Economics20 Prof Anderson 1 PanelDataMethods yit b0 b1xit1 bkxitk uit Economics20 Prof Anderson 2 ATruePanelvs APooledCrossSection Oftenlooselyusethetermpaneldatatorefertoanydatasetthathasbothacross sectionaldimensionandatime seriesdimensionMorepreciselyit sonlydatafollowingthesamecross sectionunitsovertimeOtherwiseit sapooledcross section Economics20 Prof Anderson 3 PooledCrossSections WemaywanttopoolcrosssectionsjusttogetbiggersamplesizesWemaywanttopoolcrosssectionstoinvestigatetheeffectoftimeWemaywanttopoolcrosssectionstoinvestigatewhetherrelationshipshavechangedovertime Economics20 Prof Anderson 4 Difference in Differences Sayrandomassignmenttotreatmentandcontrolgroups likeinamedicalexperimentOnecanthensimplycomparethechangeinoutcomesacrossthetreatmentandcontrolgroupstoestimatethetreatmenteffectFortime1 2 groupsA B y2 B y2 A y1 B y1 A orequivalently y2 B y1 B y2 A y1 A isthedifference in differences Economics20 Prof Anderson 5 Difference in Differences cont Aregressionframeworkusingtimeandtreatmentdummyvariablescancalculatethisdifference in differenceaswellConsiderthemodel yit b0 b1treatmentit b2afterit b3treatmentit afterit uitTheestimatedb3willbethedifference in differencesinthegroupmeans Economics20 Prof Anderson 6 Difference in Differences cont Whendon ttrulyhaverandomassignment theregressionformbecomesveryusefulAdditionalx scanbeaddedtotheregressiontocontrolfordifferencesacrossthetreatmentandcontrolgroupsSometimesreferredtoasa naturalexperiment especiallywhenapolicychangeisbeinganalyzed Economics20 Prof Anderson 7 Two PeriodPanelData It spossibletouseapaneljustlikepooledcross sections butcandomorethanthatPaneldatacanbeusedtoaddresssomekindsofomittedvariablebiasIfcanthinkoftheomittedvariablesasbeingfixedovertime thencanmodelashavingacompositeerror Economics20 Prof Anderson 8 UnobservedFixedEffects Supposethepopulationmodelisyit b0 d0d2t b1xit1 bkxitk ai uitHerewehaveaddedatime constantcomponenttotheerror uit ai uitIfaiiscorrelatedwiththex s OLSwillbebiased sinceweaiispartoftheerrortermWithpaneldata wecandifference outtheunobservedfixedeffect Economics20 Prof Anderson 9 First differences Wecansubtractoneperiodfromtheother toobtainDyi d0 b1Dxi1 bkDxik DuiThismodelhasnocorrelationbetweenthex sandtheerrorterm sonobiasNeedtobecarefulaboutorganizationofthedatatobesurecomputecorrectchange Economics20 Prof Anderson 10 Differencingw MultiplePeriods CanextendthismethodtomoreperiodsSimplydifferenceadjacentperiodsSoif3periods thensubtractperiod1fromperiod2 period2fromperiod3andhave2observationsperindividualSimplyestimatebyOLS assumingtheDuitareuncorrelatedovertime