计量经济学(英文版)ppt课件

.,1,Chapter4StatisticalPropertiesoftheOLSEstimators,XiAnInstituteofPost2=0.3means2iseithergreaterthanorlessthan0.3.ButsupposepriorexperiencesuggeststousthattheMPCisexpectedtobegreaterthan0.3.Inthiscasewehave:H0:20.3andH1:20.3.AlthoughH1isstillacompositehypothesis,Itisnowone-sided.,.,54,Totestthishypothesis,weusetheone-tailtest(therighttail),asshowninFigure5.5.Thetestprocedureisthesameasbeforeexceptthattheupperconfidencelimitorcriticalvaluenowcorrespondstot=t.05,thatis,the5percentlevel.AsFigure5.5shows,weneednotconsiderthelowertailofthetdistributioninthiscase.Whetheroneusesatwo-orone-tailtestofsignificancewilldependuponhowthealternativehypothesisisformulated,which,inturn,maydependuponsomeaprioriconsiderationsorpriorempiricalexperience.,5.30,.,55,5.31,.,56,HYPOTHESISTESTING:2THETEST-OF-SIGNIFICANCEAPPROACHTestingtheSignificanceofRegressionCoefficients:ThetTestAnalternativebutcomplementaryapproachtotheconfidence-intervalmethodoftestingstatisticalhypothesesisthetest-of-significanceapproachdevelopedalongindependentlinesbyR.A.FisherandjointlybyNeymanandPearson.Broadlyspeaking,atestofsignificanceisaprocedurebywhichsampleresultsareusedtoverifythetruthorfalsityofanullhypothesis.Thekeyideabehindtestsofsignificanceisthatofateststatistic(estimator)andthesamplingdistributionofsuchastatisticunderthenullhypothesis.ThedecisiontoacceptorrejectH0ismadeonthebasisofthevalueoftheteststatisticobtainedfromthedataathand.Asanillustration,recallthatunderthenormalityassumptionthevariablefollowsthetdistributionwithn-2df.Ifthevalueoftrue2isspecifiedunderthenullhypothesis,thetvaluecanreadilybecomputedfromtheavailablesample,andthereforeitcanserveasateststatistic.,5.32,.,57,5.33,.,58,5.34,.,59,5.35,.,60,5.36,.,61,APPLICATIONOFREGRESSIONANALYSIS:THEPROBLEMOFPREDICTIONOnthebasisofthesampledataofTable3.2weobtainedthefollowingsampleregression:Y=24.4545+0.5091Xi,5.37,.,62,5.38,.,63,.,64,5.39,.,65,5.40,.,66,SUMMARYANDCONCLUSIONS,1.ThebasicframeworkofregressionanalysisistheCLRM(ClassicLinearRegressionModel).2.TheCLRMisbasedonasetofassumptions.3.Basedontheseassumptions,theleast-squaresestimatorstakeoncertainpropertiessummarizedintheGaussMarkovtheorem,whichstatesthatintheclassoflinearunbiasedestimators,theleast-squaresestimatorshaveminimumvariance.Inshort,theyareBLUE,.,67,SUMMARYANDCONCLUSIONS,4.TheprecisionofOLSestimatorsismeasuredbytheirstandarderrors.todrawinferencesonthepopulationparameters,thecoefficients.5.Theoverallgoodnessoffitoftheregressionmodelismeasuredbythecoefficientofdetermination,r2.Ittellswhatproportionofthevariationinthedependentvariable,orregressand,isexplainedbytheexplanatoryvariable,orregressor.Thisliesbetween0and1;thecloseritisto1,thebetteristhefit.,.,68,SUMMARYANDCONCLUSIONS,6.Aconceptrelatedtothecoefficientofdeterminationisthecoefficientofcorrelation,r.Itisameasureoflinearassociationbetweentwovariablesanditliesbetween-1and1.7.TheCLRMisatheoreticalconstructorabstractionbecauseitisbasedonasetofassumptionsthatmaybestringentor“unrealistic.”Butsuchabstractionisoftennecessaryintheinitialstagesofstudyinganyfieldofknowledge.OncetheCLRMismastered,onecanfindoutwhathappens.Note:ifoneormoreo