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1、5.DoubleDifferenceSummaryDouble-difference(DD)methods,comparedwithpropensityscorematching(PSM),assumethatunobservedheterogeneityinparticipationispresentbutthatsuchfac-torsaretimeinvariant.Withdataonprojectandcontrolobservationsbeforeandaftertheprograminterve
2、ntion,therefore,this?xedcomponentcanbedifferencedout.SomevariantsoftheDDapproachhavebeenintroducedtoaccountforpoten-tialsourcesofselectionbias.CombiningPSMwithDDmethodscanhelpresolvethisproblem,bymatchingunitsinthecommonsupport.Controllingforinitialareacon-d
3、itionscanalsoresolvenonrandomprogramplacementthatmightbiastheprogrameffect.Whereabaselinemightnotbeavailable,usingatriple-differencemethodwithanentirelyseparatecontrolexperimentafterprogramintervention(thatis,aseparatesetofuntreatedobservations)offersanalter
4、natecalculationoftheprogramsimpact.LearningObjectivesAftercompletingthischapter,thereaderwillbeabletodiscuss■Howtoconstructthedouble-differenceestimate■Howtoaddresspotentialviolationsoftheassumptionoftime-invarianthetero-geneity■Howtoaccountfornonrandomprogr
5、amplacement■WhattodowhenabaselineisnotavailableAddressingSelectionBiasfromaDifferentPerspective:UsingDifferencesasCounterfactualThetwomethodsdiscussedintheearlierchaptersrandomizedevaluationandPSMfocusonvarioussingle-differenceestimatorsthatoftenrequireonlya
6、nappro-priatecross-sectionalsurvey.Thischapternowdiscussesthedouble-differenceestima-tiontechnique,whichtypicallyusespaneldata.Note,however,thatDDcanbeusedonrepeatedcross-sectiondataaswell,aslongasthecompositionofparticipantandcontrolgroupsisfairlystableover
7、time.Inapanelsetting,DDestimationresolvestheproblemofmissingdatabymeasur-ingoutcomesandcovariatesforbothparticipantsandnonparticipantsinpre-and71HandbookonImpactEvaluationpostinterventionperiods.DDessentiallycomparestreatmentandcomparisongroupsintermsofoutco
8、mechangesovertimerelativetotheoutcomesobservedforaprein-terventionbaseline.Thatis,givenatwo-periodsettingwheret=0beforetheprogramTCandt=1afterprogramimplementation,lettingYtandYtbetherespectiveo
