Chap-13.---Pooling-Cross-Sections-across-Time(截面和面

AnalysisofCrossSectionandPanelDataYanZhangSchoolofEconomics,FudanUniversityCCER,FudanUniversityIntroductoryEconometricsAModernApproachYanZhangSchoolofEconomics,FudanUniversityCCER,FudanUniversityAnalysisofCrossSectionandPanelDataPart3.SomeAdvancedTopicsChap13.PoolingCrossSectionsacrossTimeDataStructurePooledCrossSection;PanelDataIndependentlyPooledCrossSectiontheyconsistofindependentlysampledobservations.与单一随机样本的差别：在不同时点对总体抽样可能导致观测点不是同分布的（notidenticallydistributed.）DifferentinterceptandslopesPolicyanalysisPanelDataThesameunitswecannotassumethattheobservationsoflongitudinaldataareindependentlydistributedacrosstime.SpecialmodelsandmethodsDifferencing(removetime-constant,unobservedattributesoftheunits.)PooledCrossSectionsPoolingcrosssectionsfromdifferentyears;Effectivelyanalyzingtheeffectsofanewgovt.policy;Similartoastandardcrosssection,exceptthatweoftenneedtoaccountforseculardifferencesinthevariablesacrossthetime.PanelorLongitudinalDataThesamecrosssectionalmembers;TocontrolcertainunobservedCharacteristicofcrosssections;Tostudytheimportanceoflagsinbehaviorortheresultofdecisionmaking13.1PoolingIndependentCrossSectionsacrossTimeIncreasethesamplesizeDummyVariablesthepopulationmayhavedifferentdistributionsindifferenttimeperiodsdifferentinterceptandslopesYeardummy:includingdummyvariablesforallbutoneyear,wheretheearliestyearinthesampleisusuallychosenasthebaseyear.Thepatternofcoef.ontheyeardummiesThechangeofthecoef.ofthekeyvariableovertimepolicyanalysisExample13.1Hasthepatternofwomen’sfertilityChanged?FactorsonWomen’sFertilityoverTime?age;education;religion;regiondependentvariable:fertilityrates;differentperiodData:FERTIL1.RAW,whichissimilartothatusedbySander(1994),comesfromtheNationalOpinionResearchCenter’sGeneralSocialSurveyfortheevenyearsfrom1972to1984Interpretationsbaseyear:1972education:.128(4)=.512.turningpointofageheteroskedasticityoferrortermovertime?B-Ptest;WLSeduc?interactioneffects(P.13.7,IV)Hastheeffectofeducationonfertilityrateschangedovertime?TheChowTestforStructuralChangeAcrossTimeOneformofthetestobtainsthesumofsquaredresidualsfromthepooledestimationastherestrictedSSR.TheunrestrictedSSRisthesumoftheSSRsforthetwoseparatelyestimatedtimeperiods.Anotherway:interactingeachvariablewithayeardummyforoneofthetwoyearsandtestingforjointsignificanceoftheyeardummyandalloftheinteractionterms.Usually,afteranallowanceforinterceptdifference,certainslopecoefficientsaretestedforconstancybyinteractingthevariableofinterestwithyeardummies.E.g.13.2ChangesinthereturntoeducationandthegenderwagegapEconometricModel:nominalvs.realvalueProvidedthedollaramountsappearinlogarithmicformanddummyvariablesareusedforalltimeperiods(except,ofcourse,thebaseperiod),theuseofaggregatepricedeflatorswillonlyaffecttheintercepts;noneoftheslopeestimateswillchange.ChowTest:Whathappensifweinteractallindependentvariableswithy85inequation(13.2)?13.2PolicyAnalysiswithPooledCrossSectionsnaturalexperiments:occurswhensomeexogenousevent—oftenachangeingovernmentpolicy—changestheenvironmentinwhichindividuals,families,firms,orcitiesoperate.controlgroup:notaffectedbythepolicychangetreatmentgroup:thoughttobeaffectedbythepolicychange.Methods:tocontrolforsystematicdifferencesbetweenthecontrolandtreatmentgroups,weneedtwoyearsofdata,onebeforethepolicychangeandoneafterthechange.thedifference-in-differencesestimator:Example13.4EffectsofWorkerCompensationLawsonDuration1980.7.15:Kentuckyraisedthecaponweeklyearningsthatwerecoveredbyworkers’compensation.Problem:itseffectsondurationinfluenced:high-incomeworkercontrolgroup(low)andtreatmentgroup(high)Meyer,ViscusiandDurbin(1995)INJURY.RAWlog(durat);fchnge;highearn;age;gender;maritalstatus;industry;typeofinjury13.3Two-periodPanelDataAnalysisTwotypesofunobservedfactorsaffectingthedependentv.inthepaneldata：keepconstant:unobservedeffect(fixedeffect)varyovertime:idiosyncraticerror(time-varyingerror)Estimationpooledcrosssections;drawback:Heterogeneitybias:Therefore,evenifweassumethattheidiosyncraticerroruitisuncorrelatedwithxit,pooledOLSisbiasedandinconsistentifaiandxitarecorrelated.Inmostapplications,themainreasonforcollectingpaneldataistoallowfortheunobservedeffect,ai,tobecorrelatedwiththeexplanatoryv.-s.first-differencedequationFirst-DifferencedEquationKeyassumptions:strictexogeneity:duiisuncorrelatedwithdxi.first-differencedestimatordximusthavesomevariationacrossi.(13.17)satisfiesthehomoskedasticityassumption.E.g.13.5Sleepingvs.WorkingSLP75_81.RAW13.5DifferencingwithMorethanTwoTimeperiodsDataStructure(fixedeffect&time-varyingerror)KeyAssumption(strictexogeneity):Thatis,theexplanatoryvariablesarestrictlyexogenousafterwetakeouttheunobservedeffect,ai.Caseswhenstrictexogeneitybefalse:Ifxitjisalaggeddependentvariable.Ifwehaveomittedanimportanttime-varyingvariableMeasurementerrorinoneormoreexplanatoryvariablesDifferencingDifferencing:WhenTissmallrelativetoN,weshouldincludeadummyvariableforeachtimeperiodtoaccountforsecularchangesthatarenotbeingmodeled.