42 -0.200.290.20-0.28 0.10-0.130.23-0.32 NetTransfer,FixedTaxes 0.581.50 0.711.420.961.06 0.881.170.961.05 NetEarn,FixedTaxes 0.701.42 0.801.291.200.72 1.100.871.230.68 NetEarnings 0.12-0.35 0.20-0.460.57-0.99 0.50-0.870.63-1.04 FiscalExternality -0.100.05 -0.090.04-0.070.02 -0.090.04-0.080.03 Unitsintablearechangesindollarsofearningssummedacrossdemographicgroups.Note: / ˝ = F !Œ/ # = ¹ 1 g º F ! .Alldatafrom1993MarchCPS,WomenfromTaxUnitsLabor supplyelasticitiesintable1.2,except`Rothstein'whichuses Y ! = 0 Ł 75 forall. alwaysnegativefortheNITexpansions.ThisisbecausetheEITCexpandsproductionbybringing newworkersintothelaborforcewhiletheNITdecreasesproductionbyhavingworkersleave.For someworkers,theNITdriveswagesupwhichcausesthisgrouptopaymoreintaxes,whichcan causenetearningstodecrease. Finally,thewelfarechangesarealwaysnegativefortheEITCandeitherpositiveornegative fortheNITdependingontheparameterization.Anegativewelfarechangehereimpliesthatthe governmentexpenditureincreases(thewelfaremeasureisthe`˝scalexternality'seeSection A.1.2.2).FortheEITC,thegovernmentisspendingmorebecauseitispayingenteringworkers moreinEITC.FortheNIT,thegovernmentisspendingmorebecauseitispayingexitingworkers nottowork.Balancingthesetwodi˙erentreasonsforincreasedgovernmentexpenditureisa normativequestion. A.6StructuralModelImpliedParameters UsingtheapproachoutlinedinSection1.9,Iback-outthestructuralparametersandcalculate themodelimpliedelasticitiesfortheout-of-sampleperiod.InFigureA.1Iplotthemodelimplied 149 averagelaborshiftersandaveragesupplyelasticitybymarriageandparentalstatusovertime. Thelaborshiftersappeartotrenddownwardovertimeforunmarriedwomenbutconstantfor marriedwomen.Thisimpliesthattheutilitycostoflaborsupplyisweaklyincreasingforunmarried women.Forallgroups,theelasticitiesareincreasingsincethelate1990's.Givenequation1.32, thisislargelyduetoroughlystagnantrealnetwagegrowthanddeclininglaborforceparticipation inthe2000's.Together,forunmarriedwomenthisimpliesthattheperdollare˙ectivenessofthe EITCrelativetotheearly1990'sisambiguous,butshouldbemoree˙ectiveformarriedwomen. FigureA.1:ModelImpliedParameters Supplyshifterbasedonequation1.33;elasticitybasedonequation1.32;parameter V 3 recoveredfromtaxyears1993-1997andestimatedelasticitiesfromTable1.2and taxandtransferinclusiverealnetwage. 150 APPENDIXB APPENDIXTOCHAPTERTWO B.1AdditionalDataSources InTableB.1IlistadditionalinformationaboutStateEITCreturnsandexpenditures.Mostof thisinformationcomesfromannualstatetaxexpenditurereports.Somevaluesareestimates,some arelistedasexactdata,andothersarenotdescribedinthereports.SeveralreportsstatethatEITC claimsareahighqualitydataitemcomparedwithotheritemsinthereports. TableB.1:StateEITCReturnsandAmountsSources StateYearURL Notes CA2018http://www.dof.ca.gov/Forecasting/Economics/Tax_Expenditure_Reports/documents/Tax_ExpenditureReport_2019-20_B.pngForecast1billionin2020 CO2017www.colorado.gov/paci˝c/sites/default/˝les/2019_Annual_Report_1.png CT2018portal.ct.gov/-/media/DRS/Research/annualreport/DRS-FY19-Annual-Report.png?la=en DCTY2020cfo.dc.gov/node/1456456 Estimate DEFY2020˝nance.delaware.gov/˝nancial-reports/tax-preference-report/ HITY2018˝les.hawaii.gov/tax/stats/stats/act107_2017/act107_earnedincome_txcredit_2018.png ILTY2017www2.illinois.gov/rev/research/taxstats/IndIncomeStrati˝cations/Documents/2017-IIT-1040ILReturn-Final.png INFY2018www.in.gov/sba/˝les/Tax%20Expenditure%20Report%20FY%202018-2021%20Final%20GW.pngEstimate IAFY2018tax.iowa.gov/sites/default/˝les/2019-08/Individual%20Income%20Tax%20Report%202017.pngPartialEstimate KSTY2017www.ksrevenue.org/png/ar19complete.png LAFY2018lla.la.gov/PublicReports.nsf/8F85E9838E24E5308625831B00524FF5/$FILE/0001A8EC.png MEFY2018www.maine.gov/revenue/research/tax_expenditure_report_17.pngEstimate MDFY2018dbm.maryland.gov/budget/Documents/operbudget/FiscalYear2018Tax%20ExpenditureReport.pngIncludesMontgomerycounty MAFY2018www.mass.gov/doc/2020-tax-expenditure-budget/download MIFY2018sigma.michigan.gov/EI360TransparencyApp/˝les/Tax%20Expenditure%20Reports/Tax%20Expenditure%20Report%202018.png MNTY2017www.revenue.state.mn.us/minnesota-income-tax-statistics-countyEstimate MT NotYetinE˙ect NETY2018revenue.nebraska.gov/research/statistics/nebraska-statistics-incomeTableF2 NJTY2019www.nj.gov/treasury/taxation/png/taxexpenditurereport2020.png NMTY2017real˝le.tax.newmexico.gov/2018%20NMTRD%20Tax%20Expenditure%20Report.png NYTY2018www.tax.ny.gov/research/stats/stat_pit/earned_income_tax_credit/earned_income_tax_credit_analysis_of_credit_claims_open_data_short2.htmNYS+NYCEITC OHTY2018www.tax.ohio.gov/tax_analysis/tax_data_series/individual_income/publications_tds_individual/Y1TY18.aspx OKTY2017www.ok.gov/tax/documents/Tax%20Expenditure%20Report%202017-2018.png ORTY2017www.oregon.gov/dor/programs/gov-research/Pages/research-personal.aspxReturnsarepartialyear RITY2018digitalcommons.uri.edu/cgi/viewcontent.cgi?article=1774&context=srhonorsprogEstimate SCTY2018dor.sc.gov/resources-site/publications/Publications/2018-2019_AnnualReport.png VTTY2018tax.vermont.gov/sites/tax/˝les/documents/income_stats_2018_state.png VA2019www.tax.virginia.gov/sites/default/˝les/inline-˝les/2019-annual-report.png WITY2018www.revenue.wi.gov/Pages/RA/IIT-RefundableCredits.aspx YeardescriptionsareeitherTaxYear,FiscalYear,orisambiguousbasedonlanguageofthestatetaxagency.Iincludewhenthe agencydeclaresthatvaluesareestimates,butthismaynotbecomprehensive. B.2AdditionalResults B.2.1AlternateSpeci˝cations InTableB.2Ireportcoe˚cientestimatesforalternativespeci˝cationsforlogtotalfederalEITC returnsandemploymentforwomenwithlessthanahighschooldegree,usingtheSBFEand SBRD:Lspeci˝cations.Incolumn(a),IreproducethemainresultsfromTable2.3.Forcolumn 151 (b),Idonotweighttheregressions,whichchangestheinterpretationfromanindividualpolicy e˙ecttoacountypolicye˙ect.Forcolumn(c),IomitthethestateGDPcontrol,whichwas includedasthepreviousliterature˝ndsthatstatesupplementratesarecorrelatedwiththevariable (Leigh,2010).Finally,column(d)addscounty-speci˝clinear-trends,whichisthemostaggressive speci˝cation. Ultimately,theresultsofthealternativespeci˝cationsemphasizehowsensitivetheestimates aretospeci˝cationchanges. B.2.2StateBorderRegressionResults TableB.3displaysthepredictedstatesupplementratesfromthefollowingregression: H B1C = U ¸ Õ E 2 V W 0 E 1 » C ) B1 = E ¼¸ Õ E 2 V W 1 E 1 » C ) B1 = E ¼ 1 » Two-Sided ¼ (B.1) ¸ ˇ C V 0 ¸ ˇ C 1 » Two-Sided ¼ V 1 ¸ D B1C Œ where H isthestatesupplementratefortheimplementedprogram, ) B1 istheyearthestate supplementedisimplementedfortheborder, 1 » Two-Sided ¼ isanindicatorforanincumbentprogram isalongtheborder,and ˇ C areyearindicators.Iincludetheyearindicatorstoabsorbthegeneral positivetrendinstatesupplementrates. Iusethepredictedvaluesratherthancoe˚cientstohighlightthedi˙erenceinmagnitudeofthe one-andtwo-sidedbordersovertimeandcomparedtoeachother.Thisisthesameasdisplaying thecoe˚cients f W 0 E g fortheone-sidedand f W 0 E ¸ W 1 E g forthetwo-sidedborders.Thesearethe values(andtheirclusteredstandarderrors)plottedinFigure2.2.binthemaintext. ToplotthereactionfunctionforFigure2.2.c,Iuseonlythestateborderswherethereisan incumbentprogramandlookathowthe.incumbentprogram`reacts'whenitsneighborstate implementsaprogram.TableB.4displaysthecoe˚cientsfromthefollowingregression: H B1C = U ¸ Õ E 2 V W E 1 » C ) B1 = E ¼¸ _ C ¸ _ B ¸ D B1C Œ (B.2) 152 TableB.2:AlternateSpeci˝cations:FedReturnsandEmployment MainUnweightNoStateGDPCountyTrends (a)(b)(c)(d) FULLSAMPLE-SBFE DV: ln » TotalFedEITCClaims ¼ W 0.150.070.180.04 se(0.05)(0.05)(0.05)(0.03) DV: ln » Employment,LHSWomen ¼ W -0.060.10-0.190.02 (se)(0.08)(0.08)(0.13)(0.05) ONE-SIDESAMPLE-SBFE DV: ln » TotalFedEITCClaims ¼ W 0.070.180.070.02 (se)(0.12)(0.09)(0.11)(0.07) DV: ln » Employment,LHSWomen ¼ W 0.110.150.120.15 (se)(0.15)(0.14)(0.14)(0.09) FULLSAMPLE-SBRD:L DV: ln » TotalFedEITCClaims ¼ W 0.210.080.320.04 (se)(0.17)(0.07)(0.23)(0.07) DV: ln » Employment,LHSWomen ¼ W -0.200.12-0.40-0.03 (se)(0.16)(0.14)(0.27)(0.08) ONE-SIDESAMPLE-SBRD:L DV: ln » TotalFedEITCClaims ¼ W -0.07-0.13-0.07-0.08 (se)(0.25)(0.11)(0.25)(0.11) DV: ln » Employment,LHSWomen ¼ W 0.54-0.130.420.31 (se)(0.55)(0.34)(0.52)(0.36) State-borderclusteredstandarderrorsparentheses.Controlsalwaysincludeyearbypairorborder- statusindicatorsandeitherlogtotalcountyreturnsorpopulation. where H isthestatesupplementratefortheincumbentprogram, ) B1 istheyearthe new state supplementedisimplementedfortheborder, _ C and _ B areyearandstateFEsrespectively.The yearandstateFEsabsorbageneralpositivetrendinstatesupplementratesbytimeandageof incumbentprograms.Figure2.2( c )plotsthecoe˚cients f W E g andtheirWhitestandarderrors. 153 TableB.3:StateSupplementRatesbyBorderStatus:One-vsTwo-sidedBorders MarginsofStateSupplementRate EventTime One-Sided Two-Sided -5 0.00 0.01 (0.00) (0.00) -4 0.00 0.00 (0.01) (0.02) -3 0.00 0.00 (0.01) (0.02) -2 0.00 -0.01 (0.00) (0.02) -1 0.00 -0.01 (0.01) (0.02) 0 0.07 0.16 (0.00) (0.02) 1 0.08 0.18 (0.01) (0.03) 2 0.09 0.17 (0.01) (0.03) 3 0.09 0.19 (0.01) (0.03) 4 0.10 0.18 (0.01) (0.03) 5 0.10 0.19 (0.01) (0.03) 6 0.10 0.19 (0.01) (0.04) 7 0.10 0.16 (0.01) (0.04) 8 0.10 0.16 (0.01) (0.04) 9 0.12 0.17 (0.01) (0.05) 10 0.12 0.19 (0.02) (0.06) N 597 Bothcolumnsshowpredictedvaluesbyborder-statusfromthesameregression.State-border clusteredstandarderrorsareinparentheses.Controls:yearbyborder-statusindicators.Event timeisrelativetothestateimplementationyear,wheretheomittedbaseyearistheyearbefore implementation.Thesampleisallstate-borderswheretheimplementingstatesatleast10years apart,theimplementedsupplementactivatesbetween2000-2018,andtheimplementationisnot reversed. B.2.3EventStudyRegressionResults ThefollowingtablesunderlietheplotsinFigure2.4.Speci˝cally,theyare`stacked'eventstudies ofstateEITCsupplementintroductionsbetween2000and2018.Foreachempiricaldesign,SBFE 154 TableB.4:StateSupplementRatesbyBorderStatus:One-vsTwo-sidedBorders EventTime IncumbentReaction -5 -0.02 (0.00) -4 -0.02 (0.02) -3 -0.01 (0.02) -2 -0.01 (0.01) 0 0.00 (0.01) 1 0.01 (0.01) 2 0.03 (0.01) 3 0.02 (0.01) 4 0.02 (0.02) 5 0.03 (0.01) N 110 Whitestandarderrorsparentheses.Controls:yearandstateFEs.Eventtimeisrelativetothestate implementationyear,wheretheomittedbaseyearistheyearbeforeimplementation.Samplesisall state-borderswheretheimplementingstatesatleast10yearsapart,theimplementedsupplement activatesbetween2000-2018,andtheimplementationisnotreversed. orSBRD,Ipresentthreesamples:pooled,one-sided,andtwo-sided.Thepooledsampleincludes allstateborderswithastatesupplementintroduced;theone-sidedareonlythosestateborders wherethereisnoincumbentprogramoneonesideoftheborder;thetwo-sidedarethosewhere thereisanincumbentprogramwhenthesupplementisintroduced. Theregressionequationsaredescribedinthemaintextwiththe˝gures.Notethatthestandard errorsareclusteredbystateborders,butthenumberofclustersstartsat36andgoesto9inthe two-sidedsample.Thisisgenerallyconsideredtobetoofewclustersthatcausesthestandarderrors tobetoosmall(notconservativeenough).However,evenifthestandarderrorsaretoosmall,the majorityofestimatesarestillnotstatisticallydi˙erentfromzero.Inlightofthis,Idonotattempt amoreformaltreatmentofthestandarderhasananalyticbiascorrectioninthevariance matrixoranappropriatebootstrapinsteadadviseaninterestedreadertofollowthe 155 simpleadviceofCameronandMiller(2015)andusea ) distributionwithdegreesoffreedom equaltothenumberofclusters. TableB.5:StackedEventStudies:LogEITCReturns DV:LogEITCReturns SBFESBRD:L EventTime PooledOne-SidedTwo-Sided PooledOne-SidedTwo-Sided -5 -0.01-0.01-0.02 0.00-0.010.04 (0.01)(0.01)(0.01) (0.01)(0.01)(0.04) -4 0.00-0.010.00 0.00-0.010.06 (0.01)(0.01)(0.01) (0.01)(0.01)(0.02) -3 0.000.00-0.01 0.010.000.06 (0.00)(0.01)(0.01) (0.01)(0.01)(0.02) -2 0.000.000.00 0.000.000.03 (0.00)(0.00)(0.00) (0.01)(0.01)(0.01) 0 0.00-0.010.02 -0.01-0.010.00 (0.00)(0.00)(0.00) (0.01)(0.01)(0.01) 1 0.01-0.010.03 0.00-0.010.01 (0.01)(0.01)(0.01) (0.01)(0.02)(0.02) 2 0.01-0.010.03 0.000.020.01 (0.01)(0.01)(0.02) (0.01)(0.02)(0.02) 3 0.010.000.04 0.010.020.01 (0.01)(0.01)(0.02) (0.02)(0.03)(0.03) 4 0.020.000.05 0.020.010.02 (0.01)(0.01)(0.02) (0.02)(0.03)(0.03) 5 0.02-0.020.05 0.02-0.020.02 (0.02)(0.02)(0.02) (0.02)(0.02)(0.03) 6 0.02-0.010.05 0.02-0.020.03 (0.02)(0.01)(0.02) (0.02)(0.02)(0.03) 7 0.02-0.020.05 0.02-0.030.03 (0.03)(0.02)(0.04) (0.03)(0.02)(0.05) 8 0.00-0.020.03 0.00-0.010.01 (0.02)(0.02)(0.04) (0.03)(0.02)(0.04) 9 0.00-0.020.03 0.000.010.01 (0.03)(0.02)(0.04) (0.04)(0.02)(0.05) 10 0.02-0.010.05 0.020.000.02 (0.02)(0.02)(0.03) (0.02)(0.03)(0.03) Counties 457348115 457348115 Obs 11,8868,8803,006 6,3254,7151,610 Clusters 36279 36279 State-borderclusteredstandarderrorsparentheses.Regressionsweightedcountypopulationin 2000.Controls:logofcountypopulationortotalreturns,logofstaterealGDP,anddesignspeci˝c FEs.Eventtimeisrelativetothestateimplementationyear,wheretheomittedbaseyearistheyear beforeimplementation.Samplesarebasedonthewhetheratthetimeofimplementationofagiven statesupplementforagivenstateborderthereisanincumbentprogram. 156 TableB.6:StackedEventStudies:LogEmployment:Women,LessHS DV:LogEmployment:Women,LessHS SBFESBRD:L EventTime PooledOne-SidedTwo-Sided PooledOne-SidedTwo-Sided -5 0.00-0.020.00 -0.01-0.030.11 (0.01)(0.02)(0.02) (0.02)(0.02)(0.03) -4 0.00-0.02-0.01 -0.01-0.030.06 (0.01)(0.01)(0.01) (0.01)(0.01)(0.02) -3 -0.01-0.02-0.03 -0.02-0.020.03 (0.00)(0.01)(0.01) (0.01)(0.01)(0.02) -2 0.00-0.010.00 0.000.000.02 (0.00)(0.01)(0.01) (0.01)(0.01)(0.01) 0 0.010.010.01 0.020.020.03 (0.00)(0.00)(0.01) (0.02)(0.02)(0.03) 1 0.010.020.02 0.030.040.03 (0.01)(0.01)(0.01) (0.02)(0.02)(0.04) 2 0.020.030.03 0.030.050.04 (0.01)(0.01)(0.01) (0.02)(0.02)(0.04) 3 0.030.040.04 0.030.070.04 (0.01)(0.01)(0.02) (0.03)(0.02)(0.05) 4 0.030.040.04 0.040.090.04 (0.01)(0.01)(0.01) (0.03)(0.03)(0.04) 5 0.040.040.06 0.050.110.05 (0.02)(0.01)(0.01) (0.03)(0.04)(0.04) 6 0.040.050.06 0.060.110.06 (0.02)(0.02)(0.01) (0.03)(0.05)(0.04) 7 0.040.050.06 0.050.090.05 (0.03)(0.02)(0.01) (0.03)(0.06)(0.04) 8 0.070.050.08 0.080.100.08 (0.02)(0.02)(0.01) (0.03)(0.07)(0.04) 9 0.080.070.09 0.080.110.09 (0.03)(0.02)(0.01) (0.03)(0.06)(0.04) 10 0.090.060.12 0.100.110.10 (0.02)(0.02)(0.02) (0.03)(0.07)(0.05) Counties 475366114 475366114 N 48,64936,21812,431 25,82419,1926,632 CL 37289 37289 State-borderclusteredstandarderrorsparentheses.Regressionsweightedcountypopulationin 2000.Controls:logofcountypopulationortotalreturns,logofstaterealGDP,anddesignspeci˝c FEs.Eventtimeisrelativetothestateimplementationyear,wheretheomittedbaseyearistheyear beforeimplementation.Samplesarebasedonthewhetheratthetimeofimplementationofagiven statesupplementforagivenstateborderthereisanincumbentprogram. 157 TableB.7:StackedEventStudies:LogAvgMonthlyEarnings:Women,LessHS DV:LogAvgMonthlyEarnings:Women,LessHS SBFESBRD:L EventTime PooledOne-SidedTwo-Sided PooledOne-SidedTwo-Sided -5 0.00-0.01-0.01 0.00-0.010.00 (0.00)(0.01)(0.01) (0.01)(0.01)(0.03) -4 0.000.00-0.01 0.00-0.01-0.02 (0.00)(0.01)(0.01) (0.01)(0.01)(0.03) -3 -0.01-0.01-0.02 -0.01-0.01-0.03 (0.00)(0.00)(0.01) (0.01)(0.01)(0.03) -2 0.00-0.010.00 -0.01-0.01-0.02 (0.00)(0.00)(0.01) (0.00)(0.00)(0.02) 0 0.010.000.01 0.000.02-0.01 (0.00)(0.00)(0.00) (0.01)(0.01)(0.01) 1 0.010.010.02 0.010.030.00 (0.00)(0.00)(0.01) (0.01)(0.01)(0.01) 2 0.010.010.02 0.000.030.00 (0.00)(0.01)(0.01) (0.01)(0.01)(0.01) 3 0.010.000.03 0.000.020.00 (0.01)(0.01)(0.01) (0.01)(0.01)(0.01) 4 0.00-0.010.03 0.000.020.01 (0.01)(0.00)(0.01) (0.01)(0.01)(0.01) 5 0.00-0.010.03 0.000.010.01 (0.01)(0.01)(0.02) (0.02)(0.02)(0.02) 6 0.00-0.010.03 0.000.030.01 (0.02)(0.01)(0.03) (0.02)(0.02)(0.02) 7 0.000.000.02 0.000.040.00 (0.02)(0.01)(0.03) (0.03)(0.02)(0.03) 8 0.030.000.06 0.030.020.04 (0.02)(0.01)(0.02) (0.01)(0.02)(0.02) 9 0.030.000.06 0.030.010.04 (0.01)(0.02)(0.02) (0.01)(0.02)(0.02) 10 0.040.000.08 0.040.010.05 (0.02)(0.02)(0.02) (0.01)(0.02)(0.02) Counties 473364114 472363114 N 48,15035,75812,392 25,51618,9096,607 CL 37289 36289 State-borderclusteredstandarderrorsparentheses.Regressionsweightedcountypopulationin 2000.Controls:logofcountypopulationortotalreturns,logofstaterealGDP,anddesignspeci˝c FEs.Eventtimeisrelativetothestateimplementationyear,wheretheomittedbaseyearistheyear beforeimplementation.Samplesarebasedonthewhetheratthetimeofimplementationofagiven statesupplementforagivenstateborderthereisanincumbentprogram. 158 APPENDIXC APPENDIXTOCHAPTERTHREE C.1Propositions1and2 Recallthat ˇ 0 = e ˙ ¹ 0ŒH A ¹ 0 º ŒH ºš f n Í 0 0 2A f e ˙ ¹ 0 0 ŒH A ¹ 0 0 º ŒH ºš f n g " fromthemaintextusinglogitdemand.Here,we switchtoindexingbuildingsusing 9 ratherthan 0 .Tomakenotationeasier,let U = m˙ ¹ 0ŒH AŒH º mA 0 bethe(negative)marginalutilityofconsumption,andset f n = 1 . C.1.1Proposition1 Bindingzoningrestrictions,byreducingquantitiesataplot : ,increaserentsatthatplot.Therest ofProposition1willfollowaslongasplots,ascompetingproducts,arestrategiccomplementsin pricingdecisions. De˝nitionC.1.1. StrategicComplements:Ifthecrossderivativeofagivenplayer'sownpayo˙ functionwithrespecttoheractionandthatarival'sactionispositive,thentheactionsarestrategic complements. InourBertrandoligopolysetting,rentsarestrategiccomplementsif m 2 c 9 mA 9 mA : = m mˇ 9 š mA 9 mA : A 9 ˘ 9 ¹ ˇ 9 º ¸ mˇ 9 mA 9 m˘ 9 mˇ 9 mˇ 9 mA : ¸ mˇ 9 mA : 0 Ł (C.1) Denotethederivativeofmarginalcostas m˘ 9 mˇ 9 : = 2 9 .WhenweapplyLogitdemandfunctions, thisbecomes: m 2 c 9 mA 9 mA : = U 2 ˇ 9 ˇ : ¹ 1 2 ˇ 9 º¹ A 9 ˘ 9 º 2 9 Uˇ 9 ¹ 1 ˇ 9 º Uˇ 9 ˇ : (C.2) = Uˇ 9 ˇ : | {z } ¡ 0 2 6 6 6 6 6 6 6 6 4 ˇ 9 ¹ 1 ˇ9 º | {z } ¡ 0 ¸¹ 2 9 Uˇ 9 ¹ 1 ˇ 9 ºº | {z } ¡ 0 if 2 9 ¡ 0 3 7 7 7 7 7 7 7 7 5 Ł (C.3) Note,weusetheequilibriumrelationshipthat ¹ A 9 ˘ 9 º = A 9 š Y 9 . 159 Thus,generallythestrategicnatureofpricingdecisionsisambiguous.Asu˚cientcondition forstrategiccomplementsinthelogitcaseisthat 2 9 0 8 9 .Thisistruewithconstantmarginal costsordiseconomiesofscaleforthebuilding.Withdecreasingmarginalcosts,thestrategic complementaryofpricingdecisionsisambiguousandmayvarybetweenpairsofbuildings. Ifmarginalcostisconstant,thentherentincreasecouldonlybeduetoanincreaseinmonopoly markups.Withvariablemarginalcost,thisthedegreethatthemarkupchangesisambiguous. Decreasingmarginalcostswouldpushthelandownertoexpandquantitysuppliedandtravelfurther downthedemandcurve,whichmayleadtoasmallermarkupperunitbutgreaterpro˝t(andlower rent).Ontheotherhand,increasingmarginalcostsattenuatethelandowner'sdesiretoexpand keepingthelandownerinasteeperpartofthedemandcurvebutwithgreatermarginalcostseating intothemarkup. Iflongasmarginalcostis`locallyconstant'inequilibrium(i.e.,itschangeis`smallenough'), thenwecansaybuildingsarestrategiccomplementsinthelogitcase.Givenstrategiccomplements ofpricestrategies,anincreaseinzoningconstrainedbuilding : 'srentwillincreasedemandfor unzonedbuilding 9 ,andincreasesthepriceat 9 accordingly. Ifthereissorting;e.g.,preferenceheterogeneityforbuildingattributes,thentherelationshipis againtheoreticallyambiguousevenwithconstantmarginalcost.WithinourManhattandata,we explorethisempiricallyinSection3.8. C.1.2Proposition2 AmoredetailedproofofProposition2follows.First,weprovethatwhenanlandlord'sparcel ownershipconcentrationincreases,thelandlordincreasesthepricesatallproperties.Weapplythe frameworkofNockeandSchutz(2018b)andNockeandSchutz(2018a)tocalculatethepricee˙ect byutilizingthe ] -markupofthelandlord.Theauthorsuseanested-logitmodel,butwesimplify theresultremovingthenestingstructure. 1 1 Theseresultsalsoremoveindividualheterogeneityinrenterpreferencesinordertotake advantageoftheIIAproperty. 160 Wewishtoshowthatinthelogitcasewithnon-decreasingmarginalcost, mA 9 mB 5 ¡ 0 Œ 8 9 2 5 , whichprovestheproposition.Below,weshowthisinthetwoproductforintuitionandtheninthe generalcasewitharbitrarynumberofproducts. C.1.3OligopolistPricingEquation First,weshowthatlandowner 5 choosesacommonmarkup(NockeandSchutz,2018a,b).Let eachlandlordsolvesthefollowingjoint-pro˝tequation: max f A 9 g 9 2 5 Õ 9 2 5 A 9 ˇ 9 ˘ 9 ¹ ˇ 9 º Ł (C.4) FollowingtheinsightfromNockeandSchutz(2018b),the˝rstorderforeachpropertysatis˝es: A 9 m˘ 9 mˇ 9 = 1 U ¸ c 5 = 1 U ¹ 1 B 5 º Ł (C.5) WecanrearrangeC.5tosolveforrent: A 9 = m˘ 9 mˇ 9 1 U ¹ 1 B 5 º ¡ 0 Œ (C.6) wheremarginalcostispositivetoyieldanupwardslopingsupplycurve.Denotemarginalcostas m˘ 9 mˇ 9 = 2 9 .Wewillassumethatitsderivativeispositive: ~ 2 9 : = m2 mˇ 0 Œ 8 2 ˜ . 2 C.1.4TwoProductCase Recallagainthatunderlogitdemand: mˇ 9 mA 9 = Uˇ 9 ¹ 1 ˇ 9 º 0 (C.7) mˇ : mA 9 = Uˇ 9 ˇ : ¡ 0 (C.8) 2 Amicro-foundationisthattheresidentialspaceproductionfunctionisconcaveininputswhich impliesthatthecostfunctioninconvexinquantity;hence,marginalcostisnon-decreasingin quantity. 161 PriceE˙ects: A 9 = 1 U ¹ 1 B 5 º ¸ 2 9 ¹ ˇ 9 º (C.9) = ) mA 9 mB 5 = 1 U ¹ 1 B 5 º 2 ¸ m2 9 mˇ 9 mˇ 9 mA 9 mA 9 mB 5 ¸ mˇ 9 mA 9 mA : mB 5 (C.10) bysymmetry mA 9 mB 5 = 1 U ¹ 1 B 5 º 2 ¸ m2 9 mˇ 9 mˇ 9 mA : 2 6 6 6 6 6 6 4 1 U ¹ 1 B 5 º 2 ¸ m2 : mˇ : mˇ : mA 9 mA 9 mB 5 1 m2 : mˇ : mˇ : mA : 3 7 7 7 7 7 7 5 1 m2 9 mˇ 9 mˇ 9 mA 9 (C.11) = 1 U ¹ 1 B 5 º 2 2 6 6 6 6 6 6 6 4 1 m2 : mˇ : mˇ : mA : ¸ m2 9 mˇ 9 mˇ 9 mA : 1 m2 : mˇ : mˇ : mA : 1 m2 9 mˇ 9 mˇ 9 mA 9 m2 9 mˇ 9 mˇ 9 mA : m2 : mˇ : mˇ : mA 9 3 7 7 7 7 7 7 7 5 (C.12) imposingLogit = 1 U ¹ 1 B 5 º 2 2 6 6 6 6 6 6 4 1 m2 : mˇ : mˇ : mA : ¸ m2 9 mˇ 9 mˇ 9 mA : 1 m2 : mˇ : mˇ : mA : m2 9 mˇ 9 mˇ 9 mA 9 m2 9 mˇ 9 m2 : mˇ : mˇ : mA 9 U ¹ 1 B 5 º 3 7 7 7 7 7 7 5 ¡ 0 (C.13) C.1.5GeneralProductCase Notethatwehavethefollowing: » A 8 ¼ = » ¹ B 5 º 1 5 ¼¸» 2 8 ¹ ˇ 8 º¼ (C.14) D B 5 A = 0 ¹ B 5 º 1 5 ¸ D ˇ 2 D A ˇ D B 5 A (C.15) = ) D B 5 A » I D ˇ 2 D A ˇ ¼ = 0 ¹ B 5 º 1 5 (C.16) = ) D B 5 A = » I D ˇ 2 D A ˇ ¼ : 1 0 ¹ B 5 º 1 5 (C.17) 162 C.1.5.1De˝nitionsandLemmas De˝nitionC.1.2. Strictly(Row)DiagonallyDominant:foreveryrow, 8 ,theelementalongthe diagonal, 0 88 ,isgreaterinmagnitudethanthesumofthemagnitudesofeachnon-diagonalelement intherow 0 8Œ9 Œ9 < 8 .Thatis, j 0 8Œ8 j ¡ Í 9 < 8 j 0 8Œ9 j . De˝nitionC.1.3. Z -matrix:amatrixwhoseo˙-diagonalentriesarelessthanorequaltozero. De˝nitionC.1.4. M -matrix:a Z -matrixwhereeveryrealeigenvalueofAispositive. Lemma1. If isa Z -matrixthatisstrictlydiagonallydominant,then isan M -matrixby GershgorinCircleTheorem . Lemma2. If isan M -matrixwithpositivediagonalsandnegativeo˙diagonals,then = : 1 is monotonepositive;i.e., 1 89 ¡ 0 Œ 8 8Œ9 ;proofinFan1958. C.1.5.2GeneralCaseProof Weneedtoshowthatthelemmaholdsandthatthevector 0 ¹ B º isamonotonepositivevector. Let » I D ˇ 2 D A ˇ ¼ = . First,seethat is(a)a Z -matrixthatis(b)Strictly(Row)DiagonallyDominant: (a)foreachrow,usinglogitdemand,wehave 0 8Œ8 = 1 ~ 2 8 Uˇ 8 ¹ 1 ˇ 8 º ¡ 0 (C.18) 0 8Œ9 = ~ 2 8 Uˇ 8 ˇ 9 0 (C.19) (b)plugintode˝nitionof(row)diagonallydominant = ) 1 ¸ ~ 2 8 j U j ˇ 8 ¹ 1 ˇ 8 º ¡ Õ 9 2 5 n 8 ~ 2 8 j U j ˇ 8 ˇ 9 = ~ 2 8 j U j ˇ 8 Õ 9 2 5 n 8 ˇ 9 (C.20) = ) 1 ¸ ~ 2 8 j U j ˇ 8 ¡ ~ 2 8 j U j ˇ 8 B 5 Ł (C.21) Thus satis˝eslemma2,so isamonotonepositivematrix. Second, 0 ¹ B 5 º = d d B 5 1 U ¹ 1 B 5 º = 1 U ¹ 1 B 5 º 2 ¡ 0 . 163 Thusas 0 ¹ B 5 º isaseriesofmultiplicationandadditionofpositivenumbers,so D B 5 A mustbe amonotonepositivevector. C.2SeparateDeveloperandLandlordDecisions Thestandardassumptionintheurbanliteratureisthatacompetitiveconstructionsectorpur- chaseslandtoproduceurbanspacethatisthenputontherentalmarket(orsoldtoinitialowners). Wehavemodeledthechoiceenvironmentaslandownersproducingtheurbanspacetheyprovideto therentalmarket.Inthissection,weshowthatundertheassumptionofcompetitiveconstruction andtheexistenceofownersofdi˙erentiatedlandthatourmodelleadstothesameallocation.This impliesthatthestandardassumptionsimplythaturbanspaceisconstrained.Weshowthisinthe horizontalsortingcase. Consideradeveloperwhoas already purchasedlandfromaland-ownerandmustnowdecide howmuchurbanspacetoprovidetotherentalmarket.Theconstruction˝rmsarepricetakers infactorsandspace,butcanmakeaquantitychoice.Weconsiderthedualbuilder'sproblemof maximizinglocationconditionalpro˝torminimizingcostssubjecttoalevelofdemandbychoosing laborandcapital: max :Œ f A @ 9 ¹ :Œ º 8: F g() min :Œ f 8: ¸ F s.t. @ 9 ¹ :Œ º = 3 9 ¹ A ºg Giventhatthesearedualproblems,theyeachyieldthesamesolution.Let'sconsiderthecost minimizationproblem'ssolutionofabuildingcost 9 ¹ AŒ3 9 ¹ A ºº .Withfreeentry, c 9 = A 3 9 ¹ A º 9 ¹ AŒ3 9 ¹ A ºº 0 .Thisprovidesthebuilder'ssolutionifthebuilderbuystherighttodevelop location 9 2 ˜ .Thebuilderwilldevelopaplanforeach 9 2 ˜ andseekstopurchaselandfrom land-owners. Now,wemustconsiderhowland-ownerssetthepriceofland, A 9 .Clearly, A 9 = c 9 ,elseanother developerwouldbiduptheprice.Thiscreatesanopenbidauctionforeachlocation,sotheland pricemustalsobebiduptothehighestpotentiallocationpro˝t,whichisthemonopolylocation pro˝t.Supposeabuilderdecidestosetrentatcostandprovideenoughspacetoclearthemarket, 164 thenthisbuildermustbid c 24 = 0 .Anotherbuilderdecidestoreducespaceandincreaserentto clearthemarket,andsobids c < ¡ 0 .Theland-ownerwillchoosethesecondbidder. Here,freeentryintotheconstructionsectorcreatestheincentivestoengageinmonopolistic behaviorintherentalmarketwhenthereisdownwardslopingdemand.Ifurbanspacewasviewed ashomogeneousbyrenters,thendeveloperswouldnotbeabletoadjustmarketrentsandspaceand makepro˝tssinceallrenterswouldhavethesamewillingnesstopay. C.3DetailedConstructionofSamples Here,wediscusstheexactstepsinsampleconstruction.Recall,thesamplesweuseinthepaper areasfollowing: ‹ 2008-2015NYC:Ownershipmatched,unconstrained; ‹ 2010Manhattan:IV,Estimation,Unconstrained,NewUnconstrained. C.3.12008-2015NYC WebeginwithallbuildingsinNYC,andthendropbuildingsbasedon: 1. missinglocationinformation,plotsthatareunderconstruction,vacant,orareparks; 2. residentialareaiszero,therearezeroresidentialunits,ormarketvaluesequalzero; 3. plotswherethebuildingisnotclassi˝edasaprivaterentalbuilding(i.e.,wedropowner occupiedsinglefamilyresidences,condominiumandcooperativebuildings,100%publicly ownedbuildings,anyremainingcommerciallyclassi˝edbuildings,buildingsdesignatedas land-marks); 4. missingbuildingcharacteristicinformation; 5. buildinghaslessthanfourunits. Next,welinkthissampletotheMDRC˝lesthatlinkreportedbuildingownerstoshareholders usingtheBBLbuildingidenti˝ers.Wethentestifthereportedbuildingownernamematchedthe MDRCownername(theowningentity,notshareholders)usingafuzzystringmatchingalgorithm. 165 Thisresultsinamatchrateofroughly80%foreachyear.Wedropbuildingsthatdonotmatch. 3 Usingthismatchedgroup,wethencalculateHHIandleave-outHHImeasures. Finally,wearriveatourHHIEstimationsamplebydroppingbuildingsthat 1. haveover10%ofunitsrentstabilized; 2. arezoningconstrained; 3. aremixed-use. ThisyieldsthesamethatisinTable3.2. InTableC.1wepresentsummarystatisticsfortheHHIdata. C.3.22010Manhattan WebeginwithallbuildingsinManhattan,andthendropbuildingsbasedon: 1. missinglocationinformation,plotsthatareunderconstruction,vacant,orareparks; 2. residentialareaiszero,therearezeroresidentialunits,ormarketvaluesequalzero; 3. plotswherethebuildingisnotclassi˝edasaprivaterentalbuilding(i.e.,wedropowner occupiedsinglefamilyresidences,condominiumandcooperativebuildings,100%publicly ownedbuildings,anyremainingcommerciallyclassi˝edbuildings,buildingsdesignatedas land-marks); 4. missingbuildingcharacteristicinformation; 5. buildinghaslessthanfourunits. Toarriveattheestimationsample,wedropbuildingswhere 1. thereispositivecommercialbuildingarea; 2. thecensustractshasfewerthan3remainingbuildings; Thissetofbuildingsconstitutestheestimationsampleonwhichweestimatethemodel. 3 Webelievematchingfailureshappenprimarilyfortworeasons.First,theredoesnotseemto beoversightoftheownershipregistrationssomisspellingsarecommon.Second,theMDRCisa snap-shotthatdoesnotsaveinformationacrossyearsortransactions,soitispossiblethatabuilding ownerchangesanditisnotrecordedwhenwehaveaccesstothe˝les. 166 TableC.1:SummaryStats: 2008-2015NYCUnconstrainedRentalBuildings BronxBrooklynManhattanQueens TractLevel HHI 6ŒC 0.240.210.220.33 BuildingLevel OwnerShareinTract 11%5%8%3% Leave-OutHHIinTract 0.130.070.110.06 MedianMonthlyRent $1,046$961$1,813$925 MedianRentbyMedianIncome 25%23%43%22% MedianMonthlyLandValueperUnit $205$250$2,270$222 Res.UnitsperBuilding 33.515.525.911.4 YearsSinceConstruction 81838872 YearsSinceRenovation 46653669 log(DistanceCBD) 2.361.411.531.75 log(DistanceSubway) -1.53-1.69-1.95-1.60 AvgUnitSqft 10049541,031901 Buildings 1,7927,6212,5311,773 Note: BuildingdatafromPLUTO,NPV,FAR,MDRC˝les.CensustractHHIde˝nedusingshares inequation3.8.Ownershareintractisbuildinglevelaverage.Leave-outbuildingHHIde˝ned usingadjustedsharesinequation3.9.Alldollarvaluesnominal,2008-2015.Medianincomein 2010forNYCis$50,711,usedforallyears.BuildingdatafromPLUTO,NPV,andFAR˝les. Monthlyrentalincomeisbuildingincomedividedbytotalunitsdividedby12.Medianincomein 2010forNYCis$50,711.Monthlylandvalueperunitis[LandValue/(12xResidentialUnits)]. Yearssinceconstructionandrenovationequal2010minustheconstructionyearandmostrecent majorrenovationyear.Geodesicdistancesareinlogmilesbasedonbuilding(lat,lon)coordinates. AvgUnitSqftistotalbuildingareadividedbytotalunits. Wedropbuildingswithcommercialareamixedusebuildingsbecausewecannotbesurethat weareameasuringaverageresidentialrentsaswecannotseparatecommercialandtenantincome sources.Asnotedearlier,thisisnotthesameastreatingthesebuildingsasoutsidegoodsforthe model.Utilityparametersareidenti˝edundertheassumptionthattheparametersdonotdepend onwhetherthebuildinghascommercialspace. 4 Wearriveatthe2010UnconstrainedManhattansamplesbydroppingbuildingsthat 4 Unreportedmontecarlotestsshowthatundertheassumptionsofthemodel,parametersremain unbiased.Atworst,webelievethemodelislesse˚cientlyestimatedduetosmallersamples. 167 1. haveover10%ofunitsrentstabilized; 2. arezoningconstrained; 3. aremixed-use. Finally,the2010NewUnconstrainedManhattan/NYCsamplesubsetsthisbydroppingbuildings builtbefore2000.Summarystatisticsforthe2010ManhattansamplesareinTable3.1. C.3.3SpatialDistributionofSingleUse,ZoningConstrained,&RentControl InFiguresC.1andC.2,weplotthespatialdistributionofbuildingusestatus,zoningconstrained status,andrentcontrolstatus.Wede˝neabuildingasbeingmixeduseifweobservepositive commercialspaceinthebuilding;else,singleuse.Commercialspaceincludesretailspace,o˚ce space,or(foraminorityofbuildings)industrialspace.Formixedusebuildings,wecannot di˙erentiatecommercialversusresidentialsourcesofbuildingincome. FigureC.1:DistributionofBuildingUseinManhattan 5 For˝gureC.2,abuildingisconsideredzoningconstrainedifthelandlordcouldnotlegally addanotherunitattheminimumlegallyallowedareawithouta˙ectingexistingbuildingunits. Withinourdataweabletoobservethatwhetherabuilding'sFloorAreaRation(FAR 9 )isbelow itsmaximumallowableFAR(MaxFAR 9 ).AbuildingcanbebelowitsMaxFARbutstillzoning constrainedif ¹ MaxFAR 9 º FAR 9 º islessthantheminimumallowableunitFAR,meaninga 168 landlordcannotlegallyaddanadditionalunit.Thus,abuildingiszoningconstrainedif(1) ¹ MaxFAR 9 º FAR 9 º 0 or(2) ¹ MaxFAR 9 º FAR 9 º (LegalMinUnitFAR).We˝ndthat while 80% ofrentalbuildingsarezoningconstrainedonly 30% areconstraineddueto ¹ 1 º . 6 This potentiallyimpliesthatdevelopersincorporatezoningconstraints,whichifbindingwouldlimit revenues,bybuildinglargerunitsthatmayattracthigherincomerenters. Finally,in˝gureC.2,weplotthespatialdistributionofrentcontrolledbuildings.Wede˝nerent controlledstatusbywhetherabuildingisonthe2012NYCDepartmentofHomesandCommunity BuildingRegistrationFile.Abuildingisonthislistifthebuildinghasatleastoneunitthatis rentcontrolledorrentstabilized.Beingrentcontrolledimpliesthatalandlordisnotincomplete controlofunitpricing,sotosomeextentthelandlordisconstrained. FigureC.2:DistributionofZoningConstraintsandRentStabilizationinManhattan (a)ZoningConstraints (b)RentStabilization Note: Panel(a)plotsbyCensustractthepercentofbuildingsthatarezoningconstrained.Panel(b) plots,byCensustract,thepercentofbuildingsthatarerentstabilized.Thedatais2010Manhattan residentialbuildingswith4+units.Zoningconstrainedisde˝nedasbuildingbeinglegallynot allowedtoaddoneminimumsizeresidentialunitbasedon˛oor-area-ratios.Abuildingisrent stabilizedifmorethan10%ofbuildingunitsarerentstabilized. 6 Forsingle-usebuildingsthisis 81 Ł 7% and 34 Ł 2% andformixed-usebuildingsthisis 79 Ł 2% and 25 Ł 8% ,respectively. 169 C.4HHIandOwnershipMatching C.4.1OwnershipMatching Herewedescribehowwematchbuildingstoownergroups.Thisprocedureisnecessarybecause alargeportionofreportedrentalbuildingownersareacorporateentitythatisitselfowneda holdingcompany. 7 Thusthereportedownershipstructureunderestimatesthedegreeofcommon ownership.TheNYCDepartmentofHousingPreservationandDevelopment(HPD)requires thatbuildingownersregistereachbuildingwithmultipledwellings(orinhabitedbynon-family members)andcompilesthisregistrationlisttocreatetheMultipleDwellingRegistryandContacts (MDRC).Importantly,theMDRCassignsauniqueIDtoeachbuilding-ownerpairandforeach ownerliststhenamesofthemainshareholdersofthecorporateownerorpartnership.Building ownersmustre-registerannuallysothelistupdatesannually.Thuswehavealistofbuildingswith theircorporateownernamesandshareholdernames. 8 However,wefacetwodatachallengesinmatchingbuildingstoownersusingtheMDRC.First, weonlyhaveMDRClistsforthreeyears:2012,2015,and2020.Second,theMDRCdoesnotlink buildingsbycommonowners.Wedealwitheachinturn. Tocreateabuildingownerpanel,weappendthethreeMDRCannual˝lestogetherand`back-˝ll' theownershipfromMDRCinformationformissingyears.Thatis,ifweobserveabuilding-owner pairforyear2020,thenweassumetheowneristhesamefrom2020,2019,2018,andsoon. 9 We thenmergethiswithourDOF/PLUTObuildingyearpanelofrentalbuildings.Finally,weusea textmatchingproceduretoensurethatthereportedbuildingcorporateownermatchestheMDRC corporateownername. 10 TableC.2reportsthematchrateforthemainfourboroughsbyyearused 7 Wespeaklooselywiththeterms'corporateentity'and'holdingcompany';somebuilding ownersareliterallyacorporationwhileothersarelimitedliabilitycompanies,soleproprietorship, partnerships,orcooperatives. 8 Wearrangetheshareholdernamesbasedonfrequency.Forexample,ifname isassociated with5buildingsandname with4buildings,thenforanysetofbuildingswithbothnames f Œ g wedesignatename astheprimaryname. 9 We˝ndthatthe2015˝lematchesbettertoyears2016and2017thanback-˝llingthe2020˝le, soweextendthe2015˝letwoyearsaswellasback˝ll2014and2013. 10 WeusetheStatacommand matchit withathresholdof 0 Ł 5 . 170 intherentsample. TableC.2:MatchRateAcrossBoroughs BKBXMNQN 2008 0.790.820.810.80 2009 0.800.830.830.81 2010 0.830.860.860.84 2011 0.830.870.870.84 2012 0.840.890.870.85 2013 0.850.880.870.85 2014 0.840.890.870.84 2015 0.840.880.870.84 Note: 2008-2015NYCresidentialbuildingswith4+units.DatafromDOF,PLUTO,MDRC˝les. MatchratebetweenreportedownerfromPLUTO&FARandMDRCownername. To˝ndallbuildingsthathavecommonshareholders,weagainperformatextmatchingproce- dure.Weperformthisprocedureforeachtract-yearpairinthefourmainboroughsofNYCforthree setsofshareholdernames.The˝rstismatchingtheprimaryshareholder,thesecondismatching theprimaryandsecondaryshareholders,andthethirdismatchingacrossallshareholders.Using onlythe˝rstshareholdernameisthemostconservativemeasureofcommonownershipandisthe onewiththeleastexpectederrors. 11 ForanybuildingthatdoesnotmatchtotheMDRC,weuse thereportedownername(usuallyacorporateentity)andrequireanexactstringmatchwithinthe tract-year. 12 Togetasenseofthescaleoftheissue.ForManhattanrentalbuildings,we˝ndthattheaverage numberofdistinctownergroups(`landlords')inatract-yearare48.6usingthereportedownership structureand34.8usingtheMDRCmatchedownershipstructure.Forthesamesetofbuildings, we˝ndthatwithinacensustracttheaveragelandlordowns3buildingswhenweusethereported ownershipstructureand4.3buildingswhenweusetheMDRCmatchedownershipstructureTable C.3reportsthesevaluesbyyearforManhattanandtheotherthreemajorboroughs. 11 WeagainusetheStatacommand matchit butincreasethematchthresholdto 0 Ł 55 forprimary namematchingandto 0 Ł 6 forthemulti-namematching.Asthelengthofastringincreases,the fuzzytextmatchingprocedureismorelikelyto˝ndfalse-positivematches. 12 Weuseanexactmatchingbecauseourfuzzystringmatchingprocedurecannottellthedi˙erence betweencorporatenamesoftheform555StreetLLCand554StreetLLC. 171 TableC.3:Di˙erenceBetweenReportedandMDRCCCommonOwnership Manhattan Brooklyn,Bronx,Queens DistinctOwnersAvgBldperOwnerDistinctOwnersAvgBldperOwner MDRCReportedMDRCReported MDRCReportedMDRCReported 2008 34.246.94.33.0 20.924.42.52.1 2009 34.647.84.33.1 21.124.72.52.1 2010 34.848.14.23.1 21.3252.52.1 2011 35.048.54.33.0 21.525.22.52.1 2012 35.349.24.33.0 21.625.42.52.1 2013 35.349.44.43.0 21.825.62.52.1 2014 34.749.44.33.0 21.625.72.52.1 2015 34.849.44.23 21.625.72.52.1 Note: 2008-2015NYCresidentialbuildingswith4+units.DatafromDOF,PLUTO,MDRC˝les. ComparisonbetweenreportedownersinPLUTO&FARversusMDRC˝les.Ownersmatched withintract-years. C.4.2AdditionalHHIResults Inthissection,weproberobustnesstoourresultsinSection3.5usingtwoalternativespeci˝cations. First,wereplacetheleave-one-outHHIvariable ˛˛˚ 5 ¹ 9 º Œ6ŒC ,whichcalculatesforeachbuilding, theconcentrationindexatthetractlevelexcludingthebuilding'slandowner'sownbuildings,with thetract-levelvariable ˛˛˚ 6ŒC ,whichmoresimplycalculatesthetotaltract-levelconcentration. Resultsarelargelysimilartoourmainspeci˝cation,althoughthepointestimatesareslightly attenuated. Second,weexploreanalternativespeci˝cationwhereprice-per-square-footratherthantotal rentisthebuilding-leveloutcomevariable.Accordingly,inthisspeci˝cation,totalsquarefeetis nolongeracontrol.Resultsarebroadlyslimiartoourmainspeci˝cation. 172 TableC.4:TheRelationshipBetweenAggregateOwnershipConcentrationandPrices (1)(2)(3)(4)(5)(6) ln » Averager 9Œ6ŒC ] Panel(A):Manhattan ln » HHI 6ŒC ¼ -0.0120.1610.0750.0090.1620.075 (0.032)(0.080)(0.076)(0.038)(0.076)(0.076) ln » B 5 ¹ 9 º 6ŒC ¼ -0.0280.002-0.013 (0.026)(0.025)(0.027) YearFEsYYYYYY TractFEsNYNNYN BuildingFEsNNYNNY Observations2,5192,5042,3932,5192,5042,393 ' 2 0.290.630.750.290.630.75 Panel(B):Bronx,Brooklyn,Manhattan,Queens ln » HHI 6ŒC ¼ 0.0530.0920.0760.0470.0940.079 (0.016)(0.076)(0.039)(0.019)(0.076)(0.039) ln » B 5 ¹ 9 º 6ŒC ¼ 0.007-0.005-0.038 (0.014)(0.013)(0.014) Borough-yearFEsYNNYNN TractandyearFEsNYNNYN BuildingandyearFEsNNYNNY Observations13,66913,59212,75813,66913,59212,758 ' 2 0.40.640.770.400.640.77 Note: ThetablereplicatestheresultsofTable3.2usingtract-levelHHImeasures ˛˛˚ 6ŒC ,instead oftheleave-one-outHHI, ˛˛˚ 5 ¹ 9 º Œ6ŒC .Otherwise,controlsandspeci˝cationsmatchTable3.2. StandarderrorsclusteredtwowaysbyCensustractandyear. C.5DetailedConstructionofAverageBuildingRent Recoveringbuildingaverageunitrentsisakeyfeatureofthisanalysisthatreliesonthreefacts. First,bylaw,theDOFassessesrentalbuildingsbasedontheirincomegeneration.Forsingle-use, residentialrentalbuildings,thiscorrespondstotherentpaidtolandlords.Formixed-userental buildings,wecannotseparatethesourceofincomebetweencommercialandresidentaltenants. 173 TableC.5:TheRelationshipBetweenOwnershipConcentrationandPriceperSquareFoot (1)(2)(3)(4)(5)(6) ln » (Buildingr 9Œ6ŒC ºš¹ BuildingSquareFeet º ] Panel(A):Manhattan ln » HHI 5 ¹ 9 º Œ6ŒC ¼ -0.0490.2100.130-0.0120.2060.158 (0.038)(0.097)(0.094)(0.050)(0.094)(0.098) ln » B 5 ¹ 9 º 6ŒC ¼ -0.046-0.006-0.015 (0.033)(0.025)(0.037) YearFEsYYYYYY TractFEsNYNNYN BuildingFEsNNYNNY Observations2,5172,5022,3922,5172,5022,392 ' 2 0.270.650.740.280.650.75 Panel(B):Bronx,Brooklyn,Manhattan,Queens ln » HHI 5 ¹ 9 º Œ6ŒC ¼ 0.0350.1630.1390.0360.1640.133 (0.023)(0.072)(0.050)(0.023)(0.069)(0.050) ln » B 5 ¹ 9 º 6ŒC ¼ -0.0020.001-0.035 (0.017)(0.014)(0.018) Borough-yearFEsYNNYNN TractandyearFEsNYNNYN BuildingandyearFEsNNYNNY Observations13,64613,57212,73813,64613,57212,738 ' 2 0.280.590.720.280.590.73 Note: ThetablereplicatestheresultsofTable3.2usingrentpersquarefootasthedependentvariable andomittingthetotalsquarefootvariableasacontrol.Otherwise,controlsandspeci˝cationsmatch Table3.2.StandarderrorsclusteredtwowaysbyCensustractandyear. Thisleadstooursamplerestrictionofsingle-usebuildingsinourestimations. Second,weusetheweb-scrapedNPVdata.WebelievetheNPVdataishighqualitybecause itisbasedoncommunicationswithownerswhohavea˝nancialstakeinensuringtheinformation iscorrect.However,becausewerelyonathirdparty'se˙ortsinweb-scraping,wemustdealwith thefactthatthethirdpartydidnotcollectinformationonallbuildings.Primarily,theweb-scraped 174 datadoesnotincludeanybuildingwith4or5unitsandisrandomlymissingothers. Toremedythis,werelyonthethirdfact.TheDOFusesbuildingincomedatainitsassessment processtoderiveetvaluewhichisthenusedforpropertytaxes.Speci˝cally,theDOF calculatesmarketvalueusingthefollowingformula: MarketValue 9 = GIM 9 Avg ¹ AnnualRent º 9 units 9 Œ (C.22) wheretheGrossIncomeMultiplier(GIM)isdeterminedbytheDOFbasedonthebuilding'smarket valuepersquarefootanditslocation. SinceweobservemarketvalueforallbuildingsintheFARdataset,wecanusethebuildingsthat overlaptheNPVdatatobackoutthethefunctionGIM 9 = G ¹ "+ 9 (&˙) 9 Œ Units 10 Œ borough Œ year º . WeestimatetheGIMfunctionviathefollowing: 1. Forthematchedset,dividemarketvaluebyincometorecoverGIM 9 ; 2. Calculatemarketvaluebysquarefeet(mvsqft); 3. Byboroughandyear,calculatethe50-pointquantilesofmvsqft; 4. Byborough,year,andlargebuildingstatus(units 10),˝ndtheaverageGIM 9 Avg ¹ GIM j B,Y,U>10 º ; 5. Forthesetofbuildingsthatarenotinthematchedset,calculate "+ 9 Avg ¹ GIM j B,Y,U>10 º = ^ . 9 . Weusethereportedvalue . 9 forthematchedbuildingsand ^ . 9 fortheunmatchedbuildings. C.5.1AdditionalInformation TheincomedataisultimatelysourcedfromtheRealPropertyIncomeandExpense(RPIE)state- mentsthatallincomegeneratingpropertyownersarerequiredto˝leannuallyandface˝nancial penaltiesfornot˝ling.Nevertheless,notallpropertyownerswill˝lethisreport.Ifanownerdoes not˝le,theDOFhastherighttoassignamarketvaluebasedonitsbestjudgement.Inaddition,the DOFdocumentationsaysthattheywilladjustreportamountsthatseemextreme;e.g.,abuilding reportinghighcostsandnoincomeinanareawhereotherbuildingsarereportincomesabovecosts. 175 WithoutaccesstotheRPIEstatements,itisnotpossibletodeterminewhichpropertieshavebeen adjusted. TheDOFAssessmentGuidelinesshowhowIncomeandMarketValuerelatetoeachotherand howonecanbedirectlyinferredusingtheother.Inthetablebelow,wedescribetheDOFmapping thatgoesfromobservedincometomarketvalue: ˝ : . (@˙C ! " . TableC.6:ExampleMappingofMarketValuetoIncome H˝˚" !>F ˝˚" ˛86 < . 9 » H 1 ŒH 2 ¼ < 1 H 1 < 2 H 2 » < 1 Œ< 2 ¼ = "+ 9 H 2 < 2 » H 2 ŒH 3 ¼ - < 3 H 3 » < 2 Œ< 3 ¼ = "+ 9 H 3 < 3 » H 3 ŒH 4 ¼ - < 4 H 4 » < 3 Œ< 4 ¼ = "+ 9 H 4 < 4 Note: Thistableprovidesasimpli˝edexampleoftheGrossIncomeMultiplier(GIM)methodused bytheNYDOFthatweutilizetoinferbuildingincomefromobservedbuildingmarketvalue.For 80%ofourmulti-yearsample,weobservebothmarketvalueandincome,whichweusetoestimate theGIMfortheremainingproperties,asdescribedinthemaintext. C.5.1.1RobustnessofCalculations WecanchecktherobustnessofourcalculationsbyusinganauxilarydatasetbytheDOF,the Condo/CoopComparableRentalIncomedata.Bylaw,condominiumbuildingsmustbevaluedfor taxpurposesas-iftheywererentalbuildings.Toaccomplishthis,theDOFmatchescondominiums withrentalpropertiesandcalculatesandexpected,marketvalueandincomeofthecondominiums. Theypublishthesecomparisonsandincludetherentalbuildingincomeandmarketvalueusedin thecomparisons.Thus,weareabletocheckourresultsforthematchedbuildings.Ourvaluesare nearlyidenticalexceptforinconsistentroundingbehavioronthepartoftheNYCDOF,typicallyin theowner'sfavor. 13 13 ForManhattan,weareabletocheckagainst1,883rentalbuildings,andwe˝nd83buildings wheretheabsolutedi˙erencebetweenourassigned ˝˚" andtheempiricalratioofmarketvalue toincomeisgreaterthan 0 Ł 1 ;thisrepresentsanerrorratearound 4% ofbuildings.Again,these errorsareduetoinconsistentbehaviorbytheNYCDOF. 176 C.6BLPInversionStep Forintuition,ifweomittherandomcoe˚cients,thenthemodelbecomesastandardlogit speci˝cationusinggroupeddata.Berry(1994)showsthatthemeanutilitycanbesolvedforin closedformas: ln » B 9 ¼ ln » B 0 ¼ = X 9 ¸ - 9 V ¸ UA 9 Ł (C.23) Onecanusealinear2SLSspeci˝cationtoestimate f UŒV g . Withrandomcoe˚cients,theabovedoesnotwork.However,BLPshowthatthefollowingis acontractionmappingalgorithmguaranteedtoconverge: ` A ¸ 1 9 = ` A 9 ¸ ln » B 9 ¼ ln » ˇ 9 ¹ ` A 9 ; \ º¼ Œ 8 9Ł (C.24) When k ` A ¸ 1 9 ` A 9 k 1 ˇ 0 thealgorithmhasconverged. 14 Forthenestedlogitcase,Grigolonand Verboven(2014)showthatthefollowingmodi˝cationisalsoacontractionmappingandnecessary: ` A ¸ 1 9 = ` A 9 ¸ ln » B 9 ¼¹ 1 d º ln » ˇ 9 ¹ ` A 9 ; \ º¼ Œ 8 9Ł (C.25) Once ` isrecovered,thenwecanusethemodel'smomentconditionstoestimate f VŒUŒW g . C.7InstrumentConstruction WeuseDi˙erentiationInstruments,basedonGandhiandHoude(2018),witha spatialradius,asinBayeretal.(2004,2007).FortheNestedLogitspeci˝cations,wecreate withinnestdi˙erentiationinstrumentsthatexcluderivalsinthesameCensusblock-group.These instrumentsaremeanttobe an approximationtotheoptimalinstrumentsinthesenseofAmemiya (1977)andChamberlain(1987). 15 The`true'optimalinstrumentsarebasedonthepartialderivativeofthestructuralerrorterm: / opt = Var ¹ X 9 º 1 E h mX 9 mV mX 9 mU mX 9 mf / i Ł (C.26) 14 Weuseatoleranceof 10 12 ,andwealwaysstartthealgorithmwiththelinearspeci˝cation meanvalue. 15 Somewhatmoreformallytheyarea˝nite-orderbasis-functionapproximationtotheoptimal instruments. 177 Thishasexactlyasmanymomentsasparameters,soisexactlyidenti˝edandnoiterativeweighting matrixisnecessary. Tocalculatethisobject,onemusttakeastandontheconditionaldistributionofthestructural error,solvetheBertrandpricingproblem,backoutmodel-impliedstructuralerrors,andthen calculatethederivatives.Inamajormethodologicaladvancement,ConlonandGortmaker(2019) describehow,givenaninitialsetofestimates,onecancalculatethisobjectrelativelyquicklyfor mostproblems.Their pyblp softwareautomatesmostofthesestepswithvariousoptions;however, thisisnotpossibleinourproblem.Becausewedonotaccuratelyobservepricesformixed-use buildings,whichisroughlyhalfofthechoiceset,wecannotcrediblysolvetheBertrandpricing problem. 16 Evenconditionalonobtainingthetrueparametervector,ourimpliedsubstitution betweenbuildingswillbebiasedupordownbasedonwhethercommercialrentsaregreaterorless thanresidentialrentsinthosebuildings,whichwillbiasthecalculated`optimalinstrument.' Nevertheless,GandhiandHoude(2018)showthattheoptimalinstrumentscanbeapproximated, inanydataset,bysymmetricfunctionsofthedi˙erencesinbuildinglevelcovariateswithoutneeding tosolvetheBertrandpricingproblem.Theirresultsformalizetheintuitionofthemoretraditional Instrumentsthatmark-upsareshiftedbyutilizingthe`product-space-distance'between products,wheremoreisolatedproductsasmoreimmunetopriceshocks.However,therearestill manychoicesofpotential˝nitebasisfunctionsthatcanbeused. Theauthorssuggesttwo`˛avors'forpractitioners.First,theyproposeDi˙erentiation Instruments(DQ): / DQ 9 = Õ : 2f ¹ 9 ºg ¹ G : G 9 º 2 Œ (C.27) where ¹ 9 º isasetofrivalsforplot 9 .Thisisthesetthatweuseinthemaintext. Second,theyproposeDi˙erentiationInstruments / DL 9 = Õ : 2f ¹ 9 ºg 1 j G : G 9 j sd ¹ - º Œ (C.28) 16 Inaddition,withrentcontrolandzoningconstraints,wewouldneedtosolveaconstrained Bertrandpricingproblem,whichisnotcodedin pyblp . 178 where sd ¹ - º istheempiricalstandarddeviationofvariable - .Inunreportedresults,we˝nd thattheseinstrumentshavelessstrengthrelativetotheDQinstruments;although,theydostill˝nd elasticresults.Theseresultsareavailableuponrequest. Todealwithendogeneityofprices(oranycovariate),theauthorsrecommendusingapredicted priceusingplausiblyexogenousvariation,suchasthefollowingadditionalexample: / DQ AŒ9 = Õ : 2f ¹ 9 ºg E » A : j -Œ, ¼ E » A 9 j -Œ, ¼ 2 Œ (C.29) where E » A : j - = G : Œ, = F : ¼ isfroma˝rststageregressiononallexogenousinformation, ¹ -Œ, º ,where , areanyvariablesexcludedfromtheutilityfunction. 17 C.7.1BLP-FStatistic Toassessthevalidityand ability ofourinstrumentsinidentifyingdemandparameters,wereport the`˝rststage'statisticsofourinstruments,asadvisedinArmstrong(2016).Wereportarobust ˝rststageFstatisticofthelinearregressionofbuildingrentsonthemodelcontrolsandinstruments andtheBLP-FstatisticasdevisedinArmstrong(2014). TherobustFstatistichasthevirtuethatitisrobusttoheteroskedasticitybutcannotdiscern betweenthecaseswhenexcludedinstrumentsarecorrelatedwithrentsbutresearcherimposes amodelthatleadstoproductcharacteristicshavinganasymptoticallynegligiblee˙ectonmarkups (Armstrong,TheBLP-Fstatisticisbasedonthe`concentrationparameter'andisdesigned tohavepowerincaseswhentheusualFstatisticwouldfalselyrejectanullhypothesisofno identi˝cation. 18 TheBLP-Fstatisticisapost-estimationprocedurecalculatedin˝vesteps.First,regressprice onallmodelcontrolsandinstrumentsandthensavetheresidual, ¤ A 9 .Second,calculatethesample 17 Note,GandhiandHoude(2018)specify , asanyalreadyavailableinstrument,whichConlon andGortmaker(2019)interprettoinclude f / DQ 9 g 2 ˛ forthebuilding - 0 B .Currently,wedonot use f / DQ 9 g 2 ˛ aspartof , ,sothat - arebuildingcharacteristicsintheutilityfunctionand , is landvaluefromtheNYCDOF. 18 If H = -V ¸ D ,thentheconcentrationparameterisde˝nedas Var ¹ -V ºš Var ¹ D º . 179 varianceoftheresidual.Third,regressthemodel-impliedmarkup, > > > > >< > > > > > > : © « mˇ 9 mA : mˇ 9 mA 9 m 2 ˇ 9 mA 9 mA : ˇ 9 mˇ 9 mA 9 2 ª ® ® ® ® ® ¬ d A : 9 > > > > > >= > > > > > > ; (C.33) 182 Toarriveatequation3.19,weset d <2 9 = 0 ,solveC.33for d A cf 9 ,andthenmanipulatetheequation toarriveatanelasticityform.Ausefulequivalenceisthefollowing: m » mˇ 9 š mA 9 ¼ mA : A : mˇ 9 š mA 9 = mY 9 mA : A : Y 9 ¸ mˇ 9 mA : A : ˇ 9 . Withpreferenceheterogeneityi.e.,randomcoe˚cientsthentheexpressionhasnoclosed formsolution,butiseasilycalculatedwithourestimatedparametersandMonteCarlointegration. Forintuition,iftherewerenoindividualagentheterogeneityinpreferences,then d A 9 = ¹ 1 ˇ 9 º d <2 9 ¸ ˇ 9 ¹ 1 ˇ 9 º Õ : 2Z f ˇ : d A : g (C.34) = ¹ 1 ˇ 9 º d <2 9 ¸ ˇ 9 ¹ 1 ˇ 9 º Avg ˇ ¹ d A : º Ł (C.35) Withoutafullmodelofbuildingcosts,wecannotcalculate d <2 9 ,sowecannotcalculatethe truepartialequilibriumchangeinunconstrainedprices.Undertheassumptionof(locally)constant marginalcosts,thenourmeasure equals thepartialequilibriumchangeinrentalprices.Under theassumptionofstrictlyincreasingmarginalcosts,then d <2 9 0 ,soourmeasurewouldbethe lowerboundofthe magnitude oftherentchange.Withoutadditionalassumptions,ourmeasure calculatesthepartialequilibriumchangeinthemonopolymark-upofunconstrainedbuildingsdue toazoning-shock. 183 BIBLIOGRAPHY 184 BIBLIOGRAPHY Adao,Rodrigo,MichalKolesár,andEduardoMorales. 2018.designs:Theoryand inf NationalBureauofEconomicResearchWorkingPaperSeries . 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