伍德里奇计量经济学英文版各章总结.docx
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伍德里奇计量经济学英文版各章总结.docx
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伍德里奇计量经济学英文版各章总结
CHAPTER1
TEACHINGNOTES
YouhavesubstantiallatitudeaboutwhattoemphasizeinChapter1.Ifinditusefultotalkabouttheeconomicsofcrimeexample(Example1.1)andthewageexample(Example1.2)sothatstudentssee,attheoutset,thateconometricsislinkedtoeconomicreasoning,eveniftheeconomicsisnotcomplicatedtheory.
Iliketofamiliarizestudentswiththeimportantdatastructuresthatempiricaleconomistsuse,focusingprimarilyoncross-sectionalandtimeseriesdatasets,asthesearewhatIcoverinafirst-semestercourse.Itisprobablyagoodideatomentionthegrowingimportanceofdatasetsthathavebothacross-sectionalandtimedimension.
Ispendalmostanentirelecturetalkingabouttheproblemsinherentindrawingcausalinferencesinthesocialsciences.Idothismostlythroughtheagriculturalyield,returntoeducation,andcrimeexamples.Theseexamplesalsocontrastexperimentalandnonexperimental(observational)data.Studentsstudyingbusinessandfinancetendtofindthetermstructureofinterestratesexamplemorerelevant,althoughtheissuethereistestingtheimplicationofasimpletheory,asopposedtoinferringcausality.Ihavefoundthatspendingtimetalkingabouttheseexamples,inplaceofaformalreviewofprobabilityandstatistics,ismoresuccessful(andmoreenjoyableforthestudentsandme).
CHAPTER2
TEACHINGNOTES
ThisisthechapterwhereIexpectstudentstofollowmost,ifnotall,ofthealgebraicderivations.InclassIliketoderiveatleasttheunbiasednessoftheOLSslopecoefficient,andusuallyIderivethevariance.Ataminimum,Italkaboutthefactorsaffectingthevariance.Tosimplifythenotation,afterIemphasizetheassumptionsinthepopulationmodel,andassumerandomsampling,Ijustconditiononthevaluesoftheexplanatoryvariablesinthesample.Technically,thisisjustifiedbyrandomsamplingbecause,forexample,E(ui|x1,x2,…,xn)=E(ui|xi)byindependentsampling.IfindthatstudentsareabletofocusonthekeyassumptionSLR.4andsubsequentlytakemywordabouthowconditioningontheindependentvariablesinthesampleisharmless.(Ifyouprefer,theappendixtoChapter3doestheconditioningargumentcarefully.)Becausestatisticalinferenceisnomoredifficultinmultipleregressionthaninsimpleregression,IpostponeinferenceuntilChapter4.(Thisreducesredundancyandallowsyoutofocusontheinterpretivedifferencesbetweensimpleandmultipleregression.)
Youmightnoticehow,comparedwithmostothertexts,IuserelativelyfewassumptionstoderivetheunbiasednessoftheOLSslopeestimator,followedbytheformulaforitsvariance.ThisisbecauseIdonotintroduceredundantorunnecessaryassumptions.Forexample,onceSLR.4isassumed,nothingfurtherabouttherelationshipbetweenuandxisneededtoobtaintheunbiasednessofOLSunderrandomsampling.
CHAPTER3
TEACHINGNOTES
Forundergraduates,Idonotworkthroughmostofthederivationsinthischapter,atleastnotindetail.Rather,Ifocusoninterpretingtheassumptions,whichmostlyconcernthepopulation.Otherthanrandomsampling,theonlyassumptionthatinvolvesmorethanpopulationconsiderationsistheassumptionaboutnoperfectcollinearity,wherethepossibilityofperfectcollinearityinthesample(evenifitdoesnotoccurinthepopulation)shouldbetouchedon.Themoreimportantissueisperfectcollinearityinthepopulation,butthisisfairlyeasytodispensewithviaexamples.Thesecomefrommyexperienceswiththekindsofmodelspecificationissuesthatbeginnershavetroublewith.
Thecomparisonofsimpleandmultipleregressionestimates–basedontheparticularsampleathand,asopposedtotheirstatisticalproperties –usuallymakesastrongimpression.SometimesIdonotbotherwiththe“partiallingout”interpretationofmultipleregression.
Asfarasstatisticalproperties,noticehowItreattheproblemofincludinganirrelevantvariable:
noseparatederivationisneeded,astheresultfollowsformTheorem3.1.
Idoliketoderivetheomittedvariablebiasinthesimplecase.ThisisnotmuchmoredifficultthanshowingunbiasednessofOLSinthesimpleregressioncaseunderthefirstfourGauss-Markovassumptions.Itisimportanttogetthestudentsthinkingaboutthisproblemearlyon,andbeforetoomanyadditional(unnecessary)assumptionshavebeenintroduced.
Ihaveintentionallykeptthediscussionofmulticollinearitytoaminimum.Thispartlyindicatesmybias,butitalsoreflectsreality.Itis,ofcourse,veryimportantforstudentstounderstandthepotentialconsequencesofhavinghighlycorrelatedindependentvariables.Butthisisoftenbeyondourcontrol,exceptthatwecanasklessofourmultipleregressionanalysis.Iftwoormoreexplanatoryvariablesarehighlycorrelatedinthesample,weshouldnotexpecttopreciselyestimatetheirceterisparibuseffectsinthepopulation.
Ifindextensivetreatmentsofmulticollinearity,whereone“tests”orsomehow“solves”themulticollinearityproblem,tobemisleading,atbest.EventheorganizationofsometextsgivestheimpressionthatimperfectmulticollinearityissomehowaviolationoftheGauss-Markovassumptions:
theyincludemulticollinearityinachapterorpartofthebookdevotedto“violationofthebasicassumptions,”orsomethinglikethat.Ihavenoticedthatmaster’sstudentswhohavehadsomeundergraduateeconometricsareoftenconfusedonthemulticollinearityissue.Itisveryimportantthatstudentsnotconfusemulticollinearityamongtheincludedexplanatoryvariablesinaregressionmodelwiththebiascausedbyomittinganimportantvariable.
IdonotprovetheGauss-Markovtheorem.Instead,Iemphasizeitsimplications.Sometimes,andcertainlyforadvancedbeginners,IputaspecialcaseofProblem3.12onamidtermexam,whereImakeaparticularchoiceforthefunctiong(x).Ratherthanhavethestudentsdirectlycomparethevariances,theyshouldappealtotheGauss-MarkovtheoremforthesuperiorityofOLSoveranyotherlinear,unbiasedestimator.
CHAPTER4
TEACHINGNOTES
AtthestartofthischapterisgoodtimetoremindstudentsthataspecificerrordistributionplayednoroleintheresultsofChapter3.ThatisbecauseonlythefirsttwomomentswerederivedunderthefullsetofGauss-Markovassumptions.Nevertheless,normalityisneededtoobtainexactnormalsamplingdistributions(conditionalontheexplanatoryvariables).IemphasizethatthefullsetofCLMassumptionsareusedinthischapter,butthatinChapter5werelaxthenormalityassumptionandstillperformapproximatelyvalidinference.Onecouldarguethattheclassicallinearmodelresultscouldbeskippedentirely,andthatonlylarge-sampleanalysisisneeded.But,fromapracticalperspective,studentsstillneedtoknowwherethetdistributioncomesfrombecausevirtuallyallregressionpackagesreporttstatisticsandobtainp-valuesoffofthetdistribution.IthenfinditveryeasytocoverChapter5quickly,byjustsayingwecandropnormalityandstillusetstatisticsandtheassociatedp-valuesasbeingapproximatelyvalid.Besides,occasionallystudentswillhavetoanalyzesmallerdatasets,especiallyiftheydotheirownsmallsurveysforatermproject.
Itiscrucialtoemphasizethatwetesthypothesesaboutunknownpopulationparameters.ItellmystudentsthattheywillbepunishediftheywritesomethinglikeH0:
=0onanexamor,evenworse,H0:
.632=0.
OneusefulfeatureofChapter4isitsillustrationofhowtorewriteapopulationmodelsothatitcontainstheparameterofinterestintestingasinglerestriction.Ifindthisiseasier,boththeoreticallyandpractically,thancomputingvariancesthatcan,insomecases,dependonnumerouscovarianceterms.Theexampleoftestingequalityofthereturntotwo-andfour-yearcollegesillustratesthebasicmethod,andshowsthattherespecifiedmodelcanhaveausefulinterpretation.Ofcourse,somestatisticalpackagesnowprovideastandarderrorforlinearcombinationsofestimateswithasimplecommand,andthatshouldbetaught,too.
OnecanuseanFtestforsinglelinearrestrictionsonmultipleparameters,butthisislesstransparentthanattestanddoesnotimmediatelyproducethestandarderrorneededforaconfidenceintervalorfortestingaone-sidedalternative.Thetrickofrewritingthepopulationmodelisusefulinseveralinstances,includingobtainingconfidenceintervalsforpredictionsinChapter6,aswellasforobtainingconfidenceintervalsformarginaleffectsinmodelswithinteractions(alsoinChapter6).
Themajorleaguebaseballplayersalaryexampleillustratesthedifferencebetweenindividualandjointsignificancewhenexplanatoryvariables(rbisyrandhrunsyrinthiscase)arehighlycorrelated.ItendtoemphasizetheR-squaredformoftheFstatisticbecause,inpractice,itisapplicablealargepercentageofthetime,anditismuchmorereadilycomputed.Idoregretthatthisexampleisbiasedtowardstudentsincountrieswherebaseballisplayed.Still,itisoneofthebetterexamplesofmulticollinearitythatIhavecomeacross,andstudentsofallbackgroundsseemtogetthepoint.
CHAPTER5
TEACHINGNOTES
Chapter5isshort,butitisconceptuallymoredifficultthantheearlierchapters,primarilybecauseitrequiressomeknowledgeofasymptoticpropertiesofestimators.Inclass,Igiveabrief,heuristicdescriptionofconsistencyandasymptoticnormalitybeforestatingtheconsistencyandasymptoticnormalityofOLS.(Conveniently,thesameassumptionsthatworkforfinitesampleanalysisworkforasymptoticanalysis.)Moreadvancedstudentscanfollowtheproofofconsistencyoftheslopecoefficientinthebivariateregressioncase
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