双向固定效应和双重差分ppt课件.ppt

1 Two wayfixed effectmodelsDifferenceindifference 2 Two wayfixedeffects Balancedpanelsi 1 2 3 Ngroupst 1 2 3 Tobservations groupEasiesttothinkofdataasvaryingacrossstates timeWritemodelassingleobservationYit Xit ui vt itXitis 1xk vector 3 Three parterrorstructureui groupfixed effects Controlforpermanentdifferencesbetweengroupsvt timefixedeffects Impactscommontoallgroupsbutvarybyyear it idiosyncraticerror 4 Excisestaxesonpoorhealth Alcoholandcigarettesaretaxedatthefederal stateandlocallevelSomestatessellliquorratherthantaxit VA PA etc Mostofthesetaxesareexcisetaxes thetaxisperunitRatesdifferbytypeofalcohol alcoholcontentNearlyallcigarettestaxedthesame 5 Currentexcisetaxrates CigarettesLow SC 0 07 MO 0 17 VA 0 30 High RI 3 46 NY 2 75 NJ 2 70 Averageof 1 32acrossstatesAverageintobaccoproducingstates 0 40Averageinnon tobaccostates 1 44Averagepriceperpackis 5 12BeerLow WY 0 02 gallon High SC 0 77 gallon 6 7 Federaltaxes Cigarettes 1 01 packWine 0 21 750mlbottlefor14 alcoholorless 0 31 750mlbottlefor14 21 alcoholBeer 0 02acanLiquor 13 50per100proofgallon 50 alcohol or 2 14 750mlbottleof80proofliquorTotaltaxesoncigarettesaresuchthatinNYC youspendmoreintaxesbuyingonecaseofcigarettesthanifyoubuy33casesofwine 8 Dotaxesreduceconsumption LawofdemandFundamentalresultofmicroeconomictheoryConsumptionshouldfallaspricesriseGeneratedfromatheoreticalmodelofconsumerchoiceThoughtbyeconomiststobefairlyuniversalinapplicationMedical psychologicalview certaingoodsnotsubjecttotheselaws 9 Startingin1970s severalauthorsbegantoexaminelinkbetweencigarettepricesandconsumptionSimpleresearchdesignPricestypicallychangedduetostate federaltaxhikesStateswithchangesare treatment Stateswithoutchangesarecontrol 10 Nearuniversalagreementinresults10 increaseinpricereducesdemandby4 ChangeinsmokingevenlysplitbetweenReductionsinnumberofsmokersReductionsincigs dayamongremainingsmokersResultshavebeenreplicatedinothercountries timeperiods varietyofstatisticalmodels subgroupsForotheraddictivegoods alcohol cocaine marijuana heroin gambling 11 Taxesnowanintegralpartofantismokingcampaigns Keycomponentof MasterSettlement SurgeonGeneral sreport raisingtobaccoexcisetaxesiswidelyregardedasoneofthemosteffectivetobaccopreventionandcontrolstrategies Taxhikesarenowdesignedtoreducesmoking 12 13 14 15 16 Currentexcisetaxrates http www taxfoundation org publications show 245 htmlStatetaxes Low KY 0 30 pack VA 0 30 SC 0 07 High RI 2 46 NJ 2 58 Averageof 1 07acrossstatesFederaltaxes 39cents pack 17 Caution Inbalancedpanel two wayfixed effectsequivalenttosubtractingWithingroupmeansWithintimemeansAddingsamplemeanOnlytrueinbalancedpanelsIfunbalanced needtodothefollowing 18 Cansubtractoffmeansononedimension iort Butneedtoaddthedummiesfortheotherdimension 19 generaterealtaxesgens f rtax state tax federal tax cpilabelvars f rtax state federalrealtaxoncigs cents pack realpercapitaincomegenln pcir ln pci cpi labelvarln pcir lnofrealrealpercapitaincome generatelnpacks pcgenln packs pc ln packs pc constructstateandyeareffectsxii statei year 20 runtwowayfixedeffectmodelbybruteforce covariatesarerealtaxandlnpercapitaincomeregln packs pc I ln pcirs f rtax nowbemoreeleganttakeoutthestateeffectsbyaregaregln packs pc Iyear ln pcirs f rtax absorb state forsimplicity redefinevariablesasyx1 ln pcir x2 s f rtax geny ln packs pcgenx1 ln pcirgenx2 s f rtax 21 sortdatabystate thengetmeansofwithinstatevariablessortstatebystate egeny state mean y bystate egenx1 state mean x1 bystate egenx2 state mean x2 sortdatabystate thengetmeansofwithinstatevariablessortyearbyyear egeny year mean y byyear egenx1 year mean x1 byyear egenx2 year mean x2 22 getsamplemeansegeny sample mean y egenx1 sample mean x1 egenx2 sample mean x2 generatethedevaitionsfrommeansgeny tilda y y state y year y samplegenx1 tilda x1 x1 state x1 year x1 samplegenx2 tilda x2 x2 state x2 year x2 sample themeansshouldbemachingzerosumy tildax1 tildax2 tilda 23 runtheregressionondifferencedvalues sincemeansarezero youshouldhavenoconstant noticethatthestandarderrorsareincorrect becausethemodelisnotcountingthe51statedummies and19yeardummies TherecordedDOFare 1020 2 1018butitshouldbe1020 2 51 19 948 multiplythestandarderrorsbysqrt 1018 948 1 036262regy tildax1 tildax2 tilda noconstant 24 runtwowayfixedeffectmodelbybruteforce covariatesarerealtaxandlnpercapitaincome regln packs pc I ln pcirs f rtaxSource SSdfMSNumberofobs 1020 F 71 948 226 24Model 73 7119499711 03819648Prob F 0 0000Residual 4 35024662948 004588868R squared 0 9443 AdjR squared 0 9401Total 78 06219651019 07660667RootMSE 06774 ln packs pc Coef Std Err tP t 95 Conf Interval Istate 2 0926469 03211222 890 004 0296277 155666 Istate 3 245017 03424147 160 000 1778192 3122147Deleteresults Iyear 1998 3249588 0226916 14 320 000 3694904 2804272 Iyear 1999 3664177 0232861 15 740 000 412116 3207194 Iyear 2000 373204 0255011 14 630 000 4232492 3231589ln pcir 2818674 05857994 810 000 1669061 3968287s f rtax 0062409 0002227 28 030 000 0066779 0058039 cons 2 294338 59667983 850 0001 1233723 465304 25 Source SSdfMSNumberofobs 1020 F 2 1018 466 93Model 3 9907057521 99535287Prob F 0 0000Residual 4 350246621018 004273327R squared 0 4784 AdjR squared 0 4774Total 8 340952371020 008177404RootMSE 06537 y tilda Coef Std Err tP t 95 Conf Interval x1 tilda 2818674 056534 990 000 1709387 3927961x2 tilda 0062409 0002149 29 040 000 0066626 0058193 SEonX10 05653 1 036262 0 05858SEonX20 0002149 1 036262 0 0002227 26 Differenceindifferencemodels MaybethemostpopularidentificationstrategyinappliedworktodayAttemptstomimicrandomassignmentwithtreatmentand comparison sampleApplicationoftwo wayfixedeffectsmodel 27 Problemsetup Cross sectionalandtimeseriesdataOnegroupis treated withinterventionHavepre postdataforgroupreceivinginterventionCanexaminetime serieschangesbut unsurehowmuchofthechangeisduetosecularchanges 28 time Y t1 t2 Ya Yb Yt1 Yt2 Trueeffect Yt2 Yt1 Estimatedeffect Yb Ya ti 29 Interventionoccursattimeperiodt1TrueeffectoflawYa YbOnlyhavedataatt1andt2Ifusingtimeseries estimateYt1 Yt2Solution 30 Differenceindifferencemodels Basictwo wayfixedeffectsmodelCrosssectionandtimefixedeffectsUsetimeseriesofuntreatedgrouptoestablishwhatwouldhaveoccurredintheabsenceoftheinterventionKeyconcept cancontrolforthefactthattheinterventionismorelikelyinsometypesofstates 31 Threedifferentpresentations TabularGraphicalRegressionequation 32 DifferenceinDifference 33 time Y t1 t2 Yt1 Yt2 treatment control Yc1 Yc2 Treatmenteffect Yt2 Yt1 Yc2 Yc1 34 KeyAssumption ControlgroupidentifiesthetimepathofoutcomesthatwouldhavehappenedintheabsenceofthetreatmentInthisexample YfallsbyYc2 Yc1evenwithouttheinterventionNotethatunderlying levels ofoutcomesarenotimportant returntothisintheregressionequation 35 time Y t1 t2 Yt1 Yt2 treatment control Yc1 Yc2 Treatmenteffect Yt2 Yt1 Yc2 Yc1 TreatmentEffect 36 Incontrast whatiskeyisthatthetimetrendsintheabsenceoftheinterventionarethesameinbothgroupsIftheinterventionoccursinanareawithadifferenttrend willunder overstatethetreatmenteffectInthisexample supposeinterventionoccursinareawithfasterfallingY 37 time Y t1 t2 Yt1 Yt2 treatment control Yc1 Yc2 Truetreatmenteffect Estimatedtreatment TrueTreatmentEffect 38 BasicEconometricModel Datavariesbystate i time t OutcomeisYitOnlytwoperiodsInterventionwilloccurinagroupofobservations e g states firms etc 39 ThreekeyvariablesTit 1ifobsibelongsinthestatethatwilleventuallybetreatedAit 1intheperiodswhentreatmentoccursTitAit interactionterm treatmentstatesaftertheinterventionYit 0 1Tit 2Ait 3TitAit it 40 Yit 0 1Tit 2Ait 3TitAit it 41 Moregeneralmodel Datavariesbystate i time t OutcomeisYitManyperiodsInterventionwilloccurinagroupofstatesbutatavarietyoftimes 42 uiisastateeffectvtisacompletesetofyear time effectsAnalysisofcovariancemodelYit 0 3TitAit ui vt it 43 Whatisniceaboutthemodel SupposeinterventionsarenotrandombutsystematicOccurinstateswithhigherorloweraverageYOccurintimeperiodswithdifferentY sThisiscapturedbytheinclusionofthestate timeeffects allowscovariancebetweenuiandTitAitvtandTitAit 44 GroupeffectsCapturedifferencesacrossgroupsthatareconstantovertimeYeareffectsCapturedifferencesovertimethatarecommontoallgroups 45 Meyeretal Workers compensationStateruninsuranceprogramCompensateworkersformedicalexpensesandlostworkduetoonthejobaccidentPremiumsPaidbyfirmsFunctionofpreviousclaimsandwagespaidBenefits ofincomew cap 46 TypicalbenefitsscheduleMin pY C P percentreplacementY earningsC cape g 65 ofearningsupto 400 month 47 Concern Moralhazard BenefitswilldiscouragereturntoworkEmpiricalquestion duration benefitsgradientPreviousestimatesRegressduration y onreplacedwages x Problem givenprogressivenatureofbenefits replacedwagesrevealalotabouttheworkersReplacementrateshigherinhigherwagestates 48 Yi Xi Ri iY duration R replacementrate Expect 0ExpectCov Ri i HigherwageworkershavelowerRandhigherduration understate HigherwagestateshavelongerdurationandlongerR overstate 49 Solution QuasiexperimentinKYandMIIncreasedtheearningscapIncreasedbenefitforhigh wageworkers Treatment Didnothingtothosealreadybeloworiginalcap comparison Comparechangeindurationofspellbeforeandafterchangeforthesetwogroups 50 51 52 Model Yit durationofspellonWCAit periodafterbenefitshikeHit highearningsgroup Income E3 Yit 0 1Hit 2Ait 3AitHit 4Xit itDiff in diffestimateis 3 53 54 Questionstoask Whatparameterisidentifiedbythequasi experiment Isthisaneconomicallymeaningfulparameter Whatassumptionsmustbetrueinorderforthemodeltoprovideandunbiasedestimateof 3 Dotheauthorsprovideanyevidencesupportingtheseassumptions 55 Moregeneralmodel ManywithingroupestimatorsthatdonothavethenicediscretetreatmentsoutlinedabovearealsocalleddifferenceindifferencemodelsCookandTauchen ExamineimpactofalcoholtaxesonheavydrinkingStatestaxalcoholExamineimpactonconsumptionandresultsofheavyconsumptiondeathduetolivercirrhosis 56 Yit 0 1INCit 2INCit 1 1TAXit 2TAXit 1 ui vt itiisstate tisyearYitispercapitaalcoholconsumptionINCispercapitaincomeTAXistaxpaidpergallonofalcohol 57 SomeKeys ModelrequiresthatuntreatedgroupsprovideestimateofbaselinetrendwouldhavebeenintheabsenceofinterventionKey findadequatecomparisonsIftrendsarenotaligned cov TitAit it 0OmittedvariablesbiasHowdoyouknowyouhaveadequatecomparisonsample 58 Dothepre treatmentsampleslooksimilarTricky D in Dmodeldoesnotrequiremeansmatch onlytrends Ifmeansmatch noguaranteetrendswillHowever ifmeansdiffer aren tyoususpiciousthattrendswillaswell 59 Developteststhatcanfalsifymodel Yit 0 3TitAit ui vt itWillprovideunbiasedestimatesolongascov TitAit it 0Concern supposethattheinterventionismorelikelyinastatewithadifferenttrendIftrue coefficientmay showup priortotheintervention 60 Add leads tothemodelforthetreatmentInterventionshouldnotchangeoutcomesbeforeitappearsIfitdoes thensuspiciousthatcovariancebetweentrendsandintervention 61 Yit 0 3TitAit 1TitAit 1 2TitAit 2 3TitAit 3 ui vt itThree leads Testnull Ho 1 2 3 0 62 Pickcontrolgroupsthathavesimilarpre treatmenttrends MoststudiespickalluntreateddataascontrolsExample Somestatesraisecigarettetaxes UsestatesthatdonotchangetaxesascontrolsExample SomestatesadoptwelfarereformpriortoTANF Useallnon reformstatesascontrolsIntuitivebutnotlikelycorrect 63 CanuseeconometricproceduretopickcontrolsAppealingifinterventionsarediscreteandfewinnumberEasytoidentifypre post 64 CardandSullivan ExaminetheimpactofjobtrainingSomemenaretreatedwithjobskills othersarenotMostarelowskillmen highunemployment frequentmovementinandoutofworkEightquartersofpre treatmentdatafortreatmentandcontrols 65 LetYit 1if i workedintimetThereisthenaneightdigitsequenceofoutcomes 11110000 or 10100111 Menwithsame8digitpre treatmentsequencewillformcontrolforthetreatedPeoplewithsamepre treatmenttimeseriesare matched 66 IntuitivelyappealingandsimpleprocedureDoesnotguaranteethatposttreatmenttrendswouldbethesamebut thisisthebestyouhave 67 Moresystematicmodel Datavariesbyindividual i state s timeInterventionisinaparticularstateYist 0 Xist 2 3TstAst us vt istManystatesavailabletobecontrolsHowdoyoupickthem 68 Restrictsampletopre treatmentperiodState1isthetreatedstateStatekisapotentialcontrolRundatawithonlythesetwostatesEstimateseparateyeareffectsforthetreatmentstateIfyoucannotrejectnullthattheyeareffectsarethesame useascontrol 69 UnrestrictedmodelPretreatmentyearssoTstAstnotinmodelMpre treatmentyearsLetWt 1ifobsfromyeartYist 0 Xist 2 t 2 tWt t 2 tTiWt us istHo 2 3 m 0 70 Tyleretal ImpactofGEDonwagesGeneraleducationdevelopmentdegreeEarnaHSdegreebypassinganexamExampassratesvarybystateIntroducedin1942asawayforveteranstoearnaHSdegreeHasexpandedtothegeneralpublic 71 In1996 760KdropoutsattemptedtheexamLittlehumancapitalgeneratedbystudyingfortheexamReallymeasuresstockofknowledgeHowever passingmay signal somethingaboutability 72 Identificationstrategy UsevariationacrossstatesinpassratestoidentifybenefitofaGEDHighscoringpeoplewouldhavepassedtheexamregardlessofwhatstatetheylivedinLowscoringpeoplearesimilaracrossstates butonisgrantedaGEDandtheotherisnot 73 NY CT A B D C E F Increasingscores PassingScoresCT PassingscoreNY 74 GroupsAandBpassineitherstateGroupDpassesinCTbutnotinNYGroupClookssimilartoDexceptitdoesnotpass 75 WhatisimpactofpassingtheGEDYis earningsofpersoniinstatesLis earnedalowscoreCTis 1ifliveinastatewithagenerouspassingscoreYis 0 Lis 1 CT 2 LisCTis 3 is 76 DifferenceinDifference 77 Howdoyougetthedata FromETS testingagency getsocialsecuritynumbers SSN oftesttakes somedemographicdata state andtestscoreGiveSocialSecurityAdmin alistofSSNsbygroup lowscoreinCT highscoreinNY SSNgivesyoubackmean std dev obspercell 78 79 80 AcemogluandAngrist ada jpe doada jpe log 81 AmericanswithDisabilityAct RequiresthatemployersaccommodatedisabledworkersOutlawsdiscriminationbasedondisabilitiesPassesinJuly1990 effectiveJuly1992MaydiscourageemploymentofdisabledCostsofaccommodationsMaybemoredifficulttofiredisabled 82 Econometricmodel DifferenceindifferenceHavedatabefore afterlawgoesintoeffectTreatedgroup disabledControl non disabledTreatmentvariableisinteractionDiabled 1992andafter 83 Yit Xit Di Yeart t YeartDit t itYit labormarketoutcome personiyeartXitvectorofindividualcharacteristicsDit 1ifdisableldYeart yeareffectYeartDit completesetofyearxdisabilityinteractions 84 Coefon i sshouldbezerobeforethelawMaybenonzeroforyears 1992 85 86 87 Data MarchCPSAsksallparticipantsemployment incomedataforthepreviousyearEarnings weeksworked usualhours weekDatafrom1988 1997MarchCPSDataforcalendaryears1987 1996Menandwomen aged21 58Generateresultsforvarioussubsamples 88 ConstructssetsofdummiesForyear regionandage GenerateyearxDisabilityinteractions 89 Table2 ADAnotineffect EffectiveyearsofADA 90 Modelwithfewcontrols AfteraddingextensivelistOfcontrols resultschangelittle 91 regwkswork1 Iy disabledd y Includeallvariablesthatbeginwith ly Includeallvariablesthatbeginwithd y 92 NeedtodeleteoneyeareffectSinceconstantisinmodel Disabilitymaineffect Disabilitylawinteractions obsclosetowhatisReportedinpaper 93 Rundifferentmodel Onetreatmentvariable Disabledxafter1991 genada yearw 1992 gentreatment ada disabled Addyeareffectstomodel disabled themADAxdisabledinteraction 94 ADAreducedworkbyalmost2weeks year Regressionstatement 95 Shouldyoucluster Interventionvariesbyyear disabilityShouldbewithin yearcorrelationinerrorsPeopleareinthesampletwoyearsinarowsothereshouldbesomecorrelationovertimeCannotclusteronyearssince groupstoosmall 96 NeedlargersetthatmakessenseTwooptions manymore ClusteronstateClusteronstate disability 97 gendisabled state 100 disabled statefip regwkswork1 Ia Iy Ir whiteblackhispaniclthshsgradsomecoldisabledtreatment cluster statefip regwkswork1 Ia Iy Ir whiteblackhispaniclthshsgradsomecoldisabledtreatment cluster disabled state 98 Summaryofresultsforcluster Coefficientontreatment standarderror RegularOLS 1 998 0 315 Clusterbystate 1 998 0 487 Clusterbystate disab 1 998 0 532 99 LindenandRockoff MeganKan