2019《计量经济学导论》ch6.ppt

©2013CengageLearning.AllRightsReserved.Maynotbescanned,copiedorduplicated,orpostedtoapubliclyaccessiblewebsite,inwholeorinpart.Chapter6MultipleRegressionAnalysis:FurtherIssuesWooldridge:IntroductoryEconometrics:AModernApproach,5e©2013CengageLearning.AllRightsReserved.Maynotbescanned,copiedorduplicated,orpostedtoapubliclyaccessiblewebsite,inwholeorinpart.MoreonFunctionalFormMoreonusinglogarithmicfunctionalformsConvenientpercentage/elasticityinterpretationSlopecoefficientsofloggedvariablesareinvarianttorescalingsTakinglogsofteneliminates/mitigatesproblemswithoutliersTakinglogsoftenhelpstosecurenormalityandhomoscedasticityVariablesmeasuredinunitssuchasyearsshouldnotbeloggedVariablesmeasuredinpercentagepointsshouldalsonotbeloggedLogsmustnotbeusedifvariablestakeonzeroornegativevaluesItishardtoreversethelog-operationwhenconstructingpredictionsMultipleRegressionAnalysis:FurtherIssues©2013CengageLearning.AllRightsReserved.Maynotbescanned,copiedorduplicated,orpostedtoapubliclyaccessiblewebsite,inwholeorinpart.UsingquadraticfunctionalformsExample:WageequationMarginaleffectofexperienceThefirstyearofexperienceincreasesthewagebysome.30$,thesecondyearby.298-2(.0061)(1)=.29$etc.ConcaveexperienceprofileMultipleRegressionAnalysis:FurtherIssues©2013CengageLearning.AllRightsReserved.Maynotbescanned,copiedorduplicated,orpostedtoapubliclyaccessiblewebsite,inwholeorinpart.WagemaximumwithrespecttoworkexperienceDoesthismeanthereturntoexperiencebecomesnegativeafter24.4years?Notnecessarily.Itdependsonhowmanyobservationsinthesamplelierightoftheturnaroundpoint.Inthegivenexample,theseareabout28%oftheobservations.Theremaybeaspeci-ficationproblem(e.g.omittedvariables).MultipleRegressionAnalysis:FurtherIssues©2013CengageLearning.AllRightsReserved.Maynotbescanned,copiedorduplicated,orpostedtoapubliclyaccessiblewebsite,inwholeorinpart.Example:EffectsofpollutiononhousingpricesDoesthismeanthat,atalownumberofrooms,moreroomsareassociatedwithlowerprices?Nitrogenoxideinair,distancefromem-ploymentcenters,student/teacherratioMultipleRegressionAnalysis:FurtherIssues©2013CengageLearning.AllRightsReserved.Maynotbescanned,copiedorduplicated,orpostedtoapubliclyaccessiblewebsite,inwholeorinpart.CalculationoftheturnaroundpointThisareacanbeignoredasitconcernsonly1%oftheobservations.Increaseroomsfrom5to6:Increaseroomsfrom6to7:Turnaroundpoint:MultipleRegressionAnalysis:FurtherIssues©2013CengageLearning.AllRightsReserved.Maynotbescanned,copiedorduplicated,orpostedtoapubliclyaccessiblewebsite,inwholeorinpart.OtherpossibilitiesHigherpolynomialsMultipleRegressionAnalysis:FurtherIssues©2013CengageLearning.AllRightsReserved.Maynotbescanned,copiedorduplicated,orpostedtoapubliclyaccessiblewebsite,inwholeorinpart.ModelswithinteractiontermsInteractioneffectscomplicateinterpretationofparametersInteractiontermTheeffectofthenumberofbedroomsdependsonthelevelofsquarefootageEffectofnumberofbedrooms,butforasquarefootageofzeroMultipleRegressionAnalysis:FurtherIssues©2013CengageLearning.AllRightsReserved.Maynotbescanned,copiedorduplicated,orpostedtoapubliclyaccessiblewebsite,inwholeorinpart.Populationmeans;maybereplacedbysamplemeansReparametrizationofinteractioneffectsAdvantagesofreparametrizationEasyinterpretationofallparametersStandarderrorsforpartialeffectsatthemeanvaluesavailableIfnecessary,interactionmaybecenteredatotherinterestingvaluesEffectofx2ifallvariablestakeontheirmeanvaluesMultipleRegressionAnalysis:FurtherIssues©2013CengageLearning.AllRightsReserved.Maynotbescanned,copiedorduplicated,orpostedtoapubliclyaccessiblewebsite,inwholeorinpart.Moreongoodness-of-fitandselectionofregressorsGeneralremarksonR-squaredAhighR-squareddoesnotimplythatthereisacausalinterpretationAlowR-squareddoesnotprecludepreciseestimationofpartialeffectsAdjustedR-squaredWhatistheordinaryR-squaredsupposedtomeasure?isanestimateforPopulationR-squaredMultipleRegressionAnalysis:FurtherIssues©2013CengageLearning.AllRightsReserved.Maynotbescanned,copiedorduplicated,orpostedtoapubliclyaccessiblewebsite,inwholeorinpart.AdjustedR-squared(cont.)AbetterestimatetakingintoaccountdegreesoffreedomwouldbeTheadjustedR-squaredimposesapenaltyforaddingnewregressorsTheadjustedR-squaredincreasesif,andonlyif,thet-statisticofanewlyaddedregressorisgreaterthanoneinabsolutevalueRelationshipbetweenR-squaredandadjustedR-squaredCorrectdegreesoffreedomofnominatoranddenominatorTheadjustedR-squaredmayevengetnegativeMultipleRegressionAnalysis:FurtherIssues©2013CengageLearning.AllRightsReserved.Maynotbescanned,copiedorduplicated,orpostedtoapubliclyaccessiblewebsite,inwholeorinpart.UsingadjustedR-squaredtochoosebetweennonnestedmodelsModelsarenonnestedifneithermodelisaspecialcaseoftheotherAcomparisonbetweentheR-squaredofbothmodelswouldbeunfairtothefirstmodelbecausethefirstmodelcontainsfewerparametersInthegivenexample,evenafteradjustingforthedifferenceindegreesoffreedom,thequadraticmodelispreferredMultipleRegressionAnalysis:FurtherIssues©2013CengageLearning.AllRightsReserved.Maynotbescanned,copiedorduplicated,orpostedtoapubliclyacces