斯坦福大學計量經(jīng)濟學應用lecture1

APPLIEDECONOMETRICS

Lecture1-IdentificationDefiningIdentificationExperimentsNaturalExperimentsInstrumentalvariablesEconometricIdentificationWHATISIDENTIFICATION?GraduateandprofessionaleconomicsmainlyconcernedwithidentificationinempiricalworkConceptofunderstandingwhatisthecausalrelationshipbehindempiricalresults:ThisisessentialforlearningfromempiricalresearchTime-seriesexample:InterestratesandGDPCross-sectionexample:Management&ProductivityWHATISDRIVINGTHISRELATIONSHIP?Correlation=0.233REASONSFORCORRELATIONImaginevariablesYtandXtarecorrelated:Therecanbethreereasonsforthis,whicharenotmutuallyexclusive:Cause:ChangesinXtdrivechangesinYtReverseCause:ChangesinYtdrivechangesinXtCorrelatedvariable:ChangesinZtdrivesXtandYtWHATISDRIVINGTHISRELATIONSHIP?SOHOWDOWEGETIDENTIFICATIONFourbroadapproachesforidentificationExperiments–yougeneratethevariationNaturalExperiments–youknowwhatgeneratedthevariationInstrumentalvariables–youhaveavariablethatcanprovideyouvariationEconometricIdentification–yourelyon(testable)econometricassumptionsforidentificationDefiningIdentificationExperimentsNaturalExperimentsInstrumentalvariablesEconometricIdentificationEXPERIMENTS(1)ExperimentsaretotallystandardinScience&MedicineForexample:Setupatreatmentandcontrolgroupforanewdrug,makingsurethesearecomparable(orrandomlyselected)EnsurethesamplesizesarelargeenoughtoobtainstatisticalsignificanceEnsuretheexperimentisunbiased–i.e.thedrugandtheplaceboareassimilaraspossibleRuntheexperimentEXPERIMENTS(2)EconomistsliketousethelanguageofScienceForexampletheUKconsideredintroducinganEducationMaintenanceAllowance,topaykidstostayonatschool.Butwanttotestfirsttoseeifthiswouldthiswork.SetupatreatmentandcontrolregionstomatchtheseincharacteristicsSelectenoughregionstogetlargesamplesizesObserveagentsactionstoevaluateimpact(ratherthanselfreportedoutcomes)RuntheexperimentEXPERIMENTS(3)Experimentsarerareineconomicsbecausetheyareexpensive,althoughtheybecomingmorepopular:Typicalareasforrunningexperimentsinclude:Developmenteconomics–cheapertorunexperimentsinthethirdWorld(watersupplyormanagementpractices)Consumereconomics–smallstakesexperimentsthatareeasytoadminister(creditcards)Individualbusinessapplications–firmscanfinancethese(retailstorelayout)Butsomefieldswillneverhaveexperiment–forexamplemacroeconomicsDefiningIdentificationExperimentsNaturalExperimentsInstrumentalvariablesEconometricIdentificationNATURALEXPERIMENTS(1)Naturalexperimentsarewherefortunatesituationscreategoodunderlyingidentification:Typicallyseveralapproaches:Taxe.g.ResponseofR&Dtothecostofcapital(Bloom,Griffith&VanReenen,2002),(ChettyandSaez,2003)Discontinuity(seeover)Shock-financialcrisisandKibutzim(Abramitzky,2007)Disasters-EthiopianJewsairlift(Gould,Levy&Passerman,2004)NATURALEXPERIMENTS(2)NaturalexperimentsarealmostthehollygrailofmodernappliedeconomicsIntheabsenceoftrueexperimentstheyprovidethebestwaytoprovidesimpleidentificationCoupleofstandardwaytousenaturalexperimentsinpracticeDiscountinunityanalysisand/orDifferenceindifferencesDISCONTINUITYANALYSIS–example1RegionA

(notax)RegionB

(50%tax)Imaginea50%taxisleviedoninvestmentintherichcoastalregionAbutnotinthepoorinlandregionB.Ifyousawthegraphbelowcouldyousaywhattheimpactofthetaxisoninvestment?InvestmentEstimatedimpactofthetaxDISCONTINUITYANALYSIS–example2ImpactoftelephonesonpriceoffishinKerala(India)DIFFERNCESINDIFFERENCESt0denotespre-treatmentperiodsforwhichdataareavailablet1denotespost-treatmentperiodsforwhichdataareavailableAveragechangeinoutcome(preandpost-treatment)fortreatmentgroupminusaveragechangeinoutcomeforcontrolgroupIdentificationcomesfromthedifferentialchangebetweenthetwogroupspreandpost-treatmentdifferenceoutunobservedfixedeffectsdifferenceoutcommontimeeffectsKeyassumptionofcommontimeeffectsforthetwogroupsPOLICYEXAMPLEOF“DIFF-IN-DIFF”SmallfirmsR&Dtaxcreditintroducedin2000forfirmswith250orlessemployeesSocouldlookatfirmsbeforeandaftercreditButotherthingsalsochanging(2000peakofdotcomboometc…)Soneedtosetupacontrolgroupofcompanieslooksimilartofirmsgettingthecreditexceptdon’tgetthecreditComparefirmswith240employeestothosewith260Thisisdouble-diff(ordiffindiffs)tocomparedifferences:Betweenpreandpostthecredit(1999versus2001)Betweenthetreated(240employees)anduntreatedfirms(260employees)DefiningIdentificationExperimentsNaturalExperimentsInstrumentalvariablesEconometricIdentificationINSTRUMENTALVARIABLES(1)Wanttolookateffectofschooling(Si)onearnings(Yi)Assumethetruemodelis: Yi=α+β1Si+β2Ai+viwhereAiis(unobserved)abilitywhichispositivelycorrelatedwithSi,andviisrandomindependentnoiseWhatwouldhappenifweestimatedthefollowinginstead? Yi=a+b1Si+eiwhereei=β2Ai+viINSTRUMENTALVARIABLES(2)------BackgroundAssumeestimatingequationbelowinOrdinaryLeastSquares Y=α+βX+eTheestimateofβ =E(Y’X)/E(X’X) =E((βX+e)’X)/E(X’X) =β+E(e’X)/E(X’X) =βonlyifeandXareindependentButifeandXarecorrelatedthentheestimatedisbiased,andXiscalled“endogenous”(correlatedwiththeerror)---------------------INSTRUMENTALVARIABLES(3)Thus,estimationofthefollowingwouldbebiased: Yi=a+b1Si+eibecauseSiandeiarecorrelatedaseiisafunctionofability E[b1]

=E[Y’S]/E[S’S] =E[(β1Si+β2Ai+vi)’S]/E[S’S] =β1+E[(β2Ai+vi)’S]/E[S’S] =β1+β2E[Ai’S]/E[S’S] >β1Sobecauseignoreability,whichiscorrelatedwithschooling,weoverestimatetheimpactofschoolingonearningsINSTRUMENTALVARIABLES(4)Imaginewehadavariable–calledaninstrumentZ–thatwascorrelatedwithschoolingbutnotability.WecouldthenusethistoexplainvariationinschoolingasitisnotcorrelatedwithabilityOneexampleofthiswouldbeiftheGovernmentpaideveryonebornonevendaystostayinschoolThen“bornonanevenday”wouldbeaninstrumentforschooling–correlatedwithschoolingbutnotabilityInpracticeinstrumentsareoftenhardtofindINSTRUMENTALVARIABLES(5)AssumethatZiscorrelatedwithSbutnotA.ThenthefollowinginstrumentalvariableestimatorisconsistentE[b1IV] =E[Y’Z]/E[S’Z] =E[(β1Si+β2Ai+vi)’Z]/E[S’Z] =E[β1Si’Z+β2Ai’Z

+vi’Z]/E[S’Z] =β1+(β2E[Ai’S]+E[vi’Z])/E[S’Z] =β1Statawillcalculatethisforyou.AllyouneedtofindisavariablethatonlyaffectsyourdependentvariableviathevariableyouareinterestedinINSTRUMENTALVARIABLESAnyquestionsonthis?Imagine