计量经济学英文课件-5

Chapter6FurtherInferenceintheMultipleRegressionModelAdaptedfromVeraTabakova’snotesECON4550EconometricsMemorialUniversityofNewfoundlandChapter6:

FurtherInferenceintheMultipleRegressionModel6.1TheF-Test6.2TestingtheSignificanceoftheModel6.3 AnExtendedModel6.4 TestingSomeEconomicHypotheses6.5 TheUseofNonsampleInformation6.6 ModelSpecification6.7 PoorData,CollinearityandInsignificance6.8 PredictionSlide6-2PrinciplesofEconometrics,3rdEdition6.1TheF-Test

Slide6-3PrinciplesofEconometrics,3rdEdition(6.1)(6.2)6.1TheF-Test

Ifthenullhypothesisisnottrue,thenthedifferencebetweenSSERandSSEUbecomeslarge,implyingthattheconstraintsplacedonthemodelbythenullhypothesishavealargeeffectontheabilityofthemodeltofitthedata.Slide6-4PrinciplesofEconometrics,3rdEdition(6.3)6.1TheF-Test Hypothesistestingsteps:Specifythenullandalternativehypotheses:SpecifytheteststatisticanditsdistributionifthenullhypothesisistrueSetanddeterminetherejectionregion Usingα=.05,thecriticalvaluefromthe-distributionis. Thus,H0isrejectedif.Slide6-5PrinciplesofEconometrics,3rdEdition6.1TheF-Test Calculatethesamplevalueoftheteststatisticand,ifdesired,thep-valueStateyourconclusion Since,werejectthenullhypothesisandconcludethatpricedoeshaveasignificanteffectonsalesrevenue.Alternatively,werejectH0because .Slide6-6PrinciplesofEconometrics,3rdEdition

6.1.1 TheRelationshipBetweent-andF-Tests

TheelementsofanF-test:ThenullhypothesisconsistsofoneormoreequalityrestrictionsJ.Thenullhypothesismaynotincludeany‘greaterthanorequalto’or‘lessthanorequalto’hypotheses.Thealternativehypothesisstatesthatoneormoreoftheequalitiesinthenullhypothesisisnottrue.Thealternativehypothesismaynotincludeany‘greaterthan’or‘lessthan’options.TheteststatisticistheF-statisticSlide6-7PrinciplesofEconometrics,3rdEdition

6.1.1 TheRelationshipBetweent-andF-Tests

Ifthenullhypothesisistrue,FhastheF-distributionwithJnumeratordegreesoffreedomandN-Kdenominatordegreesoffreedom.Thenullhypothesisisrejectedif.Whentestingasingleequalitynullhypothesisitisperfectlycorrecttouseeitherthet-orF-testprocedure;theyareequivalent.Slide6-8PrinciplesofEconometrics,3rdEdition6.2TestingtheSignificanceoftheModel

Slide6-9PrinciplesofEconometrics,3rdEdition(6.4)(6.5)(6.6)6.2TestingtheSignificanceoftheModel

Slide6-10PrinciplesofEconometrics,3rdEdition(6.7)6.2TestingtheSignificanceoftheModel Example:BigAndy’ssalesrevenue

IfthenullistrueH0isrejectedif

Since29.95>3.12werejectthenullandconcludethatpriceoradvertisingexpenditureorbothhaveaninfluenceonsales.

Slide6-11PrinciplesofEconometrics,3rdEdition6.3AnExtendedModelFigure6.1AModelWhereSalesExhibitsDiminishingReturnstoAdvertisingExpenditureSlide6-12PrinciplesofEconometrics,3rdEdition6.3AnExtendedModel

Slide6-13PrinciplesofEconometrics,3rdEdition(6.8)(6.9)(6.10)6.3AnExtendedModel

Slide6-14PrinciplesofEconometrics,3rdEdition(6.11)6.4 TestingSomeEconomicHypotheses6.4.1TheSignificanceofAdvertising

Slide6-15PrinciplesofEconometrics,3rdEdition(6.12)(6.13)6.4 TestingSomeEconomicHypotheses

Since,werejectthenullhypothesisandconcludethatadvertisingdoeshaveasignificanteffectuponsalesrevenue.

Slide6-16PrinciplesofEconometrics,3rdEdition6.4.2TheOptimalLevelofAdvertising Economictheorytellsusthatweshouldundertakeallthoseactionsforwhichthemarginalbenefitisgreaterthanthemarginalcost.ThisoptimizingprincipleappliestoBigAndy’sBurgerBarnasitattemptstochoosetheoptimallevelofadvertisingexpenditure.Slide6-17PrinciplesofEconometrics,3rdEdition6.4.2TheOptimalLevelofAdvertising BigAndyhasbeenspending$1,900permonthonadvertising.Hewantstoknowwhetherthisamountcouldbeoptimal. ThenullandalternativehypothesesforthistestareSlide6-18PrinciplesofEconometrics,3rdEdition6.4.2TheOptimalLevelofAdvertising

Slide6-19PrinciplesofEconometrics,3rdEdition6.4.2TheOptimalLevelofAdvertising Because,wecannotrejectthenullhypothesisthattheoptimallevelofadvertisingis$1,900permonth.ThereisinsufficientevidencetosuggestAndyshouldchangehisadvertisingstrategy.Slide6-20PrinciplesofEconometrics,3rdEdition6.4.2TheOptimalLevelofAdvertising

Slide6-21PrinciplesofEconometrics,3rdEdition6.4.2a AOne-TailedTestwithMorethanOneParameter RejectH0ift≥1.667. t=.9676 Because.9676<1.667,wedonotrejectH0. Thereisnotenoughevidenceinthedatatosuggesttheoptimallevelofadvertisingexpenditureisgreaterthan$1900.Slide6-22PrinciplesofEconometrics,3rdEdition6.4.2UsingComputerSoftware

Slide6-23PrinciplesofEconometrics,3rdEdition6.5TheUseofNonsampleInformation

Slide6-24PrinciplesofEconometrics,3rdEdition(6.14)(6.15)6.5TheUseofNonsampleInformation

Slide6-25PrinciplesofEconometrics,3rdEdition(6.16)(6.17)6.5TheUseofNonsampleInformation

Slide6-26PrinciplesofEconometrics,3rdEdition6.5TheUseofNonsampleInformation

Slide6-27PrinciplesofEconometrics,3rdEdition(6.18)6.5TheUseofNonsampleInformation

Slide6-28PrinciplesofEconometrics,3rdEdition(6.19)6.6ModelSpecification6.6.1OmittedVariables

Slide6-29PrinciplesofEconometrics,3rdEdition(6.20)6.6.1OmittedVariables

Slide6-30PrinciplesofEconometrics,3rdEdition6.6.1OmittedVariables

Slide6-31PrinciplesofEconometrics,3rdEdition(6.21)(6.22)6.6.1OmittedVariables

Slide6-32PrinciplesofEconometrics,3rdEdition(6.23)(6.24)6.6.2IrrelevantVariables

Slide6-33PrinciplesofEconometrics,3rdEdition6.6.3ChoosingtheModelChoosevariablesandafunctionalformonthebasisofyourtheoreticalandgeneralunderstandingoftherelationship.Ifanestimatedequationhascoefficientswithunexpectedsigns,orunrealisticmagnitudes,theycouldbecausedbyamisspecificationsuchastheomissionofanimportantvariable.

Slide6-34PrinciplesofEconometrics,3rdEdition6.6.3ChoosingtheModelOnemethodforassessingwhetheravariableoragroupofvariablesshouldbeincludedinanequationistoperformsignificancetests.Thatis,t-testsforhypothesessuchas

orF-testsforhypothesessuchas.

Failuretorejecthypothesessuchasthesecanbeanindicationthatthevariable(s)areirrelevant.TheadequacyofamodelcanbetestedusingageneralspecificationtestknownasRESET.

Slide6-35PrinciplesofEconometrics,3rdEdition6.6.3aTheRESETTest

Slide6-36PrinciplesofEconometrics,3rdEdition(6.25)6.6.3aTheRESETTest

Slide6-37PrinciplesofEconometrics,3rdEdition(6.26)(6.27)6.6.3aTheRESETTest

Slide6-38PrinciplesofEconometrics,3rdEdition6.7Poordata,CollinearityandInsignificance6.7.1TheConsequencesofCollinearity

Slide6-39PrinciplesofEconometrics,3rdEdition(6.28)6.7.1TheConsequencesofCollinearityTheeffectsofimpreciseinformation:Whenestimatorstandarderrorsarelarge,itislikelythattheusualt-testswillleadtotheconclusionthatparameterestimatesarenotsignificantlydifferentfromzero.ThisoutcomeoccursdespitepossiblyhighorF-valuesindicatingsignificantexplanatorypowerofthemodelasawhole.

Slide6-40PrinciplesofEconometrics,3rdEdition6.7.1TheConsequencesofCollinearityTheestimatorsmaybeverysensitivetotheadditionordeletionofafewobservations,orthedeletionofanapparentlyinsignificantvariable.Despitethedifficultiesinisolatingtheeffectsofindividualvariablesfromsuchasample,accurateforecastsmaystillbepossibleifthenatureofthecollinearrelationshipremainsthesamewithinthenew(future)sampleobservations.

Slide6-41PrinciplesofEconometrics,3rdEdition6.7.2AnExampleMPG=milespergallonCYL=numberofcylindersENG=enginedisplacementincubicinchesWGT=vehicleweightinpounds

Slide6-42PrinciplesofEconometrics,3rdEdition6.7.2AnExample

Slide6-43PrinciplesofEconometrics,3rdEdition6.7.3IdentifyingandMitigatingCollinearity

IdentifyingCollinearityExaminingpairwisecorrelations.Usingauxiliaryregression

IftheR2fromthisartificialmodelishigh,above.80say,theimplicationisthatalargeportionofthevariationinisexplainedbyvariationintheotherexplanatoryvariables.

Slide6-44PrinciplesofEconometrics,3rdEdition6.7.3IdentifyingandMitigatingCollinearity

MitigatingCollinearityObtainmoreinformationandincludeitintheanalysis.Introducenonsampleinformationintheformofrestrictionsontheparameters.

Slide6-45PrinciplesofEconometrics,3rdEdition6.8Prediction

Slide6-46PrinciplesofEconometrics,3rdEdition(6.29)6.8Prediction

Slide6-47PrinciplesofEconometrics,3rdEditionKeywordsSlide6-48PrinciplesofEconometrics,3rdEditionasinglenullhypothesiswithmorethanoneparameterauxiliaryregressionscollinearityF-testirrelevantvariablenonsampleinformationomittedvariableomittedvariablebiasoverallsignificanceofareg