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NickBloom,AppliedEconometrics,Winter2010APPLIEDECONOMETRICSLecture1-IdentificationNickBloom,AppliedEconometrics,Wint

er2010DefiningIdentificationExperimentsNaturalExperimentsInstrumentalvariablesEconometricIdentificationNickBloom,Appli

edEconometrics,Winter2010WHATISIDENTIFICATION?Graduateandprofessionaleconomicsmainlyconcernedwithidentificationinempir

icalworkConceptofunderstandingwhatisthecausalrelationshipbehindempiricalresults:Thisisessentialforlearningfromempiricalresear

ch–Time-seriesexample:InterestratesandGDP–Cross-sectionexample:Management&ProductivityNickBloom,AppliedEconometrics,Winter2010WHATISDRIVINGTHIS

RELATIONSHIP?05101520Federalfundsrate-.15-.1-.050.05.1196019701980199020002010ym...DetrendedlogindustrialoutputFederalfundsrateCorrel

ation=0.233NickBloom,AppliedEconometrics,Winter2010REASONSFORCORRELATIONImaginevariablesYtandXtarecorrelated:Therecan

bethreereasonsforthis,whicharenotmutuallyexclusive:•Cause:ChangesinXtdrivechangesinYt•ReverseCause:ChangesinYtdrivechange

sinXt•Correlatedvariable:ChangesinZtdrivesXtandYtNickBloom,AppliedEconometrics,Winter2010WHATISDRIVINGTH

ISRELATIONSHIP?246812345ManagementNickBloom,AppliedEconometrics,Winter2010SOHOWDOWEGETIDENTIFICATIONFourbroadapproac

hesforidentification•Experiments–yougeneratethevariation•NaturalExperiments–youknowwhatgeneratedthevariation•Instrumentalvariables–youhaveav

ariablethatcanprovideyouvariation•EconometricIdentification–yourelyon(testable)econometricassumptionsforidentificationNickBloom,AppliedEco

nometrics,Winter2010DefiningIdentificationExperimentsNaturalExperimentsInstrumentalvariablesEconometricIdentificationNi

ckBloom,AppliedEconometrics,Winter2010EXPERIMENTS(1)ExperimentsaretotallystandardinScience&MedicineFor

example:•Setupatreatmentandcontrolgroupforanewdrug,makingsurethesearecomparable(orrandomlyselected)•Ensurethesample

sizesarelargeenoughtoobtainstatisticalsignificance•Ensuretheexperimentisunbiased–i.e.thedrugandtheplac

eboareassimilaraspossible•RuntheexperimentNickBloom,AppliedEconometrics,Winter2010EXPERIMENTS(2)Economistsli

ketousethelanguageofScienceForexampletheUKconsideredintroducinganEducationMaintenanceAllowance,topaykids

tostayonatschool.Butwanttotestfirsttoseeifthiswouldthiswork.•Setupatreatmentandcontrolregionstomatchtheseincharacteristics•Selectenou

ghregionstogetlargesamplesizes•Observeagentsactionstoevaluateimpact(ratherthanselfreportedoutcomes)•Runth

eexperimentNickBloom,AppliedEconometrics,Winter2010EXPERIMENTS(3)Experimentsarerareineconomicsbecausetheyar

eexpensive,althoughtheybecomingmorepopular:Typicalareasforrunningexperimentsinclude:•Developmenteconomics–che

apertorunexperimentsinthethirdWorld(watersupplyormanagementpractices)•Consumereconomics–smallstakesexperimentsthatareeasytoa

dminister(creditcards)•Individualbusinessapplications–firmscanfinancethese(retailstorelayout)Butsomefiel

dswillneverhaveexperiment–forexamplemacroeconomicsNickBloom,AppliedEconometrics,Winter2010DefiningIdentificationExperimen

tsNaturalExperimentsInstrumentalvariablesEconometricIdentificationNickBloom,AppliedEconometrics,Winter2010NAT

URALEXPERIMENTS(1)Naturalexperimentsarewherefortunatesituationscreategoodunderlyingidentification:Typicallyseveralapproaches:•Taxe.g.Response

ofR&Dtothecostofcapital(Bloom,Griffith&VanReenen,2002),(ChettyandSaez,2003)•Discontinuity(seeover)•Shock-financialcri

sisandKibutzim(Abramitzky,2007)•Disasters-EthiopianJewsairlift(Gould,Levy&Passerman,2004)NickBloom,AppliedEconometrics,

Winter2010NATURALEXPERIMENTS(2)NaturalexperimentsarealmostthehollygrailofmodernappliedeconomicsIntheabsenceoftrueexperimentst

heyprovidethebestwaytoprovidesimpleidentificationCoupleofstandardwaytousenaturalexperimentsinpractice–Di

scountinunityanalysisand/or–DifferenceindifferencesNickBloom,AppliedEconometrics,Winter2010DISCONTINUITYANALYSIS–example1RegionA(notax)

RegionB(50%tax)Imaginea50%taxisleviedoninvestmentintherichcoastalregionAbutnotinthepoorinlandregionB.Ifyo

usawthegraphbelowcouldyousaywhattheimpactofthetaxisoninvestment?InvestmentEstimatedimpactofthetaxNickBloom,Appli

edEconometrics,Winter2010DISCONTINUITYANALYSIS–example2ImpactoftelephonesonpriceoffishinKerala(India)NickBloom,AppliedEconometrics,Winter2010DIFF

ERNCESINDIFFERENCESt0denotespre-treatmentperiodsforwhichdataareavailablet1denotespost-treatmentperiodsforwhichdataa

reavailableAveragechangeinoutcome(preandpost-treatment)fortreatmentgroupminusaveragechangeinoutcomeforcontrolgroup()()Con

troltControltTreattTreattRRRR0101Impact−−−=Identificationcomesfromthedifferentialchangebetweenthetwogroups

preandpost-treatment–differenceoutunobservedfixedeffects–differenceoutcommontimeeffectsKeyassumptionofcommontimeeffectsforthetwogro

upsNickBloom,AppliedEconometrics,Winter2010POLICYEXAMPLEOF“DIFF-IN-DIFF”•SmallfirmsR&Dtaxcreditintroducedin2000forfirmswit

h250orlessemployees•Socouldlookatfirmsbeforeandaftercredit–Butotherthingsalsochanging(2000peakofdotcom

boometc…)–Soneedtosetupacontrolgroupofcompanieslooksimilartofirmsgettingthecreditexceptdon’tgetthecr

edit•Comparefirmswith240employeestothosewith260•Thisisdouble-diff(ordiffindiffs)tocomparedifferences:–Betweenpreandpost

thecredit(1999versus2001)–Betweenthetreated(240employees)anduntreatedfirms(260employees)NickBloom,Appli

edEconometrics,Winter2010DefiningIdentificationExperimentsNaturalExperimentsInstrumentalvariablesEconometricIde

ntificationNickBloom,AppliedEconometrics,Winter2010INSTRUMENTALVARIABLES(1)Wanttolookateffectofschooling(Si)onearnings(Yi)Assumethetruem

odelis:Yi=α+β1Si+β2Ai+viwhereAiis(unobserved)abilitywhichispositivelycorrelatedwithSi,andviisrandomindependentnoiseWhatwouldhappenifweestimatedthe

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

gequationbelowinOrdinaryLeastSquaresY=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”(correlatedwith

theerror)---------------------NickBloom,AppliedEconometrics,Winter2010INSTRUMENTALVARIABLES(3)Thus,estimationofthefollowin

gwouldbebiased:Yi=a+b1Si+eibecauseSiandeiarecorrelatedaseiisafunctionofabilityE[b1]=E[Y’S]/E[S’S]=E[(β1Si+β2Ai+vi)’S]/E[S’S]=β1+E[(β2Ai+v

i)’S]/E[S’S]=β1+β2E[Ai’S]/E[S’S]>β1Sobecauseignoreability,whichiscorrelatedwithschooling,weoverestimatetheimpactofschoolingonearningsNickBl

oom,AppliedEconometrics,Winter2010INSTRUMENTALVARIABLES(4)Imaginewehadavariable–calledaninstrumentZ–thatwascorrelatedwithschoolingbutn

otability.WecouldthenusethistoexplainvariationinschoolingasitisnotcorrelatedwithabilityOneexampleofthiswouldbeift

heGovernmentpaideveryonebornonevendaystostayinschoolThen“bornonanevenday”wouldbeaninstrumentforschooling–correlatedwithschoolingbutnotabilityIn

practiceinstrumentsareoftenhardtofindNickBloom,AppliedEconometrics,Winter2010INSTRUMENTALVARIABLES(5)AssumethatZiscorrelat

edwithSbutnotA.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.Allyouneedtofindisavariablethatonlyaffectsyourdependen

tvariableviathevariableyouareinterestedinNickBloom,AppliedEconometrics,Winter2010INSTRUMENTALVARIABLESAnyquestionsonthis?Imagineyouwan

tedtoevaluatetheimpactofcropyieldsonfarmersbehavior–cananyonesuggestagoodinstrumentNickBloom,AppliedEconometrics,Winter2010DefiningId

entificationExperimentsNaturalExperimentsInstrumentalvariablesEconometricIdentificationNickBloom,AppliedEconometrics,Winter2010ECONOMETRICIDENTIFICAT

IONAnotherwaytoobtainidentificationistrytomodeleverything•Forexample,weclaimweknowhowabilityiscorrelatedwithschoolingandsomodelthewholesystemTh

eproblemwiththisis:•Itisalotmorecomplicated•ItrequiresstrongassumptionsThus,thisisusuallyonlyundertakenwhenthereisnoobviousinstrumentorna

turalexperimentNickBloom,AppliedEconometrics,Winter2010SUMMARYIdentification–understandingthecausalityinaregression–isessentialforgeneratingmeaningfu

lresultsTherearearangeofapproaches–buttheyallneedsomeprioreconomicthought(i.e.istheiranaturalexperiment?)