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NickBloom,AppliedEconometrics,Winter2010APPLIEDECONOMETRICSLecture1-IdentificationNickBloom,AppliedEconometrics,Winter2010DefiningIdenti

ficationExperimentsNaturalExperimentsInstrumentalvariablesEconometricIdentificationNickBloom,AppliedEconometrics,

Winter2010WHATISIDENTIFICATION?GraduateandprofessionaleconomicsmainlyconcernedwithidentificationinempiricalworkConc

eptofunderstandingwhatisthecausalrelationshipbehindempiricalresults:Thisisessentialforlearningfromempiricalresearch–Time-seriesexa

mple:InterestratesandGDP–Cross-sectionexample:Management&ProductivityNickBloom,AppliedEconometrics,Winter2010WHATISDRIVINGTHISRELATIONSHIP

?05101520Federalfundsrate-.15-.1-.050.05.1196019701980199020002010ym...DetrendedlogindustrialoutputFederalfundsrateCorrelation=0.233NickB

loom,AppliedEconometrics,Winter2010REASONSFORCORRELATIONImaginevariablesYtandXtarecorrelated:Therecanbethreereasonsforthis,whicharenotmutuallyexcl

usive:•Cause:ChangesinXtdrivechangesinYt•ReverseCause:ChangesinYtdrivechangesinXt•Correlatedvariable:Changesin

ZtdrivesXtandYtNickBloom,AppliedEconometrics,Winter2010WHATISDRIVINGTHISRELATIONSHIP?246812345ManagementNickB

loom,AppliedEconometrics,Winter2010SOHOWDOWEGETIDENTIFICATIONFourbroadapproachesforidentification•Experiments–yougeneratethevariation•NaturalExperi

ments–youknowwhatgeneratedthevariation•Instrumentalvariables–youhaveavariablethatcanprovideyouvariation•EconometricIdentification–yourelyon

(testable)econometricassumptionsforidentificationNickBloom,AppliedEconometrics,Winter2010DefiningIdentificatio

nExperimentsNaturalExperimentsInstrumentalvariablesEconometricIdentificationNickBloom,AppliedEconometrics,Winter2010EXPERIMENTS(1)Experimentsa

retotallystandardinScience&MedicineForexample:•Setupatreatmentandcontrolgroupforanewdrug,makingsurethese

arecomparable(orrandomlyselected)•Ensurethesamplesizesarelargeenoughtoobtainstatisticalsignificance•Ensuretheexperimentisunbiased–i.e.thedrugand

theplaceboareassimilaraspossible•RuntheexperimentNickBloom,AppliedEconometrics,Winter2010EXPERIMENTS(2)EconomistsliketousethelanguageofSci

enceForexampletheUKconsideredintroducinganEducationMaintenanceAllowance,topaykidstostayonatschool.Butwanttotestfirsttoseeifthiswoul

dthiswork.•Setupatreatmentandcontrolregionstomatchtheseincharacteristics•Selectenoughregionstogetlargesamplesiz

es•Observeagentsactionstoevaluateimpact(ratherthanselfreportedoutcomes)•RuntheexperimentNickBloom,Applied

Econometrics,Winter2010EXPERIMENTS(3)Experimentsarerareineconomicsbecausetheyareexpensive,althoughtheybecomingmorepopular:Typicalareasforrunninge

xperimentsinclude:•Developmenteconomics–cheapertorunexperimentsinthethirdWorld(watersupplyormanagementpract

ices)•Consumereconomics–smallstakesexperimentsthatareeasytoadminister(creditcards)•Individualbusinessapplications–firmscanfi

nancethese(retailstorelayout)Butsomefieldswillneverhaveexperiment–forexamplemacroeconomicsNickBloom,AppliedEconometrics,Winter

2010DefiningIdentificationExperimentsNaturalExperimentsInstrumentalvariablesEconometricIdentificationNickBloom,AppliedEconometrics,Win

ter2010NATURALEXPERIMENTS(1)Naturalexperimentsarewherefortunatesituationscreategoodunderlyingidentification:Typicallyseveralapproaches:•

Taxe.g.ResponseofR&Dtothecostofcapital(Bloom,Griffith&VanReenen,2002),(ChettyandSaez,2003)•Discontinuity(seeover)•Sh

ock-financialcrisisandKibutzim(Abramitzky,2007)•Disasters-EthiopianJewsairlift(Gould,Levy&Passerman,2

004)NickBloom,AppliedEconometrics,Winter2010NATURALEXPERIMENTS(2)Naturalexperimentsarealmostthehollygrailofmoderna

ppliedeconomicsIntheabsenceoftrueexperimentstheyprovidethebestwaytoprovidesimpleidentificationCoupleofstandardwaytousenaturalexperi

mentsinpractice–Discountinunityanalysisand/or–DifferenceindifferencesNickBloom,AppliedEconometrics,Wint

er2010DISCONTINUITYANALYSIS–example1RegionA(notax)RegionB(50%tax)Imaginea50%taxisleviedoninvestmentintherichcoastalregionAbutn

otinthepoorinlandregionB.Ifyousawthegraphbelowcouldyousaywhattheimpactofthetaxisoninvestment?InvestmentEstimatedim

pactofthetaxNickBloom,AppliedEconometrics,Winter2010DISCONTINUITYANALYSIS–example2ImpactoftelephonesonpriceoffishinK

erala(India)NickBloom,AppliedEconometrics,Winter2010DIFFERNCESINDIFFERENCESt0denotespre-treatmentperiod

sforwhichdataareavailablet1denotespost-treatmentperiodsforwhichdataareavailableAveragechangeinoutcome(prea

ndpost-treatment)fortreatmentgroupminusaveragechangeinoutcomeforcontrolgroup()()ControltControltTreattTreattRRRR0101Impact−−−=Identificationcomes

fromthedifferentialchangebetweenthetwogroupspreandpost-treatment–differenceoutunobservedfixedeffects–differenceoutcommontimee

ffectsKeyassumptionofcommontimeeffectsforthetwogroupsNickBloom,AppliedEconometrics,Winter2010POLICYEXAMPLEOF“DIFF-IN-DIFF”•SmallfirmsR&Dtaxcr

editintroducedin2000forfirmswith250orlessemployees•Socouldlookatfirmsbeforeandaftercredit–Butotherthingsalsochanging(20

00peakofdotcomboometc…)–Soneedtosetupacontrolgroupofcompanieslooksimilartofirmsgettingthecreditexceptdon’tgetthecredit•Comparefirmswith240employ

eestothosewith260•Thisisdouble-diff(ordiffindiffs)tocomparedifferences:–Betweenpreandpostthecredit(1999ve

rsus2001)–Betweenthetreated(240employees)anduntreatedfirms(260employees)NickBloom,AppliedEconometrics,Winter2010Def

iningIdentificationExperimentsNaturalExperimentsInstrumentalvariablesEconometricIdentificationNickBloom,AppliedEconometri

cs,Winter2010INSTRUMENTALVARIABLES(1)Wanttolookateffectofschooling(Si)onearnings(Yi)Assumethetruemodelis:Yi=α+β1Si+β2Ai+viwhereAiis(unobserve

d)abilitywhichispositivelycorrelatedwithSi,andviisrandomindependentnoiseWhatwouldhappenifweestimatedthefollowin

ginstead?Yi=a+b1Si+eiwhereei=β2Ai+viNickBloom,AppliedEconometrics,Winter2010INSTRUMENTALVARIABLES(2)-

-----BackgroundAssumeestimatingequationbelowinOrdinaryLeastSquaresY=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)------

---------------NickBloom,AppliedEconometrics,Winter2010INSTRUMENTALVARIABLES(3)Thus,estimationofthefollowingwouldbebiased:Yi

=a+b1Si+eibecauseSiandeiarecorrelatedaseiisafunctionofabilityE[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,weoverestimatetheimpactofschoolingonearningsNickBloom,AppliedEconometrics,Win

ter2010INSTRUMENTALVARIABLES(4)Imaginewehadavariable–calledaninstrumentZ–thatwascorrelatedwithschoolingbut

notability.WecouldthenusethistoexplainvariationinschoolingasitisnotcorrelatedwithabilityOneexampleofthiswouldbeiftheGovernmentpaidev

eryonebornonevendaystostayinschoolThen“bornonanevenday”wouldbeaninstrumentforschooling–correlatedwithsc

hoolingbutnotabilityInpracticeinstrumentsareoftenhardtofindNickBloom,AppliedEconometrics,Winter2010INSTRUMENTALVARIABLES(5)AssumethatZiscor

relatedwithSbutnotA.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.Allyouneedtofindisavariablethatonlyaffectsyourdependent

variableviathevariableyouareinterestedinNickBloom,AppliedEconometrics,Winter2010INSTRUMENTALVARIABLESAnyquest

ionsonthis?Imagineyouwantedtoevaluatetheimpactofcropyieldsonfarmersbehavior–cananyonesuggestagoodinstrumentNickBloo

m,AppliedEconometrics,Winter2010DefiningIdentificationExperimentsNaturalExperimentsInstrumentalvariabl

esEconometricIdentificationNickBloom,AppliedEconometrics,Winter2010ECONOMETRICIDENTIFICATIONAnotherwaytoobtainidentificationistrytomodeleverythi

ng•Forexample,weclaimweknowhowabilityiscorrelatedwithschoolingandsomodelthewholesystemTheproblemwiththisis:•Itisalotmorecomplicated•I

trequiresstrongassumptionsThus,thisisusuallyonlyundertakenwhenthereisnoobviousinstrumentornaturalexperimentNickBloom,AppliedEconometrics,Win

ter2010SUMMARYIdentification–understandingthecausalityinaregression–isessentialforgeneratingmeaningful

resultsTherearearangeofapproaches–buttheyallneedsomeprioreconomicthought(i.e.istheiranaturalexperiment?)