计量经济学导论 PPT 课件.ppt

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1、MultipleRegressionAnalysisy=b0+b1x1+b2x2+...bkxk+u2.Inference1Economics20-Prof.AndersonAssumptionsoftheClassicalLinearModel(CLM)Sofar,weknowthatgiventheGauss-Markovassumptions,OLSisBLUE,Inordertodoclassicalhypothesistesting,weneedtoaddanotherassumption(beyondtheGauss-Markova

2、ssumptions)Assumethatuisindependentofx1,x2,…,xkanduisnormallydistributedwithzeromeanandvariances2:u~Normal(0,s2)2Economics20-Prof.AndersonCLMAssumptions(cont)UnderCLM,OLSisnotonlyBLUE,butistheminimumvarianceunbiasedestimatorWecansummarizethepopulationassumptionsofCLMasfollow

3、sy

4、x~Normal(b0+b1x1+…+bkxk,s2)Whilefornowwejustassumenormality,clearthatsometimesnotthecaseLargesampleswillletusdropnormality3Economics20-Prof.Anderson..x1x2ThehomoskedasticnormaldistributionwithasingleexplanatoryvariableE(y

5、x)=b0+b1xyf(y

6、x)Normaldistributions4Economics20-Pr

7、of.AndersonNormalSamplingDistributions5Economics20-Prof.AndersonThetTest6Economics20-Prof.AndersonThetTest(cont)KnowingthesamplingdistributionforthestandardizedestimatorallowsustocarryouthypothesistestsStartwithanullhypothesisForexample,H0:bj=0Ifacceptnull,thenacceptthatxjha

8、snoeffectony,controllingforotherx’s7Economics20-Prof.AndersonThetTest(cont)8Economics20-Prof.AndersontTest:One-SidedAlternativesBesidesournull,H0,weneedanalternativehypothesis,H1,andasignificancelevelH1maybeone-sided,ortwo-sidedH1:bj>0andH1:bj<0areone-sidedH1:bj0isatwo-side

9、dalternativeIfwewanttohaveonlya5%probabilityofrejectingH0ifitisreallytrue,thenwesayoursignificancelevelis5%9Economics20-Prof.AndersonOne-SidedAlternatives(cont)Havingpickedasignificancelevel,a,welookupthe(1–a)thpercentileinatdistributionwithn–k–1dfandcallthisc,thecriticalval

10、ueWecanrejectthenullhypothesisifthetstatisticisgreaterthanthecriticalvalueIfthetstatisticislessthanthecriticalvaluethenwefailtorejectthenull10Economics20-Prof.Andersonyi=b0+b1xi1+…+bkxik+uiH0:bj=0H1:bj>0c0a(1-a)One-SidedAlternatives(cont)Failtorejectreject11Economics20-Prof.

11、AndersonOne-sidedvsTwo-sidedBecausethetdistributionissymmetric,testingH1:bj