伍德里奇計(jì)量經(jīng)濟(jì)學(xué)英文版各章總結(jié)經(jīng)濟(jì)

ormalityassumptionandstillperformapproximatelyvali

gmorethantwoperiodsofpaneldatacausesslightcomplica

ercise9.3isalsoagoodillustrationofthismethod.Irare

emandzero15/18atthegoingprice,whilesomewilldemandp

i12n

CHAPTER1

TEACHINGNOTES

YouhavesubstantiallatitudeaboutwhattoemphasizeinChapter1.

Ifinditusefultotalkabouttheeconomicsofcrimeexample(Example

1.1)andthewageexample(Example1.2)sothatstudentssee,attheoutset,thateconometricsislinkedtoeconomicreasoning,eveniftheeconomicsisnotcomplicatedtheory.

Iliketofamiliarizestudentswiththeimportantdatastructuresthatempiricaleconomistsuse,focusingprimarilyoncross-sectionalandtimeseriesdatasets,asthesearewhatIcoverinafirst-semestercourse.

Itisprobablyagoodideatomentionthegrowingimportanceofdatasetsthathavebothacross-sectionalandtimedimension.

Ispendalmostanentirelecturetalkingabouttheproblemsinherentindrawingcausalinferencesinthesocialsciences.Idothismostly

throughtheagriculturalyield,returntoeducation,andcrimeexamples.Theseexamplesalsocontrastexperimentalandnonexperimental

(observational)data.Studentsstudyingbusinessandfinancetendto

findthetermstructureofinterestratesexamplemorerelevant,althoughtheissuethereistestingtheimplicationofasimpletheory,asopposedtoinferringcausality.Ihavefoundthatspendingtimetalkingabout

theseexamples,inplaceofaformalreviewofprobabilityandstatistics,ismoresuccessful(andmoreenjoyableforthestudentsandme).

CHAPTER2

TEACHINGNOTES

ThisisthechapterwhereIexpectstudentstofollowmost,ifnot

all,ofthealgebraicderivations.InclassIliketoderiveatleast

theunbiasednessoftheOLSslopecoefficient,andusually

variance.Ataminimum,ItalkaboutthefactorsaffectingTosimplifythenotation,afterIemphasizetheassumptionsinthe

Iderivethethevariance.

populationmodel,andassumerandomsampling,Ijustconditiononthe

valuesoftheexplanatoryvariablesinthesample.Technically,thisis

justifiedbyrandomsamplingbecause,forexample,E(u|x,x,…,x)=

E(u|x)byindependentsampling.Ifindthatstudentsareabletofocus

onthekeyassumptionSLR.4andsubsequentlytakemywordabouthowconditioningontheindependentvariablesinthesampleisharmless.(Ifyouprefer,theappendixtoChapter3doestheconditioningargument

ii

carefully.)Becausestatisticalinferenceisnomoredifficultin

multipleregressionthaninsimpleregression,Ipostponeinferenceuntil

Chapter4.(Thisreducesredundancyandallowsyoutofocusonthe

interpretivedifferencesbetweensimpleandmultipleregression.)

Youmightnoticehow,comparedwithmostothertexts,Iuse

relativelyfewassumptionstoderivetheunbiasednessoftheOLSslope

estimator,followedbytheformulaforitsvariance.ThisisbecauseI

donotintroduceredundantorunnecessaryassumptions.Forexample,once

1/18

sionmodel.Whenweaddtheappropriatehomoskedasticitya

tcollinearityinthesample(evenifitdoesnotthanrandom

ldbeskippedwithoutlossofcontinuity.CHAPTER12TEACHI

ntemporaneouslyexogenous,OLSisconsistent.Thisresul

SLR.4isassumed,nothingfurtherabouttherelationshipbetweenuand

xisneededtoobtaintheunbiasednessofOLSunderrandomsampling.

CHAPTER3

TEACHINGNOTES

Forundergraduates,Idonotworkthroughmostofthederivationsin

thischapter,atleastnotindetail.Rather,Ifocusoninterpreting

theassumptions,whichmostlyconcernthepopulation.Othersampling,theonlyassumptionthatinvolvesmorethanpopulationconsiderationsistheassumptionaboutnoperfectcollinearity,possibilityofperfectcollinearityinthesample(evenifitdoesnot

thanrandom

wherethe

occurinthepopulation)shouldbetouchedon.Themoreimportantissue

isperfectcollinearityinthepopulation,butthisisfairlyeasyto

dispensewithviaexamples.Thesecomefrommyexperiencesofmodelspecificationissuesthatbeginnershavetroublewith.

Thecomparisonofsimpleandmultipleregressionestimatesontheparticularsampleathand,asopposedtotheirstatistical

withthekinds

based

propertiesusuallymakesastrongimpression.SometimesIdonot

botherwiththe“partiallingout”interpretationofmultiple

regression.

Asfarasstatisticalproperties,noticehowItreattheproblemof

includinganirrelevantvariable:noseparatederivationisneeded,as

theresultfollowsformTheorem3.1.

Idoliketoderivetheomittedvariablebiasinthesimplecase.This

isnotmuchmoredifficultthanshowingunbiasednessofOLSinthesimple

regressioncaseunderthefirstfourGauss-Markovassumptions.Itis

importanttogetthestudentsthinkingaboutthisproblemearlyon,and

beforetoomanyadditional(unnecessary)assumptionshavebeen

introduced.

Ihaveintentionallykeptthediscussionofmulticollinearitytoa

minimum.Thispartlyindicatesmybias,butitalsoreflectsreality.

Itis,ofcourse,veryimportantforstudentstounderstandthepotential

consequencesofhavinghighlycorrelatedindependentvariables.But

thisisoftenbeyondourcontrol,exceptthatwecanasklessofour

multipleregressionanalysis.Iftwoormoreexplanatoryvariablesare

highlycorrelatedinthesample,weshouldnotexpecttoprecisely

estimatetheirceterisparibuseffectsinthepopulation.

Ifindextensivetreatmentsofmulticollinearity,whereone

“tests”orsomehow“solves”themulticollinearityproblem,tobe

misleading,atbest.Eventheorganizationofsometextsgivesthe

impressionthatimperfectmulticollinearityissomehowaviolationofthe

Gauss-Markovassumptions:theyincludemulticollinearityinachapter

orpartofthebookdevotedto“violationofthebasicassumptions,”

orsomethinglikethat.Ihavenoticedthatmaster’sstudentswhohave

hadsomeundergraduateeconometricsareoftenconfusedonthe

2/18

erdispersionisoftenpresentincountregressionmodels,

alformforcornersolutionoutcomes.Inmostcasesitiswro

atedasfixedparametersorrandomvariables.WithlargeNa

tendtofindthetermstructureofinterestratesexamplemo

:

0

multicollinearityissue.Itisveryimportantthatstudentsnotconfuse

multicollinearityamongtheincludedexplanatoryvariablesina

regressionmodelwiththebiascausedbyomittinganimportantvariable.

IdonotprovetheGauss-Markovtheorem.Instead,Iemphasizeitsimplications.Sometimes,andcertainlyforadvancedbeginners,Iputa

specialcaseofProblem3.12onamidtermexam,whereImakeaparticular

choiceforthefunctiong(x).Ratherthanhavethestudentsdirectly

comparethevariances,theyshouldappealtotheGauss-MarkovtheoremforthesuperiorityofOLSoveranyotherlinear,unbiasedestimator.

CHAPTER4

TEACHINGNOTES

Atthestartofthischapterisgoodtimetoremindstudentsthata

specificerrordistributionplayednoroleintheresultsofChapter3.

Thatisbecauseonlythefirsttwomomentswerederivedunderthefull

setofGauss-Markovassumptions.Nevertheless,normalityisneededto

obtainexactnormalsamplingdistributions(conditionalonthe

explanatoryvariables).IemphasizethatthefullsetofCLMassumptions

areusedinthischapter,butthatinChapter5werelaxthenormality

assumptionandstillperformapproximatelyvalidinference.Onecould

arguethattheclassicallinearmodelresultscouldbeskippedentirely,andthatonlylarge-sampleanalysisisneeded.But,fromapractical

perspective,studentsstillneedtoknowwherethefrombecausevirtuallyallregressionpackagesreport

tdistributioncomeststatisticsand

obtainp-valuesoffofthetdistribution.Ithenfinditveryeasyto

coverChapter5quickly,byjustsayingwecandropnormalityandstill

usetstatisticsandtheassociatedp-valuesasbeingapproximatelyvalid.

Besides,occasionallystudentswillhavetoanalyzesmallerdatasets,

especiallyiftheydotheirownsmallsurveysforatermproject.

Itiscrucialtoemphasizethatwetesthypothesesaboutunknown

populationparameters.Itellmystudentsthattheywillbepunishedif

theywritesomethinglikeH

=0.

01

=0onanexamor,evenworse,H

:.632

OneusefulfeatureofChapter4isitsillustrationofhowtorewrite

apopulationmodelsothatitcontainstheparameterofinterestintesting

asinglerestriction.Ifindthisiseasier,boththeoreticallyand

practically,thancomputingvariancesthatcan,insomecases,dependon

numerouscovarianceterms.Theexampleoftestingequalityofthereturn

totwo-andfour-yearcollegesillustratesthebasicmethod,andshows

thattherespecifiedmodelcanhaveausefulinterpretation.Ofcourse,

somestatisticalpackagesnowprovideastandarderrorforlinear

combinationsofestimateswithasimplecommand,andthatshouldbetaught,too.

3/18

stingexampleshavedistributedlagdynamics.Indiscussi

toobtainmorereasonablefunctionalformsfortherespons

mationprocedure.CHAPTER18TEACHINGNOTESSeveralofthe

lysisappropriateforamaster’slevelcourse.Anexplicit

OnecanuseanFtestforsinglelinearrestrictionsonmultiple

parameters,butthisislesstransparentthanattestanddoesnot

immediatelyproducethestandarderrorneededforaconfidenceinterval

orfortestingaone-sidedalternative.Thetrickofrewritingthe

populationmodelisusefulinseveralinstances,includingobtaining

confidenceintervalsforpredictionsinChapter6,aswellasfor

obtainingconfidenceintervalsformarginaleffectsinmodelswith

interactions(alsoinChapter6).

Themajorleaguebaseballplayersalaryexampleillustratesthe

differencebetweenindividualandjointsignificancewhenexplanatory

variables(rbisyrandhrunsyrinthiscase)arehighlycorrelated.Itend

toemphasizetheR-squaredformoftheFstatisticbecause,inpractice,

itisapplicablealargepercentageofthetime,anditismuchmorereadily

computed.Idoregretthatthisexampleisbiasedtowardstudentsin

countrieswherebaseballisplayed.Still,itisoneofthebetter

examplesofmulticollinearitythatIhavecomeacross,andstudentsof

allbackgroundsseemtogetthepoint.

CHAPTER5

TEACHINGNOTES

Chapter5isshort,butitisconceptuallymoredifficultthanthe

earlierchapters,primarilybecauseitrequiressomeknowledgeof

asymptoticpropertiesofestimators.Inclass,Igiveabrief,heuristic

descriptionofconsistencyandasymptoticnormalitybeforestatingthe

consistencyandasymptoticnormalityofOLS.(Conveniently,thesame

assumptionsthatworkforfinitesampleanalysisworkforasymptotic

analysis.)Moreadvancedstudentscanfollowtheproofofconsistency

oftheslopecoefficientinthebivariateregressioncase.SectionE.4

containsafullmatrixtreatmentofasymptoticanalysisappropriatefor

amaster’slevelcourse.

Anexplicitillustrationofwhathappenstostandarderrorsasthe

samplesizegrowsemphasizestheimportanceofhavingalargersample.

IdonotusuallycovertheLMstatisticinafirst-semestercourse,and

Ionlybrieflymentiontheasymptoticefficiencyresult.Withoutfull

useofmatrixalgebracombinedwithlimittheoremsforvectorsand

matrices,itisverydifficulttoproveasymptoticefficiencyofOLS.

Ithinktheconclusionsofthischapterareimportantforstudents

toknow,eventhoughtheymaynotfullygraspthedetails.OnexamsI

usuallyincludetrue-falsetypequestions,withexplanation,totestthestudents’understandingofasymptotics.[Forexample:“Inlarge

sampleswedonothavetoworryaboutomittedvariablebias.”(False).Or“Eveniftheerrortermisnotnormallydistributed,inlargesamples

4/18

evarianceoftheidiosyncraticerror.IthinkExample14.4

hapter15,therankconditiontest).emphasis.)Giventhei

s,noticehowItreattheproblemofincludinganirrelevant

lresultscouldbeskippedentirely,andthatonlylarge-sa

wecanstillcomputeapproximatelyvalidconfidenceintervalsunderthe

Gauss-Markovassumptions.”(True).]

CHAPTER6

TEACHINGNOTES

IcovermostofChapter6,butnotallofthematerialingreatdetail.

IusetheexampleinTable6.1toquicklyrunthroughtheeffectsofdata

scalingontheimportantOLSstatistics.(Studentsshouldalreadyhave

afeelfortheeffectsofdatascalingonthecoefficients,fittingvalues,

andR-squaredbecauseitiscoveredinChapter2.)Atmost,Ibriefly

mentionbetacoefficients;ifstudentshaveaneedforthem,theycanread

thissubsection.

Thefunctionalformmaterialisimportant,andIspendsometimeonmore

complicatedmodelsinvolvinglogarithms,quadratics,andinteractions.

Animportantpointformodelswithquadratics,andespecially

interactions,isthatweneedtoevaluatethepartialeffectat

interestingvaluesoftheexplanatoryvariables.Often,zeroisnotan

interestingvalueforanexplanatoryvariableandiswelloutsidethe

rangeinthesample.UsingthemethodsfromChapter4,itiseasyto

obtainconfidenceintervalsfortheeffectsatinteresting

Asfarasgoodness-of-fit,Ionlyintroducetheadjusted

xvalues.

R-squared,as

Ithinkusingaslewofgoodness-of-fitmeasurestochooseamodelcan

beconfusingtonovices(anddoesnotreflectempiricalpractice).It

isimportanttodiscusshow,ifwefixateonahighR-squared,wemaywindupwithamodelthathasnointerestingceterisparibusinterpretation.

Ioftenhavestudentsandcolleaguesaskifthereisasimplewaytopredictywhenlog(y)hasbeenusedasthedependentvariable,andtoobtaina

goodness-of-fitmeasureforthelog(theusualR-squaredobtainedwhen

y)modelthatcanbecomparedwithyisthedependentvariable.The

methodsdescribedinSection6.4areeasytoimplementand,unlikeotherapproaches,donotrequirenormality.

Thesectiononpredictionandresidualanalysiscontainsseveral

importanttopics,includingconstructingpredictionintervals.Itis

usefultoseehowmuchwiderthepredictionintervalsarethanthe

confidenceintervalfortheconditionalmean.Iusuallydiscusssomeoftheresidual-analysisexamples,astheyhavereal-worldapplicability.

CHAPTER7

TEACHINGNOTES

5/18

placeofkidslt6(withnoyoungchildrenbeingthebasegrou

lygettoteachthemeasurementerrormaterial,althoughth

atoryvariablesthatarenotstrictlyexogenous.Whatthes

tchedpairssampleshavebeenprofitablyusedinrecenteco

Thisisafairlystandardchapteronusingqualitativeinformationin

regressionanalysis,althoughItrytoemphasizeexampleswithpolicy

relevance(andonlycross-sectionalapplicationsareincluded.).

Inallowingfordifferentslopes,itisimportant,asinChapter6,to

appropriatelyinterprettheparametersandtodecidewhethertheyareofdirectinterest.Forexample,inthewageequationwherethereturnto

educationisallowedtodependongender,thecoefficientonthefemale

dummyvariableisthewagedifferentialbetweenwomenandmenatzeroyears

ofeducation.Itisnotsurprisingthatwecannotestimatethisvery

well,norshouldwewantto.Inthisparticularexamplewewoulddrop

theinteractiontermbecauseitisinsignificant,buttheissueof

interpretingtheparameterscanariseinmodelswheretheinteractionterm

issignificant.

IndiscussingtheChowtest,Ithinkitisimportanttodiscusstesting

fordifferencesinslopecoefficientsafterallowingforanintercept

difference.Inmanyapplications,asignificantChowstatisticsimply

indicatesinterceptdifferences.(SeetheexampleinSection7.4on

student-athleteGPAsinthetext.)Fromapracticalperspective,itis

importanttoknowwhetherthepartialeffectsdifferacrossgroupsor

whetheraconstantdifferentialissufficient.

Iadmitthatanunconventionalfeatureofthischapterisitsintroductionofthelinearprobabilitymodel.IcovertheLPMhereforseveralreasons.First,theLPMisbeingusedmoreandmorebecauseitiseasiertointerpret

thanprobitorlogitmodels.Plus,oncetheproperparameterscalings

aredoneforprobitandlogit,theestimatedeffectsareoftensimilar

totheLPMpartialeffectsnearthemeanormedianvaluesofthe

explanatoryvariables.ThetheoreticaldrawbacksoftheLPMareoften

ofsecondaryimportanceinpractice.ComputerExerciseC7.9isagood

onetoillustratethat,evenwithover9,000observations,theLPMcan

deliverfittedvaluesstrictlybetweenzeroandoneforallobservations.IftheLPMisnotcovered,manystudentswillneverknowaboutusing

econometricstoexplainqualitativeoutcomes.Thiswouldbeespecially

unfortunateforstudentswhomightneedtoreadanarticlewhereanLPM

isused,orwhomightwanttoestimateanLPMforatermpaperorsenior

thesis.Oncetheyareintroducedtopurposeandinterpretationofthe

LPM,alongwithitsshortcomings,theycantacklenonlinearmodelson

theirownorinasubsequentcourse.

AusefulmodificationoftheLPMestimatedinequation(7.29)istodrop

kidsge6(becauseitisnotsignificant)andthendefinetwodummy

variables,oneforkidslt6equaltooneandtheotherforkidslt6atleast

two.Thesecanbeincludedinplaceofkidslt6(withnoyoungchildren

beingthebasegroup).Thisallowsadiminishingmarginaleffectinan

LPM.Iwasabitsurprisedwhenadiminishingeffectdidnotmaterialize.

CHAPTER8

6/18

d,orwhomightwanttoestimateanLPMforatermpaperorseni

ndefinetwodummyvariables,oneforkidslt6equaltoonean

ling,Ijustconditiononthevaluesoftheexplanatoryvari

,butitalsoexplicitlyconsidersheteroskedasticityint

TEACHINGNOTES

Thisisagoodplacetoremindstudentsthathomoskedasticityplayedno

roleinshowingthatOLSisunbiasedfortheparametersintheregressionequation.Inaddition,youprobablyshouldmentionthatthereisnothing

wrongwiththeR-squaredoradjustedR-squaredasgoodness-of-fit

measures.ThekeyisthattheseareestimatesofthepopulationR-squared,

1[Var(u)/Var(y)],wherethevariancesaretheunconditional

variancesinthepopulation.Theusualversion,consistentlyestimatethepopulationVar(u|x)=Var(y|x)dependsonx.Oftheusualstandarderrors,tstatistics,

R-squared,andtheadjustedR-squaredwhetherornot

course,heteroskedasticitycauses

andFstatisticstobeinvalid,

eveninlargesamples,withorwithoutnormality.

Byexplicitlystatingthehomoskedasticityassumptionasconditionalon

theexplanatoryvariablesthatappearintheconditionalmean,itisclearthatonlyheteroskedasticitythatdependsontheexplanatoryvariables

inthemodelaffectsthevalidityofstandarderrorsandteststatistics.

TheversionoftheBreusch-Pagantestinthetext,andtheWhitetest,

areideallysuitedfordetectingformsofheteroskedasticitythat

invalidateinferenceobtainedunderhomoskedasticity.If

heteroskedasticitydependsonanexogenousvariablethatdoesnotalso

appearinthemeanequation,thiscanbeexploitedinweightedleast

squaresforefficiency,butonlyrarelyissuchavariableavailable.Onecasewheresuchavariableisavailableiswhenanindividual-level

equationhasbeenaggregated.IdiscussthiscaseinthetextbutIrarely

havetimetoteachit.

AsImentioninthetext,othertraditionaltestsforheteroskedasticity,

suchastheParkandGlejsertests,donotdirectlytestwhatwewant,

oraddtoomanyassumptionsunderthenull.TheGoldfeld-Quandttestonlyworkswhenthereisanaturalwaytoorderthedatabasedononeindependent

variable.Thisisrareinpractice,especiallyforcross-sectional

applications.

Somearguethatweightedleastsquaresestimationisarelic,andisno

longernecessarygiventheavailabilityofheteroskedasticity-robust

standarderrorsandteststatistics.WhileIamsympathetictothis

argument,itpresumesthatwedonotcaremuchaboutefficiency.Even

inlargesamples,theOLSestimatesmaynotbepreciseenoughtolearn

muchaboutthepopulationparameters.Withsubstantial

heteroskedasticitywemightdobetterwithweightedleastsquares,even

iftheweightingfunctionismisspecified.Asdiscussedinthetexton

pages288-289,onecan,andprobablyshould,computerobuststandard

errorsafterweightedleastsquares.Forasymptoticefficiency

comparisons,thesewouldbedirectlycomparabletothe

heteroskedasiticity-robuststandarderrorsforOLS.

7/18

llowsyoutofocusontheinterpretivedifferencesbetween

hExamples9.3and9.4.Thefirstshowsthatcontrollingfor

lesisworthmentioning.Theresultonexogenoussamplesel

edtoallowstudentstochoosetheirowntopics,butthisisd

WeightedleastsquaresestimationoftheLPMisaniceexampleoffeasibleGLS,atleastwhenallfittedvaluesareintheunitinterval.

Interestingly,intheLPMexamplesinthetextandtheLPMcomputer

exercises,theheteroskedasticity-robuststandarderrorsoftendifferby

onlysmallamountsfromtheusualstandarderrors.However,inacouple

ofcasesthedifferencesarenotable,asinComputerExerciseC8.7.

CHAPTER9

TEACHINGNOTES

ThecoverageofRESETinthischapterrecognizesthatitisatestfor

neglectednonlinearities,anditshouldnotbeexpectedtobemorethan

that.(Formally,itcanbeshownthatifanomittedvariablehasa

conditionalmeanthatislinearintheincludedexplanatoryvariables,

RESEThasnoabilitytodetecttheomittedvariable.Interested

mayconsultmychapterinCompaniontoTheoreticalEconometrics

readers,2001,

editedbyBadiBaltagi.)IjustteachstudentstheFstatisticversion

ofthetest.

TheDavidson-MacKinnontestcanbeusefulfordetectingfunctionalform

misspecification,especiallywhenonehasinmindaspecificalternative,

nonnestedmodel.Ithastheadvantageofalwaysbeingaonedegreeof

freedomtest.

Ithinktheproxyvariablematerialisimportant,butthemainpointscanbemadewithExamples9.3and9.4.Thefirstshowsthatcontrollingfor

IQcansubstantiallychangetheestimatedreturntoeducation,andthe

omittedabilitybiasisintheexpecteddirection.Interestingly,

educationandabilitydonotappeartohaveaninteractiveeffect.

Example9.4isaniceexampleofhowcontrollingforapreviousvalueof

thedependentvariableandnonsurveydata

somethingthatisoftenpossiblewithsurvey

cangreatlyaffectapolicyconclusion.Computer

Exercise9.3isalsoagoodillustrationofthismethod.

Irarelygettoteachthemeasurementerrormaterial,althoughthe

attenuationbiasresultforclassicalerrors-in-variablesisworth

mentioning.

Theresultonexogenoussampleselectioniseasytodiscuss,withmore

detailsgiveninChapter17.Theeffectsofoutlierscanbeillustrated

usingtheexamples.Ithinktheinfant

isusefulforillustratinghowasingle

alargeeffectontheOLSestimates.

mortalityexample,Example9.10,influentialobservationcanhave

Withthegrowingimportanceofleastabsolutedeviations,itmakessensetoatleastdiscussthemeritsofLAD,atleastinmoreadvancedcourses.ComputerExercise9.9isagoodexampletoshowhowmeanandmedianeffectscanbeverydifferent,eventhoughtheremaynotbe“outliers”inthe

usualsense.

8/18

pplicablealargepercentageofthetime,anditismuchmore

hExamples9.3and9.4.Thefirstshowsthatcontrollingfor

mputerExerciseC17.3.]Poissonregressionwithanexpone

htforward.Unfortunately,atthebeginninglevel(andeve

CHAPTER10

TEACHINGNOTES

Becauseofitsrealismanditscareinstatingassumptions,thischapter

putsasomewhatheavierburdenontheinstructorandstudentthan

traditionaltreatmentsoftimeseriesregression.Nevertheless,Ithink

itisworthit.Itisimportantthatstudentslearnthatthereare

potentialpitfallsinherentinusingregressionwithtimeseriesdatathat

arenotpresentforcross-sectionalapplications.Trends,seasonality,

andhighpersistenceareubiquitousintimeseriesdata.Bythistime,

studentsshouldhaveafirmgraspofmultipleregressionmechanicsand

inference,andsoyoucanfocusonthosefeaturesthatmaketimeseries

applicationsdifferentfromcross-sectionalones.

Ithinkitisusefultodiscussstaticandfinitedistributedlagmodels

atthesametime,astheseatleasthaveashotatsatisfyingthe

Gauss-Markovassumptions.Manyinterestingexampleshavedistributedlagdynamics.IndiscussingthetimeseriesversionsoftheCLM

assumptions,Irelymostlyonintuition.Theiseasytodiscussintermsoffeedback.It

notionofstrictexogeneityisalsoprettyapparentthat,

inmanyapplications,therearelikelytobesomeexplanatoryvariables

thatarenotstrictlyexogenous.Whatthestudentshouldknowisthat,

toconcludethatOLSisunbiasedasopposedtoconsistentweneed

toassumeaverystrongformofexogeneityoftheregressors.Chapter

11showsthatonlycontemporaneousexogeneityisneededforconsistency.Althoughthetextiscarefulinstatingtheassumptions,inclass,afterdiscussingstrictexogeneity,IleavetheconditioningonXimplicit,especiallywhenIdiscussthenoserialcorrelationassumption.Asthis

isanewassumptionIspendsometimeonit.(Ialsodiscusswhywedid

notneeditforrandomsampling.)

OncetheunbiasednessofOLS,theGauss-Markovtheorem,andthesamplingdistributionsundertheclassicallinearmodelassumptionshavebeen

coveredwhichcanbedoneratherquicklyIfocusonapplications.

Fortunately,thestudentsalreadyknowaboutlogarithmsanddummy

variables.Itreatindexnumbersinthischapterbecausetheyarisein

manytimeseriesexamples.

Anovelfeatureofthetextisthediscussionofhowtocompute

goodness-of-fitmeasureswithatrendingorseasonaldependentvariable.Whiledetrendingordeseasonalizingyishardlyperfect(anddoesnotworkwithintegratedprocesses),itisbetterthansimplyreportingthevery

highR-squaredsthatoftencomewithtimeseriesregressionswithtrendingvariables.

CHAPTER11

9/18

rmoreexplanatoryvariablesarehighlycorrelatedinthes

tethepopulationwell-definedunderstationarity).Equa

icient,perhapsafterdetrending.TheexamplesinSection

delprovidesmorerealistictousenonefunctionalformsfo

TEACHINGNOTES

Muchofthematerialinthischapterisusuallypostponed,ornotcoveredatall,inanintroductorycourse.However,asChapter10indicates,theset