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1、IntroductiontoPooledCrossSectionsEMET8002Lecture5August13,2009AdministrativeMatters¢Consultationhours:¢Tuesdays3pmto5pm¢I’mgoingtobeawayagainnextTuesday,soI’llholdconsultationhoursnextweekonWednesday,August19thfrom3pmto5pm¢CaseStudiesprojectshavenowbeenassi
2、gned.IfyoudidnotreceivetheemailthatIsentonTuesdayyoucanviewtheassignmentsonthecoursewebsite¢Ifyouhavenotalreadydoneso,pleasecontactyoursupervisorimmediately.Afewoftheprojectswillrequireyoutoapplyfordataaccesswhichshouldbedoneimmediately!Outline¢Introducepoo
3、ledcrosssectionsregressionanalysis¢Chapter13inthetext¢Potentialpitfallusingdifference-in-differencesestimationstrategy¢Introductiontotwo-periodpaneldataandthefirstdifferenceestimatorPoolingIndependentCrossSectionsacrossTime¢Whatisit?¢Itisobtainedbysamplingr
4、andomlyfromalargepopulationattwoormorepointsintime¢Forexample,randomlysamplinghouseholdsfromACTresidentsin2000and2008A“Spreadsheet”viewPooledcrosssectionsPanelUnitPeriodUnitPeriod111121213131421252226232Formalnotation¢Wecandenotethepooledcrosssectionasarand
5、omsample:{yit,xxxi12it,it,...,kit}=1,2,...,%(&('%((&(('NN11,+++1,...,NNNN1212,...,%((&(('+...+NTPeriod12PeriodPeriodTtT=1,2,...,PoolingIndependentCrossSectionsacrossTime¢Considertheregressionmodel:y=+βββxx+++...βxu+i=1,2,...,N,NN+1,...,+NN,...,+++NN...it011
6、2it2itkkitit%(&('%((&(('1112%((&(('12TPeriod12PeriodPeriodTtT=1,2,...,¢Benefits:¢Poolingcanleadtolargersamplesizes:Thisleadstomorepreciseestimatorsandteststatisticswithmorepower.However,thisisonlytrueiftherelationshipbetweenthedependentvariableandatleastsom
7、eoftheexplanatoryvariablesremainsconstantovertime¢Ifthex’sarechangingovertime,itcanalsoprovideadditionalvariationinxwithwhichtoestimateitseffectony¢Note:theerrortermmayhavethestructureu=θ+εittit¢Fornow,we’llmakethefollowingassumptions:22θti
8、~0X(,σεσθ)andt
9、~
10、0X(,ε)¢AndthatthetwocomponentsoftheerrortermareindependentPoolingIndependentCrossSectionsacrossTime¢Supposethetrueerrorstructuredoesincludeayearcomponent,butweignorethatandrunOLSonthefollowingequation:
