计量经济学第一章课件Lecture1

1Econometrics2EconometricsInstructor:ChuiChinMan(崔展文)Office:511-2(嘉庚二)E-mail:[e-mail]3CourseRequirementLectures:Tuesday2:30-5:30p.m.(Room501嘉庚二)GradingAssignmentsandcomputerexercises10%Onemid-termtest40%Onefinalexamination50%4TextbookWooldridge,J.“IntroductoryEconometrics:Amodernapproach”3edition5StataBaum,C.,AnintroductiontomoderneconometricsusingSTATA,STATAPress.6CommunicationQQgroup:71313274Ifyouplantotakethiscourse,pleasejointhisgroup.Iwillpostalltheclassmaterialsonthegroup.IprefertocommunicatewithyouthroughQQ.Pleasedonotsendmeemailasmyaccountisalmostfull.计量_财会院2012秋季7IassumethatyouarefamiliarwiththefollowingconceptsRandomvariablesProbabilitydistributionMomentsFirstmoment–expectedvalue(alsoconditional)Secondmoment–variance,correlationHighermoment–Skewness,kurtosisWellknowndistributions:normal,t,chi-squareandF.Confidentintervalsandhypothesistesting.Youcanrefreshyourmemorybyhavingaquickreviewonthesetopicsinthetextbook(AppendixBandC).8Lecture1Quickreviewofsomeimportantconceptsinstatistics(AppendixCofWooldridge)9OutlineSampledistributionEstimationandestimatorPropertiesofestimator10PopulationandSamplePopulation—apopulationisthegroupofallitemsofinteresttoastatisticspractitioner.—frequentlyverylarge;sometimesinfinite.E.g.13billionpeopleinChinaSample—Asampleisasetofdatadrawnfromthepopulation.—Potentiallyverylarge,butlessthanthepopulation.E.g.asampleof4millionpeoplefromXiamen11StatisticalInferenceStatisticalinferenceistheprocessofmakinganestimate,prediction,ordecisionaboutapopulationparameterbasedonasamplestatistic.ParameterPopulationSampleStatistic(estimator)InferenceWhatcanweinferaboutapopulationparametersbasedonasamplestatistics?12Distributionofasampleofdatadrawnrandomlyfromapopulation:Y1,…,YnWewillassumesimplerandomsamplingChooseandindividual(district,entity)atrandomfromthepopulationRandomnessanddataPriortosampleselection,thevalueofYisrandombecausetheindividualselectedisrandomOncetheindividualisselectedandthevalueofYisobservedthenYisjustanumber–notrandomThedatasetis(Y1,Y2,…,Yn),whereYi=valueofYfortheithindividual(district,entity)sampled13DistributionofY1,…,YnundersimplerandomsamplingBecauseindividuals{Yi}areselectedatrandom,wefurthermakeassumptionsthat{Yi},i=1,…,n,areindependentlydistributed{Yi},i=1,…,n,comefromthesamedistribution,thatis,{Yi}areidenticallydistributedThatis,undersimplerandomsampling,{Yi},i=1,…,n,areindependentlyandidenticallydistributed(i.i.d.)Thisframeworkallowsrigorousstatisticalinferencesaboutmomentsofpopulationdistributionsusingasampleofdatafromthatpopulation…14ExamplePopulation{1,2,3,4}Drawsamples{Y1,Y2}withsamplesizen=2eachtime.Totalpossiblesamples{1,2},{1,3},{1,4},{2,3},{2,4},{3,4}15EstimatorsandEstimatesTypically,wecan’tobservethewholepopulation,sowemustmakeinferencesbasedontheestimatefromarandomsampleAnestimatorisjustamathematicalformulaforestimatingapopulationparameterfromsampledataAnestimateistheactualvaluetheformulaproducesfromthesampledata16CommonlyusedEstimatorsWeusesamplemeantoestimatethepopulationmeanWeusesamplevariancetoestimatethepopulationvarianceniiYY11)(122nYYSnii17EstimationYisthenaturalestimatorofthemean.But:(a)WhatarethepropertiesofY?(b)WhyshouldweuseYratherthansomeotherestimator?Y1(thefirstobservation)maybeunequalweights–notsimpleaveragemedian(Y1,…,Yn)ThestartingpointisthesamplingdistributionofY…18Yisarandomvariable,anditspropertiesaredeterminedbythesamplingdistributionofYTheindividualsinthesamplearedrawnatrandom.Thusthevaluesof(Y1,…,Yn)arerandomThusfunctionsof(Y1,…,Yn),suchasY,arerandom:hadadifferentsamplebeendrawn,theywouldhavetakenonadifferentvalueThedistributionofYoverdifferentpossiblesamplesofsizeniscalledthesamplingdistributionofY.ThemeanandvarianceofYarethemeanandvarianceofitssamplingdistribution,E(Y)andvar(Y).Theconceptofthesamplingdistributionunderpinsallofeconometrics.ThesamplingdistributionofY19PreviousexamplePopulation{1,2,3,4}populationmean=2.5Drawsamples{Y1,Y2}withsamplesizen=2.{1,2},{1,3},{1,4},{2,3},{2,4},{3,4}Samplemeansbasedonthe6samples{1.5,2,2.5,2,5,3,3.5}isthesampledistributionofExpectedvalueandvarianceof?YY20ThemeanandvarianceofthesamplingdistributionofYGeneralcase–thatis,forYii.i.d.fromanydistribution,notjustBernoulli:mean:E(Y)=E(11niiYn)=11()niiEYn=11nYin=YVariance:21Example:SupposeYtakeson0or1(aBernoullirandomvariable)withtheprobabilitydistribution,Pr[Y=0]=.22,Pr(Y=1)=.78ThenE(Y)=p1+(1–p)0=p=.782Y=E[Y–E(Y)]2=p(1–p)[rememberthis?]=.78(1–.78)=0.1716ThesamplingdistributionofYdependsonn.Considern=2.ThesamplingdistributionofYis,Pr(Y=0)=.222=.0484Pr(Y=½)=2.22.78=.3432Pr(Y=1)=.782=.6084Thesamplingdistributionof,ctd.Y22ThesamplingdistributionofwhenYisBernoulli(p=.78):Y23Howtochooseanestimator?Criteria:Unbiasedness(finitesample)Efficiency(finitesample)Consistency(largesample)Probablymore……24UnbiasednessofanEstimatorWehopetheestimatestobecorrect,onaverageAnestimatorcalledW,ofapopulationparameter,,isunbiasedifE(W)=Bias(W)=E(W)-2526EfficiencyofanestimatorH