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1CHAPTER1TEACHINGNOTESYouhavesubstantiallatitudeaboutwhattoemphasizeinChapter1.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).CHAPTER2TEACHINGNOTESThisisthechapterwhereIexpectstudentstofollowmost,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.CHAPTER32TEACHINGNOTESForundergraduates,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,Iputaspecialcaseo