伍德里奇计量经济学英文版各章总结

CHAPTER1

TEACHINGNOTES

YouhavesubstantiallatitudeaboutwhattoemphasizeinChapter1.Ifinditusefultotalkabouttheeconomicsofc rimeexample(Example1.1)andthewageexample(Example1.2)sothatstudentssee,attheoutset,thateconometri csislinkedtoeconomicreasoning,eveniftheeconomicsisnotcomplicatedtheory.

Iliketofamiliarizestudentswiththeimportantdatastructuresthatempiricaleconomistsuse,focusingprimari lyoncross-sectionalandtimeseriesdatasets,asthesearewhatIcoverinafirst-semestercourse.Itisprobablyagoodi deatomentionthegrowingimportanceofdatasetsthathavebothacross-sectionalandtimedimension.

Ispendalmostanentirelecturetalkingabouttheproblemsinherentindrawingcausalinferencesinthesocials ciences.Idothismostlythroughtheagriculturalyield,returntoeducation,andcrimeexamples.Theseexamplesals

n u and x

thepossibilityofperfectcollinearityinthesample(evenifitdoesnotoccurinthepopulation)shouldbetouchedon.T hemoreimportantissueisperfectcollinearityinthepopulation,butthisisfairlyeasytodispensewithviaexamples. Thesecomefrommyexperienceswiththekindsofmodelspecificationissuesthatbeginnershavetroublewith.

Thecomparisonofsimpleandmultipleregressionestimates–basedontheparticularsampleathand,asoppos edtotheirstatisticalproperties?–usuallymakesastrongimpression.SometimesIdonotbotherwiththe“partialling out”interpretationofmultipleregres sion.

Asfarasstatisticalproperties,noticehowItreattheproblemofincludinganirrelevantvariable:noseparateder ivationisneeded,astheresultfollowsformTheorem3.1.

Idoliketoderivetheomittedvariablebiasinthesimplecase.Thisisnotmuchmoredifficultthanshowingunbia sednessofOLSinthesimpleregressioncaseunderthefirstfourGauss-Markovassumptions.Itisimportanttogetth

estudentsthinkingaboutthisproblemearlyon,andbeforetoomanyadditional(unnecessary)assumptionshavebe enintroduced.

Ihaveintentionallykeptthediscussionofmulticollinearitytoaminimum.Thispartlyindicatesmybias,butita lsoreflectsreality.Itis,ofcourse,veryimportantforstudentstounderstandthepotentialconsequencesofhavinghig hlycorrelatedindependentvariables.Butthisisoftenbeyondourcontrol,exceptthatwecanasklessofourmultipler egressionanalysis.Iftwoormoreexplanatoryvariablesarehighlycorrelatedinthesample,weshouldnotexpecttop reciselyestimatetheirceterisparibuseffectsinthepopulation.

Ifindextensivetreatmentsofmulticollinearity,whereone“tests”orsomehow“solves”themulticollinearit yproblem,tobemisleading,atbest.Eventheorganizationofsometextsgivestheimpressionthatimperfectmulticol linearityissomehowaviolationoftheGauss-Markovassumptions:theyincludemulticollinearityinachapterorpa rtofthebookdevotedto“violationofthebasicassumptions,”orsomethinglikethat.Ihavenoticedthatmaster’sstud

function g

t ct.

meterofinterestintestingasinglerestriction.Ifindthisiseasier,boththeoreticallyandpractically,thancomputingv ariancesthatcan,insomecases,dependonnumerouscovarianceterms.Theexampleoftestingequalityofthereturn totwo-andfour-yearcollegesillustratesthebasicmethod,andshowsthattherespecifiedmodelcanhaveausefulint erpretation.Ofcourse,somestatisticalpackagesnowprovideastandarderrorforlinearcombinationsofestimates withasimplecommand,andthatshouldbetaught,too.

Onecanusean F testforsinglelinearrestrictionsonmultipleparameters,butthisislesstransparentthana t testa nddoesnotimmediatelyproducethestandarderrorneededforaconfidenceintervalorfortestingaone-sidedalterna tive.Thetrickofrewritingthepopulationmodelisusefulinseveralinstances,includingobtainingconfidenceinter valsforpredictionsinChapter6,aswellasforobtainingconfidenceintervalsformarginaleffectsinmodelswithinte ractions(alsoinChapter6).

Themajorleaguebaseballplayersalaryexampleillustratesthedifferencebetweenindividualandjointsignifi cancewhenexplanatoryvariables(rbisyr and hrunsyr inthiscase)arehighlycorrelated.Itendtoemphasizethe R-sq

uaredformofthe F statisticbecause,inpractice,itisapplicablealargepercentageofthetime,anditismuchmoreread ilycomputed.Idoregretthatthisexampleisbiasedtowardstudentsincountrieswherebaseballisplayed.Still,itison eofthebetterexamplesofmulticollinearitythatIhavecomeacross,andstudentsofallbackgroundsseemtogetthep oint.

CHAPTER5

TEACHINGNOTES

Chapter5isshort,butitisconceptuallymoredifficultthantheearlierchapters,primarilybecauseitrequiresso meknowledgeofasymptoticpropertiesofestimators.Inclass,Igiveabrief,heuristicdescriptionofconsistencyand asymptoticnormalitybeforestatingtheconsistencyandasymptoticnormalityofOLS.(Conveniently,thesameas

toobtainconfidenceintervalsfortheeffectsatinteresting x values.

Asfarasgoodness-of-fit,Ionlyintroducetheadjusted R-squared,asIthinkusingaslewofgoodness-of-fitmeasures tochooseamodelcanbeconfusingtonovices(anddoesnotreflectempiricalpractice).Itisimportanttodiscusshow, ifwefixateonahigh R-squared,wemaywindupwithamodelthathasnointerestingceterisparibusinterpretation.

Ioftenhavestudentsandcolleaguesaskifthereisasimplewaytopredict y whenlog(y)hasbeenusedasthedependent variable,andtoobtainagoodness-of-fitmeasureforthelog(y)modelthatcanbecomparedwiththeusual R-squared obtainedwhen y isthedependentvariable.ThemethodsdescribedinSection6.4areeasytoimplementand,unlikeot herapproaches,donotrequirenormality.

Thesectiononpredictionandresidualanalysiscontainsseveralimportanttopics,includingconstructingpredictio nintervals.Itisusefultoseehowmuchwiderthepredictionintervalsarethantheconfidenceintervalfortheconditio nalmean.Iusuallydiscusssomeoftheresidual-analysisexamples,astheyhavereal-worldapplicability.

CHAPTER7

TEACHINGNOTES Thisisafairlystandardchapteronusingqualitativeinformationinregressionanalysis,althoughItrytoemphasizee xampleswithpolicyrelevance(andonlycross-sectionalapplicationsareincluded.). Inallowingfordifferentslopes,itisimportant,asinChapter6,toappropriatelyinterprettheparametersandtodecide whethertheyareofdirectinterest.Forexample,inthewageequationwherethereturntoeducationisallowedtodepe ndongender,thecoefficientonthefemaledummyvariableisthewagedifferentialbetweenwomenandmenatzeroy earsofeducation.Itisnotsurprisingthatwecannotestimatethisverywell,norshouldwewantto.Inthisparticularex amplewewoulddroptheinteractiontermbecauseitisinsignificant,buttheissueofinterpretingtheparameterscana riseinmodelswheretheinteractiontermissignificant.

IndiscussingtheChowtest,Ithinkitisimportanttodiscusstestingfordifferencesinslopecoefficientsafterallowin

nplaceof

R

R-s quared,1?R-sq

y|x) eveninlargesamples,withorwithoutnormality. Byexplicitlystatingthehomoskedasticityassumptionasconditionalontheexplanatoryvariablesthatappearinthe conditionalmean,itisclearthatonlyheteroskedasticitythatdependsontheexplanatoryvariablesinthemodelaffec tsthevalidityofstandarderrorsandteststatistics.TheversionoftheBreusch-Pagantestinthetext,andtheWhitetest, areideallysuitedfordetectingformsofheteroskedasticitythatinvalidateinferenceobtainedunderhomoskedastic ity.Ifheteroskedasticitydependsonanexogenousvariablethatdoesnotalsoappearinthemeanequation,thiscanbe exploitedinweightedleastsquaresforefficiency,butonlyrarelyissuchavariableavailable.Onecasewheresuchav ariableisavailableiswhenanindividual-levelequationhasbeenaggregated.IdiscussthiscaseinthetextbutIrarely havetimetoteachit.

AsImentioninthetext,othertraditionaltestsforheteroskedasticity,suchastheParkandGlejsertests,donotdirectly testwhatwewant,oraddtoomanyassumptionsunderthenull.TheGoldfeld-Quandttestonlyworkswhenthereisan

aturalwaytoorderthedatabasedononeindependentvariable.Thisisrareinpractice,especiallyforcross-sectional applications.

Somearguethatweightedleastsquaresestimationisarelic,andisnolongernecessarygiventheavailabilityofheter oskedasticity-robuststandarderrorsandteststatistics.WhileIamsympathetictothisargument,itpresumesthatwe donotcaremuchaboutefficiency.Eveninlargesamples,theOLSestimatesmaynotbepreciseenoughtolearnmuch aboutthepopulationparameters.Withsubstantialheteroskedasticitywemightdobetterwithweightedleastsquare s,eveniftheweightingfunctionismisspecified.Asdiscussedinthetextonpages288-289,onecan,andprobablysho uld,computerobuststandarderrorsafterweightedleastsquares.Forasymptoticefficiencycomparisons,thesewo uldbedirectlycomparabletotheheteroskedasiticity-robuststandarderrorsforOLS. WeightedleastsquaresestimationoftheLPMisaniceexampleoffeasibleGLS,atleastwhenallfittedvaluesareinth eunitinterval.Interestingly,intheLPMexamplesinthetextandtheLPMcomputerexercises,theheteroskedasticit

F stat https://www.360docs.net/doc/d719084619.html,puterExercise9.9isagoodexampletoshowhowmeanandmedianeffectscanbever

ydifferent,eventhoughtheremaynotbe“outliers”intheusualsense.

CHAPTER10

TEACHINGNOTES

Becauseofitsrealismanditscareinstatingassumptions,thischapterputsasomewhatheavierburdenontheinstruct orandstudentthantraditionaltreatmentsoftimeseriesregression.Nevertheless,Ithinkitisworthit.Itisimportantth atstudentslearnthattherearepotentialpitfallsinherentinusingregressionwithtimeseriesdatathatarenotpresentf orcross-sectionalapplications.Trends,seasonality,andhighpersistenceareubiquitousintimeseriesdata.Bythist ime,studentsshouldhaveafirmgraspofmultipleregressionmechanicsandinference,andsoyoucanfocusonthose featuresthatmaketimeseriesapplicationsdifferentfromcross-sectionalones.

Ithinkitisusefultodiscussstaticandfinitedistributedlagmodelsatthesametime,astheseatleasthaveashotatsatisf yingtheGauss-Markovassumptions.Manyinterestingexampleshavedistributedlagdynamics.Indiscussingthet imeseriesversionsoftheCLMassumptions,Irelymostlyonintuition.Thenotionofstrictexogeneityiseasytodiscu ssintermsoffeedback.Itisalsoprettyapparentthat,inmanyapplications,therearelikelytobesomeexplanatoryvar iablesthatarenotstrictlyexogenous.Whatthestudentshouldknowisthat,toconcludethatOLSisunbiased–asopp osedtoconsistent–weneedtoassumeaverystrongformofexogeneityoftheregressors.Chapter11showsthatonlyc ontemporaneousexogeneityisneededforconsistency. Althoughthetextiscarefulinstatingtheassumptions,inclass,afterdiscussingstrictexogeneity,Ileavetheconditio ningon X implicit,especiallywhenIdiscussthenoserialcorrelationassumption.AsthisisanewassumptionIspend sometimeonit.(Ialsodiscusswhywedidnotneeditforrandomsampling.) OncetheunbiasednessofOLS,theGauss-Markovtheorem,andthesamplingdistributionsundertheclassicallinea

r18.)

els.

Section11.4isnovelinanintroductorytext,andsimplypointsoutthat,ifamodelisdynamicallycompleteinawell-d efinedsense,itshouldnothaveserialcorrelation.Therefore,weneednotworryaboutserialcorrelationwhen,say,w etesttheefficientmarkethypothesis.Section11.5furtherinvestigatesthehomoskedasticityassumption,and,inati meseriescontext,emphasizesthatwhatiscontainedintheexplanatoryvariablesdetermineswhatkindofhetero-skedasticityisruledoutbytheusualOLSinference.Thesetwosectionscouldbeskippedwithoutlossofcontinuity.

CHAPTER12

TEACHINGNOTES

Mostofthischapterdealswithserialcorrelation,butitalsoexplicitlyconsidersheteroskedasticityintimeseriesregr essions.Thefirstsectionallowsareviewofwhatassumptionswereneededtoobtainbothfinitesampleandasymptot

icresults.Justaswithheteroske-

dasticity,serialcorrelationitselfdoesnotinvalidate R-squared.Infact,ifthedataarestationaryandweaklydepende nt,R-squaredandadjusted R-squaredconsistentlyestimatethepopulation R-squared(whichiswell-definedunder stationarity).

Equation(12.4)isusefulforexplainingwhytheusualOLSstandarderrorsarenotgenerallyvalidwithAR(1)serialc orrelation.Italsoprovidesagoodstartingpointfordiscussingserialcorrelation-robuststandarderrorsinSection12 .5.ThesubsectiononserialcorrelationwithlaggeddependentvariablesisincludedtodebunkthemyththatOLSisal waysinconsistentwithlaggeddependentvariablesandserialcorrelation.Idonotteachittoundergraduates,butIdot omaster’sstudents.

Section12.2issomewhatuntraditionalinthatitbeginswithanasymptotic t testforAR(1)serialcorrelation(u nderstrictexogeneityoftheregressors).ItmayseemhereticalnottogivetheDurbin-Watsonstatisticitsusualpromi

-semeste rcourse).

time.

Thenaturalexperimentmaterialandextensionsofthedifference-in-differencesestimatoriswidelyapplicableand ,withtheaidoftheexamples,easytounderstand.

Twoyearsofpaneldataareoftenavailable,inwhichcasedifferencingacrosstimeisasimplewayofremovinggunob servedheterogeneity.IfyouhavecoveredChapter9,youmightcomparethiswitharegressioninlevelsusingthesec ondyearofdata,butwherealaggeddependentvariableisincluded.(Thesecondapproachonlyrequirescollectingi nformationonthedependentvariableinapreviousyear.)Theseoftengivesimilaranswers.Twoyearsofpaneldata, collectedbeforeandafterapolicychange,canbeverypowerfulforpolicyanalysis. Havingmorethantwoperiodsofpaneldatacausesslightcomplicationsinthattheerrorsinthedifferencedequation maybeseriallycorrelated.(However,thetraditionalassumptionthattheerrorsintheoriginalequationareseriallyu ncorrelatedisnotalwaysagoodone.Inotherwords,itisnotalwaysmoreappropriatetousedfixedeffects,asinChapt er14,thanfirstdifferencing.)Withlarge N andrelativelysmall T,asimplewaytoaccountforpossibleserialcorrelati

onafterdifferencingistocomputestandarderrorsthatarerobusttoarbitraryserialcorrelationandhetero-skedasticity.Econometricspackagesthatdoclusteranalysis(suchasStata)oftenallowthisbyspecifyingeachcros s-sectionalunitasitsowncluster.

CHAPTER14

TEACHINGNOTES Mypreferenceistoviewthefixedandrandomeffectsmethodsofestimationasapplyingtothe same underlyinguno bservedeffectsmodel.Thename“unobservedeffect”isneutraltotheissueofwhetherthetime-constanteffectssho uldbetreatedasfixedparametersorrandomvariables.Withlarge N andrelativelysmall T,italmostalwaysmakesse nsetotreatthemasrandomvariables,sincewecanjustviewtheunobserved a i asbeingdrawnfromthepopulationalo ngwiththeobservedvariables.Especiallyforundergraduatesandmaster’sstudents,itseemssensibletonotraiseth

R(1)modelwithAR(1)serialcorrelation. Theomittedvariableproblemisconceptuallymucheasierthansimultaneity,andstatingtheconditionsneededfora nIVtobevalidinanomittedvariablecontextisstraightforward.Besides,mostmodernapplicationsofIVhavemore ofanunobservedheterogeneitymotivation.Aleadingexampleisestimatingthereturntoeducationwhenunobserv edabilityisintheerrorterm.Wearenotthinkingthateducationandwagesarejointlydetermined;forthevastmajorit yofpeople,educationiscompletedbeforewebegincollectinginformationonwagesorsalaries.Similarly,instudyi ngtheeffectsofattendingacertaintypeofschoolonstudentperformance,thechoiceofschoolismadeandthenweob serveperformanceonatest.Again,weareprimarilyconcernedwithunobservedfactorsthataffectperformancean dmaybecorrelatedwithschoolchoice;itisnotanissueofsimultaneity.

TheasymptoticsunderlyingthesimpleIVestimatorarenomoredifficultthanfortheOLSestimatorinthebivariater

egressionmodel.Certainlyconsistencycanbederivedinclass.Itisalsoeasytodemonstratehow,evenjustintermso finconsistency,IVcanbeworsethanOLSiftheIVisnotcompletelyexogenous.

Ataminimum,itisimportanttoalwaysestimatethereducedformequationandtestwhethertheIVispartiallycorrela tedwithendogenousexplanatoryvariable.Thematerialonmulticollinearityand2SLSestimationisadirectextensi https://www.360docs.net/doc/d719084619.html,ingequation(15.43),itiseasytoexplainwhymulticollinearityisgenerallymoreofaproblem with2SLSestimation. AnotherconceptuallystraightforwardapplicationofIVistosolvethemeasurementerrorproblem,although,beca useitrequirestwomeasures,itcanbehardtoimplementinpractice. Testingforendogeneityandtestinganyoveridentificationrestrictionsissomethingthatshouldbecoveredinsecon dsemestercourses.Thetestsarefairlyeasytomotivateandareveryeasytoimplement.

orshould ourse.Oncestudentshaveseenfirstdifferencingorthewithintransformation,alongwithIVmethods,theywillfind specifyingandestimatingmodelsofthesortcontainedinExample16.8straightforward.Levitt’sexampleconcern

ingprisonpopulationsisespeciallyconvincingbecausehisinstrumentsseemtobetrulyexogenous.

CHAPTER17

TEACHINGNOTES

Iemphasizetothestudentsthat,firstandforemost,thereasonweusetheprobitandlogitmodelsistoobtainmo rereasonablefunctionalformsfortheresponseprobability.Oncewemovetoanonlinearmodelwithafullyspecifie dconditionaldistribution,itmakessensetousetheefficientestimationprocedure,maximumlikelihood.Itisimport anttospendsometimeoninterpretingprobitandlogitestimates.Inparticular,thestudentsshouldknowtherules-of-thumbforcomparingprobit,logit,andLPMestimates.Beginnerssometimesmistakenlythinkthat,becausethepro

bitandespeciallythelogitestimatesaremuchlargerthantheLPMestimates,theexplanatoryvariablesnowhavelar gerestimatedeffectsontheresponseprobabilitiesthanintheLPMcase.Thismayormaynotbetrue. IviewtheTobitmodel,whenproperlyapplied,asimprovingfunctionalformforcornersolutionoutcomes.Inmostc asesitiswrongtoviewaTobitapplicationasadata-censoringproblem(unlessthereistruedatacensoringincollecti ngthedataorbecauseofinstitutionalconstraints).Forexample,inusingsurveydatatoestimatethedemandforanew product,sayasaferpesticidetobeusedinfarming,somefarmerswilldemandzeroatthegoingprice,whilesomewill demandpositivepoundsperacre.Thereisnodatacensoringhere;somefarmersfinditoptimaltousenoneofthenew pesticide.TheTobitmodelprovidesmorerealisticfunctionalformsforE(y|x)andE(y|y?>?0,x)thanalinearmodelf or y.WiththeTobitmodel,studentsmaybetemptedtocomparetheTobitestimateswiththosefromthelinearmodela ndconcludethattheTobitestimatesimplylargereffectsfortheindependentvariables.But,aswithprobitandlogit,t heTobitestimatesmustbescaleddowntobecomparablewithOLSestimatesinalinearmodel.[SeeEquation(17.27

orE(y|x

lem.

esoneparticularinterpretationofdynamicregressionmodels.Butonemustemphasizethatonlyunderfairlyrestric tiveassumptionsontheserialcorrelationintheerroroftheinfiniteDLmodeldoesthedynamicregressionconsistent https://www.360docs.net/doc/d719084619.html,puterExerciseC18.1providesagoodillustrationofhowtheG DLmodel,andasimpleRDLmodel,canbetoorestrictive.

Example18.5testsforcointegrationbetweenthegeneralfertilityrateandthevalueofthepersonalexemption.Ther eisnotmuchevidenceofcointegration,whichshedsfurtherdoubtontheregressionsinlevelsthatwereusedinChapt er10.TheerrorcorrectionmodelforholdingyieldsinExample18.7islikelytobeofinteresttostudentsinfinance.As aclassproject,oratermprojectforastudent,itwouldbeinterestingtoupdatethedatatoseeiftheerrorcorrectionmod elisstableovertime. Theforecastingsectionisheavilyorientedtowardsregressionmethodsand,inparticular,autoregressivemodels.T hesecanbeestimatedusinganyeconometricspackage,andforecastsandmeanabsoluteerrorsorrootmeansquared

errorsareeasytoobtain.Theinterestratedatasets(forexample,INTQRT.RAW)canbeupdatedtodomuchmorerec entout-of-sampleforecastingexercises.

CHAPTER19

TEACHINGNOTES

Thisisachapterthatstudentsshouldreadifyouhaveassignedthematermpaper.Iusedtoallowstudentstocho osetheirowntopics,butthisisdifficultinafirst-semestercourse,andplacesaheavyburdenoninstructorsorteachin gassistants,orboth.Inowassignacommontopicandprovideadatasetwithaboutsixweeksleftintheterm.Thedatas etiscross-sectional(becauseIteachtimeseriesattheendofthecourse),andIprovideguidelinesofthekindsofquesti onsstudentsshouldtrytoanswer.(Forexample,Imightaskthemtoanswerthefollowingquestions:Isthereamarria gepremiumforNBAbasketballplayers?Ifso,doesitdependonrace?Canthepremium,ifitexists,beexplainedbypr oductivitydifferences?)Thespecificsareuptothestudents,andtheyaretocrafta10-to15-pagepaperontheirown.T