计量经济学2ppt课件.ppt

1 Cross SectionalDataAnalysis SimpleRegressionAnalysisMultipleRegressionAnalysis Estimation Inference ForecastingBinaryorDummyVariableHeteroskedasticity 异方差性 FunctionalFormSpecification 2 RecallonSimpleRegression SimpleLinearRegressionModel OLSEstimator Assumptions PropertiesofOLSestimators Goodness of Fit coefficientofdetermination R squared 3 y4 y1 y2 y3 x1 x2 x3 x4 u1 u2 u3 u4 x y Populationregressionline sampledatapointsandtheassociatederrorterms E y x b0 b1x 4 y4 y1 y2 y3 x1 x2 x3 x4 1 2 3 4 x y Sampleregressionline sampledatapointsandtheassociatedestimatederrorterms residual 5 MotivationforMultipleRegression Example1 returnandeducationWeareinterestedintheeffectofeducationonwageholdingfixedallotherfactorsaffectingwage Hereweusespecifyingthefollowingmodel Comparingthismodelwiththesimpleone 6 MotivationforMultipleRegression Example2 CEOcompensationandfirmperformanceWeareinterestedintherelationshipbetweenCEOsalaryandaspecifyingfactormeasuringfirmperformance salesandCEOsalary returnofequityandCEOsalary 7 MultipleRegressionAnalysis Estimation y b0 b1x1 b2x2 bkxk u intercept slopeparameters disturbance ExplainedVariableRegressandResponsevariableDependentvaiable ExplanatoryVariableRegressorControrlvariableIndependentvariable Populationmodel 8 OrdinaryLeastSquares Theordinaryleastsquares OLS estimatorisdefinesasthevaluethatminimizesthesumofsquaredresiduals Thatistominimize HowtoderivetheOLSestimators WhatassumptionsarenecessaryforOLSestimatorexisting Thinkingofotherestimatorsbasedonothermetrics 9 OLSestimatorsforSimpleRegressionmodel 10 OLSestimatorsforMultipleRegressionModel Whatisthematrixform Howtoderivetheestimators InordertogetOLSestimator doweneedanyothercondition 11 InterpretingMultipleRegression 12 A PartiallingOut Interpretation对排除其他变量影响的解释 13 PartiallingOut continued Considerthecasewithk 2independentvariables Previousequationimpliesthatregressingyonx1andx2givessameeffectofx1asregressingyonresidualsfromaregressionofx1onx2Thismeansonlythepartofxi1thatisuncorrelatedwithxi2arebeingrelatedtoyi sowe reestimatingtheeffectofx1onyafterx2hasbeen partialledout 14 SimplevsMultipleRegEstimate 15 16 Example Participationin401 K PensionPlans 17 Goodness of Fit 18 Goodness of Fit continued Howdowethinkabouthowwelloursampleregressionlinefitsoursampledata Cancomputethefractionofthetotalsumofsquares SST thatisexplainedbythemodel callthistheR squaredofregressionR2 SSE SST 1 SSR SST 19 Goodness of Fit continued 20 MoreaboutR squared R2canneverdecreasewhenanotherindependentvariableisaddedtoaregression andusuallywillincreaseBecauseR2willusuallyincreasewiththenumberofindependentvariables itisnotagoodwaytocomparemodels 21 AssumptionsforUnbiasedness Populationmodelislinearinparameters y b0 b1x1 b2x2 bkxk uWecanusearandomsampleofsizen xi1 xi2 xik yi i 1 2 n fromthepopulationmodel sothatthesamplemodelisyi b0 b1xi1 b2xi2 bkxik uiE u x1 x2 xk 0 implyingthatalloftheexplanatoryvariablesareexogenousNoneofthex sisconstant andtherearenoexactlinearrelationshipsamongthem 22 TooManyorTooFewVariables Whathappensifweincludevariablesinourspecificationthatdon tbelong Thereisnoeffectonourparameterestimate andOLSremainsunbiasedWhatifweexcludeavariablefromourspecificationthatdoesbelong OLSwillusuallybebiased 23 OmittedVariableBias 遗漏变量引起的偏误 24 OmittedVariableBias cont 25 OmittedVariableBias cont 26 OmittedVariableBias cont 27 SummaryofDirectionofBias 28 OmittedVariableBiasSummary Twocaseswherebiasisequaltozerob2 0 thatisx2doesn treallybelonginmodelx1andx2areuncorrelatedinthesampleIfcorrelationbetweenx2 x1andx2 yisthesamedirection biaswillbepositiveIfcorrelationbetweenx2 x1andx2 yistheoppositedirection biaswillbenegative 29 TheMoreGeneralCase Technically wecansignthebiasforthemoregeneralcaseonlyifalloftheincludedx sareuncorrelatedTypically ignoringallotherexplanatoryvariablesisavalidpracticeonlywheneachoneisuncorrelatedwiththeincludedvariables 30 VarianceoftheOLSEstimators InadditiontoknowingthecentraltendenciesoftheOLSestimators wewanttothinkabouthowtheOLSestimatorsspreadouttothetrueparameters Assumption5 Var u x1 x2 xk s2 Homoskedasticity 31 VarianceofOLS cont Letxstandfor x1 x2 xk AssumingthatVar u x s2alsoimpliesthatVar y x s2The4assumptionsforunbiasedness plusthishomoskedasticityassumptionareknownastheGauss Markovassumptions 32 VarianceofOLS cont 33 ComponentsofOLSVariances Theerrorvariance alargers2impliesalargervariancefortheOLSestimatorsThetotalsamplevariation alargerSSTjimpliesasmallervariancefortheestimatorsLinearrelationshipsamongtheindependentvariables alargerRj2impliesalargervariancefortheestimators 34 MisspecifiedModels 35 MisspecifiedModels cont Whilethevarianceoftheestimatorissmallerforthemisspecifiedmodel unlessb2 0themisspecifiedmodelisbiasedAsthesamplesizegrows thevarianceofeachestimatorshrinkstozero makingthevariancedifferencelessimportant模型中包含多余的解释变量会引起估计方差偏大 模型中遗漏了重要的变量会引起估计不再无偏 且方差偏小 但是当包含的或遗漏的变量与保留变量无关时 不会对估计量的无偏性和方差产生影响 36 EstimatingtheErrorVariance Wedon tknowwhattheerrorvariance s2 is becausewedon tobservetheerrors uiWhatweobservearetheresiduals iWecanusetheresidualstoformanestimateoftheerrorvariance 37 ErrorVarianceEstimate cont df n k 1 ordf n k 1df i e degreesoffreedom isthe numberofobservations numberofestimatedparameters 38 TheGauss MarkovTheorem Givenour5Gauss MarkovAssumptionsitcanbeshownthatOLSis BLUE Best ofsmallestvariance Linear linearonobservationsofdependentvariable UnbiasedEstimatorThus iftheassumptionshold useOLS 39 40 ClassicalLiterature J M Keynes TheGeneralTheoryofEmplyment Intreast andMoney NewYork Harcourt Brace 1936 T Haavelmo MethodsofMeasuringtheMarginalPropensitytoConsume JASS 42 1942 105 112 Tounderstand marginalpropensitytoconsume and investmentmultiplier 41 UsingEviewsforLinearRegressions CreatingaworkfileinEviewsImportdatainEviewsDatahandlinginEviewsDataViewsinEviewsSpecifyinganequationinEviewsEstimatinganequationinEviewsEquationoutputinEviewsWorkingwithequationsinEviews 42 Estima