诺贝尔经济学奖得主Robert Engle访谈（计量经济学）.pdf 21页

Diebold,F.X.(2003),"TheETInterview:ProfessorRobertF.Engle,"EconometricTheory,19,1159-1193.TheETInterview:ProfessorRobertF.Engle1FrancisX.DieboldUniversityofPennsylvaniaandNBERJanuary2003Inthepastthirty-fiveyears,time-serieseconometricsdevelopedfrominfancytorelativematurity.AlargepartofthatdevelopmentisduetoRobertF.Engle,whoseworkisdistinguishedbyexceptionalcreativityintheempiricalmodelingofdynamiceconomicandfinancialphenomena.Engle’sfootstepsrangewidely,fromearlyworkonband-spectralregression,testing,andexogeneity,throughmorerecentworkoncointegration,ARCHmodels,andultra-high-frequencyfinancialassetreturndynamics.Theboomingfieldoffinancialeconometrics,whichdidnotexisttwenty-fiveyearsago,isbuiltinlargepartonthevolatilitymodelspioneeredbyEngle,andtheirmanyvariationsandextensions,whichhavefoundwidespreadapplicationinfinancialriskmanagement,assetpricingandassetallocation.(Webeganinfall1998atSpruceinChicago,thenightbeforetheannualNBER/NSFTimeSeriesSeminar,continuedinfall2000atTablainNewYork,continuedagaininsummer2001attheConferenceonMarketMicrostructureandHigh-FrequencyDatainFinance,SandbjergEstate,Denmark,andwrappedupbytelephoneinJanuary2003.)I.Cornell:FromPhysicstoEconomicsFXD:Let’sgobacktoyourgraduatestudentdays.IrecallthatyouwereastudentatCornell.Couldyoutellusabitaboutthat?RFE:Itdependsonhowfarbackyouwanttogo.WhenIwenttoCornellIwentasaphysicist.Icouldn’tdecidewheretogountiltheverylastminute.Infact–andI’msurethisistotallyirrelevanttothisinterview–ItelephonedBerkeleytoaccepttheirinvitationtogotoGraduateSchoolinphysicsthere,becauseBerkeleywasBerkeley.Butnooneanswered;itwaslunchtimeorsomething.SointhemeantimeIwentoverandtalkedtomyadvisoratWilliamswhosaid“YoushouldgotoCornellinstead.”So,whenBerkeleycalledback,IsaidIjustwascheckingontheapplication,andthenIacceptedCornell.FXD:BothBerkeleyandCornellwerephysicspowerhouses.RFE:Yes.ButIwasalittleambivalent,Iguess,aboutphysics.I’dalwaysfiguredIwouldbeaphysicistandsoIwasapartofateamstudyingsuper-conductivity.WehadabiglabdowninthebasementofRockefellerHallandIspentmyfirstyearatCornellhunkereddowntherewithliquidnitrogen.Whenspringcame,IdecidedthatIhadtogetoutofthere.SoIwentoverandtalkedtotheChairmanoftheEconomicsDepartment,amannamedAlfredKahn,ofwhomIhavealwaysbeenveryfondsincethattime.1Fortheircheerfulandeffectiveassistanceintranscribingthisinterview,Iwouldliketothank(withoutimplicating)SeanCampbell,MicheleSouliandClaraVega. FXD:WasthattheairlinederegulationKahn?RFE:Exactly.Ihadmanyfriendswhohadswitchedintoeconomics,soIhadjustwonderedwhetheritwouldbepossible,andhesaid,“Well,we’vejustbeenturneddownforoneofourgraduatefellowships.Doyouwantit?”andIsattheresortofinshockandsaidyes.FXD:Hadyouthoughtaboutdoingeconomicsinthebackofyourmindatsomepoint?Orwereyoustraightaheadinphysics?RFE:Iwasstraightaheadphysics.Infact,Ihadonlytakenoneeconomicscourseasanundergraduate,inmysenioryear.So,itwasalittlebitofasurprisethatIdidit,butitwasmadeveryeasyforme.Istartedofftakingundergraduateeconomicscoursestherestofthatspring,andsimultaneouslyIfinishedmymaster’sthesisinphysics.Istartedthegraduateprogramineconomicsthefollowingfall.FXD:Therearealotofgoodeconometricianswithphysicsbackgrounds:you,JoelHorowitz,JimStock,GlennRudebusch,JohnCochrane,SteveCosslett,DanMcFadden,...RFE:Yes.AndJereBehrman.FXD:Ididn’tknowthat,andheisofcoursemycolleagueatPenn!RFE:HewastwoyearsaheadofmeatWilliamsCollegeandhadgonewithaphysicsundergraduatedegreedirectlytoMIT.SothatwasoneofthereasonsIknewitcouldbedone.Anyway,Ithinkitisagreatcombinationbecausephysicistsarecontinuallyworriedaboutintegratingtheoryanddata,andthat’swhyIthinkphysiciststendtomakegoodeconometricians.That’swhateconometriciansdo.FXD:Ihavealwaysfeltthatmanyofthesciencesaredefactoorganizedintohostilecampsofempiricistsandtheorists,withmostmembersofeachcampsurprisinglyunawarethatit’sultimatelytheinterplayanddisciplineengenderedbythecross-campcompetitionthatfuelsscientificprogress.RFE:Ithinktheoristsandempiricistsactuallyuseeachotherinphysicsmorethanmightbetrueineconomics.AtCornell,therewereacoupleoftheoriststhatwouldwanderaroundthebasementtoseewhattheexperimentalistswerediscovering.FXD:Whyaretheexperimentalistsalwaysinthebasement?Thatseemstobetrueacrossalldisciplines.Infact,despiteyourmovefromphysicstoeconomics,you’veneverleftthebasement!RFE:(Laughing)that’swhatIwasgettingat!FXD:Butseriouslynow,youwoundupworkingwithapioneeringeconometrician,T.C.Liu.Canyoutellusaboutthat?Howwereyoutrainedbyhim?RFE:Well,itwasveryinteresting,becauseTaChungwasarealdynamo.TheyearwhenIwastakingeconometricshewasinTaiwanhelpingreformthetaxsystem,andsoItookmyfirsteconometricsclasswithBerndtStigum.Itwasaverysmallclass,andwewentatahighlevelusingMalinvaud’stext,whichhadjustappearedinEnglish.ThefollowingyearwhenT.C.camebackfromTaiwanItookthecourseagain,andthattimeweusedGoldberger.Thosetwobooksbacktobackprovidedagreateconometricsbackground.2 FXD:T.C.isoftencreditedwithaveryearlyandveryprescientinsight,laterrefinedandamplifiedbyChrisSimsandothers,namelythattheidentifyingrestrictionsintraditionalmacroeconometricmodelsareliterallyincredibleandshouldbeabandonedtotheextentpossible.Didyouseethoseideaspercolating?RFE:Youknow,Ithinkthat’soneofthereasonsT.C.wantedtogetintohigher-frequencymodeling:hewantedtobuildrecursivemodels.IsupposethisisinfacttheVARideainanotherguise.Hismonthlymodelwas,Ithink,almostentirelyrecursive.Buthedidn’treallydiscussthephilosophicalissues.Thisactuallyhadbeenabouttenyearsoldbythetime,ormaybemorebythetimeIstartedthegraduateprogramandIdon’trememberhimcomplainingabouttheneedtofindnewinstrumentsandsoforth.Hewasconcernedaboutwhatisthebestcollectionofinstruments,andthatsortofthing,butitwasn’tlikethewayit’spresentedintheVARliteratureinwhichnothingisassumedexogenous.Ineverrememberhimsayingthat.FXD:TellusaboutyourPh.D.dissertationworkandhowyouwereledtoit.RFE:MydissertationwasverymuchalongthelinesofT.C.’sresearch,whichwasontemporalaggregation,basicallyasking“What’stherelationshipbetweenmacromodelsestimatedatdifferentdatafrequencies?”T.C.hadalreadybuiltanannualmodelandaquarterlymodel,andhewasworkingonamonthlymodel,andsothatwaswhatIwastryingtoanalyzeandreconcile,fromboththeoreticalandempiricalviewpoints.Thekeyissuewas,ifyoustartedoutwithacertainhigh-frequency(saymonthly)dynamicmodelandassumedittobetrue,andyouaggregatedtoalowerfrequency(sayannual),thenwhatwouldthelower-frequencymodellooklike.Youendedupbeingabletotalkaboutthetimeaggregationprobleminthefrequencydomain,andworkoutmomentsofaggregateddatawhenthewholethingwasdynamic,andithadtodowithintegratingoverthespectrum,stufflikethat,andtheanswerwasmessy.ButwhatT.C.hadobserved,Ithink,wasthatthelaglengthswereaffectedbyaggregation;theygotshorter,andthat’swhatIwastryingtocharacterizerigorously.Ialsonoticedthatthelongruneffectsseemedtobeapproximatelyinvarianttotemporalaggregation,whichisrelatedtosomemuchlaterworkoncointegration.FXD:Let’swrapuptheCornelldays.Isthereanythingelseinyourmindthatyourememberasshapingyourlaterthinking,anyotherfacultyorstudentswhohadaparticularinfluence?RFE:Well,mycommitteeincludedJohnFeiaswellasBerntStigum,andofcourseT.C.Liu,anditwasreallyaverygoodcommittee,becausetheyallbroughtdifferentpointsofview.IthinkIdidn’treallygettheeconomicintuitionformodelbuildingaswellfromT.C.asIshouldhave--thatkindofcamelaterwhenIwassortofbuildingitonmyown--butIthinkhegaveagreatbackgroundforhowthestatisticsandtheunderlyingmodelfittogether.AndIalsotookastatisticsclass,withJackKiefer,whichgavemereallyawonderfulideaofhowstatisticsactuallyworkedandwhatthestatisticaldecisiontheoryproblemwas.HeandWolfowitzwerethekeypeopleoverinthestatisticsdepartment,anditwasfascinating,becausephysicistsdidn’tactuallytreatstatisticsverycarefully--theyjustsortof“didit.”FXD:Yes--doanexperimentandfindtheanswer.Littleneedtoworryaboutquantifyinguncertainty.RFE:That’sright.Ididn’treallylearnstatisticsuntilIbecameaneconomist!3 II.MIT,Band-SpectralRegression,andUrbanEconomicsFXD:Now,ontoMIT.HowdidyoulandyourfirstjobatMIT?RFE:IhavenoideareallyhowIgotthejob.ItseemedmostmiraculousbecauseIdidn’tevengotothemeetings.ItwastheyearoftheChicagoRiots,andthemeetingswerecanceled,andtherewasanalternativemeetinginPhiladelphia,the“graymarket”astheycalledit,andIwentthereandhadalittleinterviewwithCaryBrown,whowasthechairmanofMIT’sdepartmentatthetime.AndthenIwenttoMITandgavealittlediscussionofmydissertationwithjustsomefacultymembers,andIdidthesamethingatYale,andbothofthemsomehowcameupwithjoboffers.FXD:Whatdidtheylikeaboutyouandyourwork?RFE:IthinkoneofthethingsthatimpressedthemwasthatIknewthingsfrommyphysicsbackgroundthathadbeenusefulinanalyzingthistimeaggregationproblem,likecontourintegralsandstufflikethat,andtheythought“Oh,anyonewhocandothatcanprobablydosomethingelse.”I’mnotsurewhethertheywereright,butatleastIcoulddocontourintegrals!FXD:DoyourememberanythingofyourvisitstoYaleandMIT?RFE:MarkNerlovewasatYale,buthetookmeasideandsaid,“Iwanttotellyou,I’mnotpromisingtobehereformuchlonger!”IalsometKenWallis,ChuckBischoffandJimTobinatYale.AtMITtherewereDuncanFoleyandEdKuh.FXD:Let’sgetbacktoyourinterestinspectralmethodsandyoureventualcreationofband-spectralregression.Doyouthinkphysicistsmakeparticularlygoodtimeserieseconometricians?Fourieranalysisandrelatedideasaresurelyanaturalpassagewayintotimeseries.RFE:Well,that’swhatIdidmydissertationon,Imeanspectralanalysiswasabigpartofit.TheyweretoolsthatIalreadyknew,soitwashelpful.Iguessphysicistsdon’tdomuchcross-section,dothey?FXD:Didyourdissertationdevelopband-spectralregressionmethods?RFE:No,theycamelater,atMIT.FXD:Whatwasthethoughtprocessthatledtoband-spectralregression?Howdidtheworkprogress,andhowitwasreceived?RFE:Theideaforbandspectrumregressionprobablycameduringsummervacation.Ihadn’trealizedthatIwassupposedtoworkallsummeraftermyfirstyearasassistantprofessor,somywifeandIboughtacar,wenttoEurope,andspenttheentiresummerinEuropetravelingaround,endingupattheWorldCongressinCambridge,whereIwasontheprogramwithPhoebusDhrymesandChrisSims,andKenWalliswasthechairofthesession.So,aspartofthesummerIhadbroughtalongJenkinsandWatts,whichisthebookonspectralanalysisthatIlikethebest,andwestayedforacoupleofweeksinaSpanishresorthotelwhereeverymorningIsatoutonthedecklookingoutovertheMediterraneanreadingJenkinsandWatts,whichissortofawildthingtodo,butitactuallyreallyappealedtome,andIlovedoingthatsortofthing.IwasworkingontheseHannanefficientestimatorsandsoforthandjusttryingtowriteallthisstuffindifferentforms,andallofasuddenbandspectrumregressionjustemergedasverysimpleyetusefulidea.Iactuallycalleditpartial-spectrumregressionbecauseitwasregressionofapartofaspectrum,butMannyParzentookalookatit,saidIhadgivenitthewrongname,andchanged4 ittoband-spectralregression.ReallythefirstdraftcamewhenIwasvisitingatCornell,whichIdidthesecondorthirdyearwhenIwasatMIT,becausemywifewascompletinghermaster’sdegreeinpsychologythere.That’swhenIwroteitandthat’swhereIgotthefirstfeedbackonit–Ididn’treallygetmuchfeedbackonitwhenIwasatMIT.FXD:IrecallthatBenMcCallumandsomeotherscriticizedband-spectralmethodsfromarationalexpectationsviewpoint,inthatrationalexpectationstendtoproducerelationshipsandrestrictionsthatholdacrossallfrequencies,notjustcertainfrequencybands.Whatisyourview,twentyyearslater,onallthat?RFE:CertainlytheMcCallumcritiqueyieldsusefulinsight.Andit’srelatedtothereasonIstoppedworkingonband-spectralmethods,whichisthatoneinterpretationofband-spectrumregressionisasadiagnostic,acheckonwhetherastaticmodeliswell-specified.Thatis,adynamicmodelcanbeperfectlywellfitatallfrequenciesjustbyfindingtherightcoefficients,andthat’sinfactwhatthecross-spectrumdoes.Thecross-spectrumtellsyouexactlyinthefrequencydomainwhattherelationshipbetweentwoseriesis,andthenyoutransformthatbackintothetimedomainandyougetadistributedlagmodel.That’swhattheseestimatorsreallydid.SowhatIwasinterpretingasdifferentcoefficientsatlowandhighfrequenciescouldalsobeinterpretedaswhetherthestaticmodelwasmisspecifiedandwhethertherereallyshouldhavebeenadistributedlagmodel.FXD:Isee.Soitultimatelyboileddowntoaspecificationtestforadequacyofdynamicspecification.RFE:Yes,andinthatsenseitwaslessinteresting.Thetimedomainprovidedplentyofwaysoftestingthatalready.Butthen,ontheotherhand,lowfrequenciesareparticularlyinteresting,andweonlyrecentlyhavefullyappreciatedwhytheyaresoparticularlyinteresting,becausetheycarrythelong-runinformationinthem.Inmodernlanguagethatisthecointegratinginformation.Andcointegratingrelationshipsareofcoursestatic.FXD:Youmentionedthatyoudidn’treallygetmuchfeedbackonyourband-spectralworkfromthefolksatMIT.Pleaseelaborate.RFE:ThepersonthatIprobablytalkedwiththemostaboutthesesortsofthingswasChrisSims,whowasatHarvardformyfirstyear,andsoChrisandIwouldgettogetherandtalkaboutalotoffrequency-domainstuffbecausehewasveryinterestedinfrequency-domain,butthenheleftafterthefirstyear,andsoIdon’tknowthatIhadalotofpeopletotalktoaboutit.FXD:Let’sstaywiththatabit.SomewouldsaythatMIT,andCambridgemoregenerally,hasneverfoundtime-serieseconometricsappealing.Isthatcorrect?Andifso,why,andhowdoyoufeelaboutit?RFE:Yes,Ihavealotoffeelingsaboutthat.Itcertainlyisinhospitableinanintellectualsenseforthetime-seriespeoplewhohavebeenthere.EverybodywasverynicetomeatMITandHarvardandIfeelagreatdealoffondnessforallthosepeople.ButIdidn’tfeelanysupport,really,forinterestintime-series.ThatwascertainlytrueandIthinkthat’sthereasonIspentsomuchofmytimedoingurbaneconomicsatMIT.TherewasthebigurbaneconomicsprojectwhichFrankFisherandJerryRothenbergweredoing,andIgotinvolvedinthatandspentmostofmyresearchtimedoingthat,butinthebackofmymindtherewasstillthistime-seriesthingthatIwantedtodomoreof.ThepersonprobablywhowasmostinterestedinmytimeseriesworkatMITwasEdKuh;hereallyencouragedandsupportedme.HehadtheTrolleconometricssoftwareprojectgoingatthattime.Hehadmeinvolvedinthatgroupandtheyprogrammedupversionsofband-spectrumregressionandHannanefficientestimators.5 FXD:WeretheyincludedintheTrollpackage?RFE:Yes,bothwereincludedintheTrollpackage.Hewasaverysupportivefriend,andIreallyenjoyedworkingwithhimalot.FXD:RelatedtoMIT,onethingI’venoticedinyourworkfromtheearlydaysthroughtothepresentisafondnessfortheBerndt,Hall,andHausmanmethodofnumericaloptimization.Doesyourfondnessforitstem,atleastinpart,fromconversationswithJerryHausmanduringyourMITdays?RFE:No.Ithinkit’slaziness.FXD:Pardonme?RFE:I’mafraidit’slaziness.Ilearneditlongago,andI’vejuststuckwithit.CertainlythoughIhadagreattimewithJerry,andIthinkveryhighlyofhim.ThebesteconometricsconversationsthatIeverhadatMITwereprobablywithJerrywherehesaid“Tellmesomething--Whydoyouthinkthisistrue?,”andwe’dreallygothroughthesethings,andwe’veremainedfriendsovertheyears.FXD:Wereyoualsothinkingaboutmacroeconomicsatthetimeandthepotentialroleofband-spectraltechniquesingettingatlow-frequencymacro-dynamicsandsoon?RFE:Yes,that’sright,verymuchso.ItaughtundergraduatemacroeconomicsallthetimeIwasatMIT,andreallyIwasveryinterestedinmacro-modeling.Ihadbeeninterestedinthatformydissertationaswell.ThiswastheperiodwhentherevolutionofwhatIsupposewewouldcall“thedemiseofthebigmodels”wasgoingon.TheSt.Louismodelwasthenewkidontheblockandwasdoingwellandeverybodywantedtoknowaboutmonetarism,andtheSargent-Lucascriticismsandsoforthwerebigissues.Soalotoftheinterestingeconometricissuesinmacroeconomicmodelingwererightthere,buttherereallywerenoeconometriciansatMITorHarvardwhowereinterestedinthosekindsofquestions.FXD:Isthereanythingelseyouwouldliketomentionabouturbaneconomics?YoualreadymentionedgettinginvolvedbecausepeoplelikeFrankFisherandothersatMITwerethinkingaboutit.Wasthatthegenesisofyourworkinurbaneconomics,ordidyouhavepreviousinterestsalongthoselines?Andareyoustillinonewayoranotherpursuingresearchinurbaneconomics?RFE:RightnowIdon’tthinkI’mdoinganymoreurban,butIhadkeptitgoinguntilprettyrecentlywithjusttheoccasionalpaper.Ihadsomereallyinterestingstudentsinthearea,suchasEdCoulson.IdidalittlepaperongrowthcontrolsafewyearsagowithRichardCarsonandPeterNavarro,whichgrewoutoftheclassesthatItaught.Itaughturbaneconomicsclassesuntiltwoyearsago,everyyear.SoIkepttryingtothinkabouthowthemodelsandthedatafittogether.Istillfeellikethereiswonderfuldatainurbaneconomicsthatprovidesagreatplaceforeconometricanalysis.Inurbaneconomicswehavetimeseriesbylocalareas,andwonderfulcrosssections,andmysenseisthattheyhavenotbeenanalyzedinaverysystematiceconometricway.FXD:Doyouthinkthatrecentadvancesinspatialeconometricmethods,suchasTimConley’sspatialGMM,willhavepayoffsinurbancontexts?RFE:Youwouldthinkso.Thespaceturnsouttobecomplicated,becausewheneveryoulookatitupclose,itisn’tverylinearduetotransportationcosts.Thenyou’vegottoworryaboutmodeoftransportation–freewaysandallthesekindsofthings–sotheabstractmodelshavetobechangedalottotakethemtothedata,andIdon’tknowwhetherspatialcorrelationsinandofthemselvesareactually6 interesting.Butmaybetheyare.It’sjustthatIdon’tknowhowinterestingthestuffI’veseensofarturnsouttobe.III.ThrivinginSanDiegoFXD:So,afewyearsgoby,yougetonaplane,andyou’reinSanDiego.Thatmusthavebeenafascinatingtime.IguessCliveGrangerhadbeenthereforatleastalittlewhile,althoughmaybenotalongwhile.RFE:Hehadcomeonceasavisitor,visitingDanOrr,hisoldfriendandthenhehadtakenapermanentjobreallyjusttheyearbeforeIcame.IhadseenhimatoneofArnoldZellner’sconferencesonseasonalityinWashington,andIhadbeenlookingaroundatvariousplacesandaskedhimiftherewereanyjobsinSanDiegoandhesaid,“Ohsure.Comeonout.”Soanyway,IcameoutinFebruaryandstayedinthisnicehotelrightonthebeachandjustdecided,“Waitaminute.WhatamIdoinginBoston?Ishouldbehere.”So,anyway,Iwasverypleasedtogo,anditwasoneofthesedecisions–sortoflikemyswitchintoeconomics–whichwasreallyabigdecisionbutitjustfeltlikeitwastherightthingtodo.Itturnedouttobegreat.FXD:WhenyouarrivedwasClivetheeconometricsgroup,orweretherealsootherpeople?RFE:TherewasastrongeconometricsgroupthereinadditiontoClive.TherewasJohnHooper,DennisSmalllwoodandDickAttiyeh,whohadbeencolleaguestogetheratYalebeforetheycameout,andRamuRamanathan,aMinnesotaPhD.whowasalsoagoodeconometrician.Ashorttimelater,HalWhitecameout,whichwasgreat.WecameveryclosetohiringNickKieferaswell.FXD:Wow,Ididn’tknowanythingaboutthat.RFE:Itwasreallytragic,lookingbackonit,thatHalandNickwereavailableatthesametime.Wehadonlyoneslot.FXD:ThedevelopmentofSanDiegoeconometricshasbeenamazing,obviously,sinceyouandClivejoined..What’sthesecret?RFE:Well,Iwashiredasanurbaneconomist.FXD:Isee.Hireeconometricians,butunderdifferentlabels!RFE:JimHamiltonwashiredasamacroeconomist.IguessHalwasactuallyhiredasaneconometrician!ButIthinkthesecretreallyisthatSanDiego’seducationalstrategywasthattherearereallyonlythreesubjectsineconomics:micro,macro,andeconometrics.Andsoitmadesensetobuildstrengthinanyofthem.Incontrast,ifyouthinkoftherebeingtensubjectsineconomics,thenyouonlywantoneeconometrician.Ormaybeahalf.Andthat’snotenough.Itwasreallyhavingenoughofusinoneplaceatthesametimethatmadeitsoproductive.Studentscamebecausetheywantedtoworkwithus.Youknow,wefedoffeachother.Wewrotepaperstogether.Seminarswereinteresting.Therewereplentyofaudiences.Itjusttakesacertaincriticalmasstomakethingshappen.AnditwasreallyquitedifferentfrommyBostonexperience.FXD:WhatdoyouthinkofSanDiegomacroeconomics?Thatseemstobeamorerecentsortofblossoming,withHamilton,Flavin,theRameys,denHaan,andsoon.Howdidthathappen?7 RFE:That’sexactlythesamesortofthing.Fromtheverybeginningwealwayssaid“Wewanttobuildanappliedgroup,andreallymacrowouldbeourfirstchoiceastowhattheappliedgroupwouldbe.”Westruggledandstruggled,tryingtofindtherightpeopleandcouldn’thirethem,andthenwehiredValerieandGarey,whoareterrific,andthenwehiredJimandMarjoriebecausetheyhadbeenonleaveinSanDiegoandlikeditanditwasagainoneoftheseveryfortuitouscircumstancesthateverybodywasveryanxioustohavethemcome,andthenWouterdenHaanhelpeditallcometogether.Ifeelthatithasbecomeareallylivelyplaceinmacro.FXD:Iagree.AndmostrecentlyIguessit’squitealivelyplaceinfinance,withAllanTimmermann,andofcourseBruceLehmann.RFE:Allanhasbeengreat.AndBruceLehmannisgreat.Imean,Brucedoesn’tactuallywritethatmuch,buthe’ssucharesourceandhe’ssoveryactiveandlively,andhehassuchgoodcommentsoneverything.It’sgreathavinghimthere.Andit’salsogreathavingAlexKane,althoughhedoesn’tpopintothedepartmentallthatoften,butBrucecomestoallofoureconometricsworkshops.Also,becauseHal,Clive,AllanandIareallinterestedinfinancialeconometrics,theeconometricsworkshophastakenonquiteastrongflavoroffinance.FXD:SanDiegostudentshavealsobeengreat.Whostandsoutinyourmind?Whosurprisedyou?RFE:I’vehadgreatstudents.Andit’sreallyoneofthepleasuresaboutSanDiego,it’soneofthereasonsthatafewyearsagoIdecidednottoleave,becauseI’vereallythoughtthatthestudentsthatI’vehadaresogood.Whohassurprisedme?Youmeanabouthowwellthey’vedoneintheprofession?FXD:No.Imeansurprisedyoubystimulatingyouandquicklyemergingascolleagues.RFE:Youknow,IfeellikethatissomethingIreallylookforinastudent.AtthebeginningIamtellingthemwhattolookforandwhattodo,stepbystep.Towardtheend,thebeststudentsaretellingmehowitworksandwhatweoughttodoandhowtogofromthere.Andthat’swhenIknowthey’rereallygoingtogooutanddowellintheprofessionandI’vehadsomestudentswhohavedonewonderfullywellatthat.Someofwhomyouknowverywellandothersofwhomarenotverywellknown,butwhoIthinkarereallyterrificandhavethepotentialtomakewonderfulcontributions.ButIguessI’dbetternotproducealistofnames,orI’llgetintrouble!FXD:Let’stalkaboutyourworkatthetime.Yourearlyworkontesting,particularlyLagrangemultipliertesting,wasveryinfluential.DidyourLSEvisitsandyourdiscussionswithDavidHendryinfluenceyoutomoveinthatdirection?RFE:Well,myrelationshipwithDavidprobablystartedwhenIfirstwenttoMIT.Ihadmethim,aswellasKenWallis,thatfirstsummerwhenIwasonthewaytotheCambridgemeetings.Daviddidn’tactuallygo,butImethimbrieflyandIfeltlikeLSEwastheplacewheretimeserieswasmostinterestinginthosedays,andIdidmyverybesttospendenoughtimewiththepeoplethere:Sargan,DurbinandMizon,aswellasDavidandKen.Eachvisitwasstimulating.SoIspentaquartertheresharinganofficewithChuckNelsonin1975.HewasonhiswayfromChicagotoWashingtonandIwasonmywayfromMITtoSanDiego,andIwasthinkingabouttesting,andKensaid,“Bytheway,youmightliketoseethispaperbyBerndtandSavinontheinequalitybetweenWald,LagrangeMultiplierandLikelihoodratiotests.”AndsoIgotveryinterestedintesting,LMtestsinparticular,andendedupwritingtheLMpaperthatappearedintheHandbookofEconometrics.8 FXD:Related,tellusabitaboutyourworkonexogeneity,alsodoneinyourearlySanDiegodays.Engle,HendryandRichardisafascinatingpaper–perhapssomethingofanoutlierrelativetoyouroverallresearchprogram,butatremendouslyinfluentialone-papercriticalmass,anditinvolvesDavidHendry.Tellusalittlebitaboutthepaththatledtothatwork,includingyourrelationshipwithDavidandhowthathasinfluencedyou.RFE:IthinkitmustalsohavebeenwhenIwasatLSE.IwenttoCOREtogiveatalkonapaperthatIhaddoneonunemployment,whichinvolvedcausalitytests.Afterward,Jean-FrancoisRichardsaid“Youknow,youthinkyou’retalkingaboutcausalitybutyou’rereallytalkingaboutexogeneity.”Isaid,“No,no,no.”Hesaid,“Well,Koopmanswouldhavecalledyourconceptexogeneity.”Isaid,“Idon’tthinkhedid.”SoanywaywepulledoutKoopmans,andwelookedatthisandrealizedthatinfactthereweredifferentconceptsofexogeneitythatcouldbeformulated--whichwewouldlatercallweakandstrongexogeneityorevensuperexogeneity--noneofwhichwasGrangercausality.Simultaneously,ChrisSimswasbusilypushingcausalitytestsasawayofassessingexogeneity.Neitherofuslikedthatideaandsowespenthoursdiscussingthisanddecidedthatreallyweshouldwriteapaperonit--justalittlenotebecause,really,howdoyouwriteapaperonadefinition?Youjustwritealittlenote.FXD:HowdidHendrygetinvolved,andhowdidtheworkprogress?RFE:Jean-FrancoisandDavidweregoodfriends,andhesaid“Oh,shouldwegetDavidinvolved?,”andIsaidgreat.Thethreeofusspentalotoftimeonthis,andweworkedandreworked.Jean-Francoisreallyhelpedthemathematicalstructure,andDavidkeptpushingtoextendthescopeanddepthofthepaper.Themainthingwasfiguringouthowallthesedifferentconceptscouldbedefined,andhowtheyallfittogether.Thatreallymadeitcometolife.Andthen--Idon’trememberwhetheritwasthesameyearorthenextyear--KenWallishadoneofhissummerinstitutesontimeseriesanddynamicmacroeconometrics,andChrisSimswasthere,aswellasHendry,RichardandI,andwespenthoursandhourstalkingaboutallthesedifferentconcepts.Thatreallyhelpedtofocusourthinking,andthenwewroteupthepaper.Thepaperwascontroversial,anditwasrejectedafewtimesbyEconometricabeforewefinallymanagedtogetthemtotakeit.FXD:ClearlyyourtimeatLSEwashighlyinfluentialonyourresearch.WhatotherplacesandpeopleoutsideofSanDiegohavebeenmostimportanttoyourresearch?RFE:GourierouxandMonfortinParishaveputtheirfingersonsomanyinterestingproblems,oftenveryearly,andputtheirstamponthem.Ithinkthey’vemadeareallypositivecontributiontotheprofessionandtomythinking.AndIalwayshaveagoodtimetalkingtoAdrianPagan.Adrianisreallytheprototypicaltoughcriticandinsightfuleconometrician.Ifyoucangethimtoagreethatsomething’sinteresting,you’vereallymadeanaccomplishment.9 IV.CointegrationFXD:Cointegration.RFE:Cointegration.FXD:Whatanamazingridefrom1980tothepresent–certainlyoneofthekeydevelopmentsofthelasttwentyyearsineconometricsandempiricalmacroeconomics.Howdiditallhappen?RFE:Well,Clivehadbeenformulatingtheproblemforsometime,andhehadproposedsomedefinitionsofcointegrationearlyon,andheandAndyWeisswroteapaperwhichwasactuallythefirstattempttotrytotestitandgetittoconnectwiththeerrorcorrectionmodel,butinfactIdon’tthinkthatpaperactuallyhangstogetherquiteright.It’sagoodattackontheproblembuttherearesomeformulationissuesthatreallydidn’twork.So,whathappenedwasthatIgotanideaofaslightlydifferentwayofwritingitdownwhichgaverisetotheteststatisticweproposedinourpaper,andofcoursealsogaverisetothetwo-stepestimationmethodwhichfollowsdirectlyfromthetestconstruction.ClivehaddonetheproofofwhatwecallintheretheGrangerRepresentationTheorem,whichinmyviewwasnotaverytightproof,althoughIsupposepeoplewouldsaythatwhatwefinallypublishedwasn’tverytighteither.Butinanycase,itwasalittletighter.SowedecidedtowritethisjointpaperwhichwasfirstpresentedattheNSF/NBERtimeseriesseminarintwosessions,onesessiononthetheoryandonesessiononthetestingandestimation.Ittookplace,Ithink,atUCDavis,andthereactionwasnotasenthusiasticasonemighthaveimagined,butalotofdiscussionensued.LaterthepaperappearedasEngleandGranger.FXD:YoumentionedtheNSF/NBERtimeseriesseminar.That’safascinatingseminar,particularlyinthatitbringstogetherthestatisticalandeconometricsidesofappliedtimeseriesintheBox-Jenkinstradition.Oneaspectofthestatisticalsideisreducedrankregression.Wereyouawareofreducedrankregressionatthetime?RFE:Notreally.Iwasn’texactlyawareofreducedrankregression,butIwasawareoftheBox-Tiaopaperonthemaximalcorrelationcoefficientbetweenmultivariateseries.Butthatworkwasforstationaryprocesses.Therewasnounitrootdistributioninthat,althoughtheframeworkofcoursewasthesameas,oralmostthesameas,theonethatJohannseneventuallyused.TheinsightofSorenJohansenandGregReinselthatcointegrationwasareduced-rankproblemwasnewtous,andofcoursewethoughtitwasverygoodandpowerful.FXD:HowdidyoumeetandgettoknowSorenJohansen?RFE:I’mtryingtorememberwhenIfirstmetSoren.IrememberhimbeinginSanDiegoforavisitandtalkingaboutallthethingsthatwecoulddowithcointegration,likeI(2)problemsandseparability,andmanyothersortsofextensionsofthesimplecointegrationmodel--thatmusthavebeenafterhewrotehisfirstpaper.ButIthinkIknewhimbeforeIsawthepaper.AndIdidaweekinCopenhagenatonepoint,talkingaboutcointegration,ARCHandstufflikethat,butIknewhimbeforethattoo.SowhendidImeethim?Youknow,Ireallycan’tquiteremember.IbetitwasatoneoftheEuropeansummermeetings.FXD:That’swhenIfirstwasexposedtohim.Irememberseeinghimandhisflamboyantandenthusiasticstyle,justsothrilledbythebeautifulgeometricstructureofcointegration.RFE:That’sright.Hewasverymuchintotheaestheticsofthestatistics,andhewasperfectlyhappytoassumefiniteautoregressionsinordertogetabeautifultheory,asopposedtoapproximatingsomeinfiniteautoregressioninwhichcasetheorderwouldhavetogrowappropriatelywiththesamplesize.Sorenhas10 alwaysbeenveryinterestingtotalkto,andIthoughtfromthebeginningthathispaperwasreallyveryinteresting.Theideaofreduced-rankregressionwasverynatural.FXD:PeterPhillipsisanotherkeycontributortothecointegrationliterature.Inyourview,howdoPeter’scontributionsfitin--thefunctionalcentrallimittheoryapproachandthetriangularrepresentation,forexample--andwhatstrikesyouaboutthem?RFE:Well,Peter,developedthefunctionalCentralLimittheoremapproachtodoingtheunit-rootasymptotics.ThefunctionalCLTwasofcoursewell-developedinstatistics,buthefounditandbroughtitintotime-serieseconometricsandshowedthatyoucouldderivetheDickey-Fullerdistributionsusingit.Healsointroducedthetriangularrepresentationthatsimplifiestheanalysisofcointegratedsystemsbecauseyou’renolongertestingfortheexistenceofcointegratingvectorsorhowmanythereare;instead,you’reonlyestimatingthemodel.Butofcoursethenitdoesn’treallysolvetheproblemthatweandJohansenweretryingtosolve:howtotestforcointegration.Alsothere’stheissueofnormalization.OneofthethingsaboutJohansen’smethod,ofcourse,isthatthere’snonormalizationinvolved,andthat’sbothstrengthandaweakness.Ontheonehand,youneverhavetheawkwardnessofhavingnormalizedonsomethingthattrulydoesn’tbelonginthemodel,butontheotherhand,itcanbehardtointerpretthecointegratingvectors.FXD:We’vealreadytalkedabitaboutDavidHendry’sinfluenceonyourthinking,inthecontextofyourworkonexogeneity.AsecondagoyoumentionedtheGrangerrepresentationtheorem,whichofcoursecharacterizestheintimaterelationshipbetweenmodelsofcointegrationandmodelsof“errorcorrection”popularintheLSEtradition.DidHendryinfluenceyourthinkingoncointegration?RFE:Absolutely.DavidandIhavehadlongconversationsonerrorcorrectionandtheLSEtradition,goingbacktotheworkofDenisSargan.He’sagreateconometricianandagreatfriend.FXD:Verygood.Nowthatwe’vetalkedaboutcointegration,let’smovetocommonfeatures.Iftwovariablesareintegratedbutthereexistsalinearcombinationthatisnot,wesaythatthey’recointegrated.Moregenerally,iftwovariableshavepropertyXbutthereexistslinearcombinationthatdoesnot,wesaythattheyhavecommonfeatureX.Soundslikeanobviouslogicalprogressionwithwideapplicability.Doyouwanttosayanythingaboutcommonfeatures?RFE:Iwasprettyenthusiasticaboutcommonfeaturesasanorganizingconceptforalotofmultivariateanalysis.Idon’tfeelthatithasactuallycaughtoninthewaythatIthoughtitmight.Itjustseemednaturaltomethatinhigh-dimensionalsystemsyou’dreallywanttolookatthingsthatwerecommonacrossabunchofdifferentseries.Ithinkmaybethetwomostattractiveapplications--besidescointegration–havebeenthevolatilitymodels,whicharereallytestsofthefactor-ARCHmodel,whereyouaskwhethertherearelinearcombinationsofreturnswhichhavenoARCHinthem,andsomeofthecommontrend/commoncyclemodels,inwhichsomerestrictionsareassociatedwiththeunitrootsandsomerestrictionsarejustassociatedwithstationaryserialcorrelation.ButatanyratethecommonfeatureideahasnotactuallybeenpickedupasmuchasIthoughtitmight.FXD:Whydoyouthinkthat’sthecase,especiallygiventhatcointegrationwassuchahit?RFE:Cointegrationexplainssomethingsthatwedidn’treallyhaveagoodtheoryfor,likewhystaticregressionsactuallygiveaprettygoodestimateforthelongruneffects:youbuildthebestdynamicmodelyoucan,andloandbeholdthelongruneffectisthesamethingasyouhadfromthestaticmodel.Orwhenyoutakeprincipalcomponentsofthings,howthefirstcomponentmightexplainninety-ninepercentofthevarianceorsomethinglikethat.Cointegrationfitsthosestylizedfacts.Ithinksomeofthe11 otherfactormodelsorcommonfeaturemodelsmightdothattoo,butwe’renotsofamiliarwiththosestylizedfacts,likehowmanyseasonalfeaturesaretherereally?Isseasonalityreallythesameforallseries?Orsomekindsofnonlinearerrors,aretheyreallythesameforallseries?IntermsofthefactorARCHmodel,Ithinktheworldismorecomplicatedthanjusthavingoneortwovolatilityfactorstoexplain,say,globalvolatilities.Perhapsamorerealisticsituationistwentycountriesandtenfactors,andthat’sahardthingtodetectinpractice.FXD:Howdoyouviewcointegrationinitsrelationtomacroeconomicsandfinance?Howusefularecointegratingtechniquesinthoseareas?RFE:Cointegrationisreallyaneconometrictechniquewhichisdesignedfirstandforemostforanalysisofmacroeconomicdata.AndIthinkthattheshort-rundynamicsofmacroeconomicsystemsareoftenthoughttobekindoftheglossontopofthefundamental,long-rundrivingforces.Cointegrationisexactlyamethodwhichisdesignedtolookforlong-runbehaviorwithoutbeingtoodistractedbytheshort-runmovements.So,Ithinkitisthesortofgenerictoolofchoiceformacromodelingandforecasting.It’salsothenaturalcompletionofthebandspectrumregressionidea,whereyouthinkthatthelong-runrelationsarewhatyouseewiththelowfrequencydataandthehighfrequencypartisdynamicsaroundthelowfrequencymovements.Andthisconnection,Ialwaysthoughtyoucouldmakealittlemorerigorously,butinfact,PeterPhillipswastheonethathasproposedestimatorsofcointegratingrelationsusingjustthelowfrequencycomponents,andIthinknotsurprisingly,hasbetterperformancethanusingthewholespectrum.FXD:Whatdoyouthinkabouttheuseofcointegrationmethodsinfinance?RFE:Cointegrationamongassetreturnsimpliesthatatleastonereturncanbepredictedbasedontheothers,soinanefficientmarketsworldonegenerallywouldnotexpectcointegration.Butthereareexceptionsinthesensethatsomeassetpricesarenottotalreturnprices,andsothefirstdifferenceofthepriceisnotthetotalreturn,suchasabondwithacouponpaymentorastockwithadividendpayment--thenyoucanhavecointegrationinpricesandstillnothavereturnpredictability.Andthat’soneofthereasonsyouseecointegrationbetweensomebondmarketprices,becauseinfactit’sjustthecouponpaymentwhichisgivingyouthepredictability.Butshortofthat,cointegrationhassomethingofanappealtofinancialpeople;thatis,ifpricesdeviatefromwheretheyareonaveragetheyareeventuallygoingtocomeback,andcointegrationmightbeawayyoucandetectthattheyaregoingeventuallytocomeback.Thissuggeststhepotentialprofitabilityofportfoliostrategiesbasedontradingagainstpricesthatdeviatefromtheir“normal”values.Somepeopleseemtothinkthatallyouhavetodoishavepatienceandyou’llmaketheprofits.I’mnotsurethatsortofenthusiasmiswarranted.Whenfinancepeoplefindevidenceofcointegration,it’softenafterrunningmanycointegratingrelations,oftenwithrelativelyshortsampleperiods,andperhapsevenfiddlingwiththesampleperiods.Allthissuggestssomedatamining,whichwouldinvalidatetestsforcointegration.Infact,manyapplicationsI’veseenhavenotevenreallytestedforcointegration;insteadtheyjustsortofobserveitorhopeforit.So,Ithinkit’seasytoabusecointegrationinfinancialsettings;“statisticalarbitrage”isnotaseasyasitsounds.I’veactuallydonesomerecentresearchlookingatwhetheryoucantellwhencointegratingrelationsarebreakingdown.Effectivelytheapproachsaysthatyoumayhavecointegrationforawhile,butthenyou’llgetbigshockstothesystemandthosewillbepermanentshocksandthey’llmovethecointegratingrelationshiptoanewplace.Andsoyounolongergetthereversiontotheoldequilibrium.12 V.ARCHandFinancialEconometricsFXD:Let’smovetoARCH.Idon’tknowwheretobegin--it’sbeenatremendousquartercentury.Canyoutellushowyoustartedthinkingaboutit,yourroleinitsdevelopment,anditsfuture.RFE:Well,GARCHorARCHisoneoftheseLSEinventionsthatIattributetomygreatsabbaticaltimeatLSEandtheconversationsthere.I’vetakensabbaticaltimeatLSEtwice.ThefirsttimewasreallywhentheLMtestsandexogeneityweredone.ThesecondtimeIdidARCH.AndARCHwasaproblemthatactuallywasstartedandfinishedwhileIwasonleaveatLSE.AlotofthediscussionsIhadoverlunchandcoffeewerewithDavidonissuesof“Howdoyouinterpretthesethings,howdoyouformulatethem,whatarethetheorems?”AndwithDurbin,Sarganandothersaroundtoo,therewasjustlotsofinput,andIreallyappreciatedallthefeedbackIhad.WhenIfinallygottheARCHmodelformulatedsoyoucoulddoitasaniteratedsetofleast-squaresregressions,Davidsaid“Okay,Iguesswecandoit.”Sowehadtheprogrammercodeit,andwetrieditout,andtheresultsseemedpromising.ThenameARCHwasactuallyDavid’ssuggestion,andtheARCHpaperturnedouttobethefirstpapertheyputintheirnewworkingpaperseries.FXD:Whatledyoutothinkaboutvolatilitydynamics?RFE:ItturnedouttobeamarriageofacoupleofdifferentideasthatIwasreallystrugglingwith.Onestrandwastryingtogetvariancesintomacroeconomicmodels,becausesomepeoplethoughtthatitwasactuallynottheexpectedvalueofeconomicvariablesbutrathertheirvariabilitythatwasrelevantforbusinesscycleanalysis.ThiswasbasicallyMiltonFriedman’sNobellecture,butIwaslookingforwaysoftyingitinwithrationalexpectationsmacroeconomics.AsecondstrandisthatineverythingIdidIwasrepeatedlyimpressedbytheimportanceoftheconditionaldistributionandhowitsimplifiedthewayyouthinkaboutbuildingmodels.AndIsupposethethirdstrandisthatbeforeIwentonleavetoLSECliveandIweretalkingaboutbilinearmodelsandheshowedmeateststatisticwhichhadalotofpower,hethought,todetectbilinearity.ItwaswhatwenowknowastheARCHtest,regressingsquaredresidualsonpastsquaredresiduals.Ihadsomesortofmodeluponmycomputerandhesaid“Squarethoseresidualsandgetanautoregression.”IdidandwasveryimpressedtoseethattheR-squaredwhenmultipliedbythesamplesizewasquitelarge.So,havingdoneallthisworkonLMtests,Ithoughttomyself,“ThisisnottheLMtestforthebilinearmodel.SowhatisittheLMtestfor?”So,puttingthatquestiontogetherwiththeattempttotrytofindtime-varyingvariances,IrealizedthatitwastheARCHmodel.So,IthinkIwouldsayIdiscoveredthemodelfromthetest,ratherthantheotherwayaround.FXD:HowaboutGARCH?HowdidTimBollerslevdevelopthat?Wasitjusttheobviousprogressionorweretheredifficultiesinvolved?RFE:Well,DavidHendrywasinvolvedinthatone,too!Davidwasconcerned,andIthinkactuallyitwasStevenHallthatpromptedhimonthisormaybeStevenTaylor,Ican’trememberexactly,thatGARCHlookednotlikeanautoregressionbutratherlikeamovingaverage.DavidwasinSanDiegoatthetimeandwestruggledwithitalittlebit,andthequestionwashowcouldyouputalaggeddependentvariableintoanARCHmodel.Timwasveryinterestedsowetalkedaboutitwithhim,andthenextdayTimcamewithitallworkedout.Hesaid“Well,youcoulddoitthiswayandhere’stheconditionsforstationarity”andthenextthingweknew,hehadprogrammedit,andhewasvery,veryquickworkingoutallthedetails.ItwasreallyawonderfulsimplificationoftheARCHmodelbecausetheparameterizationhadbeensuchastumblingblockearlyinthepureARCHmodelanditjustappearedtobemuchsimplerintheGARCHframework.So,IthinkinsomewaysDaviddeservessomecreditfortheGARCHvariation.13 FXD:It’sinterestingtoseethatARCHstartedoutwithaneyetowardmacroeconomicapplications–youmentionedtheFriedmanlecture–butquicklymovedintofinance.Withthebenefitofhindsight,itseemsclearthatfinanceisreallythenaturalplaceforGARCHapplications.Volatilitiesoffinancialassetreturnsclearlyseemtobeforecastable,andthathaslotsofimplicationsforfinance.What’syourviewonthat—thedevelopmentofGARCHfromafinancialperspective.Wherehasitbeen,andwhereisitgoing?RFE:Well,ofcourseIwastryingtofindthistradeoffbetweenriskandreturninmacroeconomics,butriskandreturnismuchmoreatradeoffinfinance,whichIsortofrecognizedbutIdidn’tknowverymuchfinance.DavidLilienwasoneofthepeoplewhosaid,“Youknow,youreallyoughttoapplythistofinance,”andthat’swhenheandRussellRobinsandIwrotetheARCH-in-Meanpaper,whichwastryingexplicitlytomeasurethisrisk-returntradeoff.IthinkthepaperthatreallykickeditoffinfinancewastheFrench-Schwert-Stambaughpaper,whichwasdonewithoutanyinput,orinteraction,withme.Ithinkitmadethefinancecommunityrealizehowinterestingthiswas.Thatpaperwaspublishedin‘87;theARCHinMeanpaperIthinkwasalso‘87andtheoriginalARCHpaperwas’82,anditwaswrittenin’79,sotherewasreallyalotoftimeintherebeforeitcaughtonandactuallymadethemigrationtofinance,whichgavemealotoftimetoworkonARCHvariations,includingintegratedGARCH,whichturnedoutIdon’tthinktobesuchagoodidea,factorGARCHmodels,andsoon.Wegotalotofresearchdonebeforeitgotsopopular,andthatwasveryhelpful.FXD:WhatareyourviewsonARCHanditscontributiontotheemerging,orperhapsemerged,financialrisk-managementindustry?RFE:It’sinterestinghowI’vegottenintothat.I’vebeenaskedperiodicallytotalktofinancegroupsandthisstartedprobablytenyearsago,andatfirstIhadnoideawhattheywouldbeinterestedin.Soinfact,Igotinvitedtotalkataconferencecalled“VolatilityModels”andanotherconferenceoncorrelation,andactuallythesecondwasespeciallypuzzlingtomebecauseIhadnoideawhatitwasthatyouwouldasksomebodytotalkaboutincorrelation.SoIaskedthemforafewreferencesandfoundoutwhatthefinancequestionsaboutcorrelationreallywere.Inanycase,IthinkthatGARCHisaverynaturaltoolfordoingrisk-managementandIthinktheideaof‘howdoyoumeasureandquantifymarketrisk?’isexactlyoneoftherealstrengthsofGARCHmodels.Theygiveyoutheabilitytotalkaboutriskwhenit’svaryingovertimeinawaythatmostothermethodssofarreallyhavenotbeenabletodo.And,youknow,thisincludesinparticularthemultivariatenotionswhereyou’retalkingaboutportfolioswhichhaveassetswithtime-varyingcorrelations.FXD:Let’sswitchforasecondtoassetpricing,inparticularderivativespricing,optionsbeingaleadingexample.ThevolatilitydynamicsliteratureingeneralandtheGARCHliteratureinparticularhavemadeimportantcontributionsthere.Canyoudescribethegenesisofyourthinkingalongthoselines,andyourviewsonthefutureofderivativespricingundertime-varyingvolatility?RFE:Alloptions-basedderivativesrequiresomesortofvolatilitynumberbecausethey’remorevaluablewhenvolatilityishigher.Itistypicaltoquotethepriceofoptionsintermsofvolatility.Soit’ssurprisingthatvolatilitymodelsweren’taveryimportantpartoftheinitialworkonoptionspricing.InfactoneviewthatIlikeisthatbuildingbetterandbettervolatilitymodelsislikedoingfundamentalanalysis.We’retryingtounderstandwhatthefundamentalvalueofanoptionreallyis,regardlessofwhereitisbeingpricedtoday.WecanviewGARCHmodelsasfacilitatingthatfundamentalanalysis.Thatlineofthinkingleadsyoutothinkabouttherelationshipbetweenimpliedvolatilities,whicharisefromtrading,andGARCHvolatilities.Butinasensethatmissesakeyfeature,whichisthatiftherealworldhastimevaryingvolatility,thenit’snotclearhowyououghttopriceoptions,sothelinkbetweenimpliedandGARCHisnotascloseasyou’dliketothink.Infact,financeliteraturehasawholeseriesofoptions14 pricingpapersonhowyouwoulddothisundervarioussettings.WenowhaveseveraldifferentversionsofhowyouactuallyoughttopriceoptionsifGARCHisinfactnotjustanapproximationbutreallythetrueunderlyingdata-generatingprocess.Andtheserevealsomestrongsimilaritieswithactualoptionpricesbutarecertainlynotascloseasyoumightlikeforactualapplications.HenceIthinkoneofthemissingfeaturesinpresentanalysesisinvestigationofriskpremia.Thatis,inaGARCHworldoptionsarenolongerredundantassetsandthereforetheymaybepricedwithariskpremium.Andthisriskpremiumcomesfromsomesortofpricingkernelwhichmustpricenotonlytheunderlyingassetandtheoption,buteverythingelse,too.Sothequestionis,whatsortofpricingkernelcanactuallyrationalizeoptionspricesinaGARCHenvironment?InarecentpaperthatJoshRosenbergandIwrote,welookedatthispricingkernelasnotbeingaconstantofnaturebutactuallyhavingtime-varyingriskaversion,sowewouldallowthepossibilitythatagentsaresometimesmorerisk-adversethanothers.AndbymatchingtheoptionspriceswiththeGARCHforecasts,youcanseethatthereareperiodswhenagentsseemtobemorerisk-adversethanothersandthisgivesyouafullrepresentationoftheoptionsinthisparticularunderlyingindex.It’spossiblethattheanalysissuffersfromover-parameterization,butit’saninterestingwayofinvestigatingtheissues.FXD:Let’smovetofinancialmarketmicrostructure.Whatcanwelearnaboutmarketmicrostructureeffectsfromhigh-frequencyreturns,andwhatcanwelearnaboutthedynamicsinhigh-frequencyreturnsfrommarketmicrostructure?Whereistheliterature,inyourview?Doesthepotentialremainlatent,orhasitbeenrealized?Areweinthemiddleofitallrightnow?RFE:Ithinkwe’reinthemiddleofit.Ithinkit’safascinatingfieldforaneconometrician,butit’salsoafascinatingfieldfromaneconomicpointofviewbecausethefundamentalissueinmarketmicrostructureishowwegetfromsomepeopleknowingsomethingtotheefficientmarkethypothesis.Howdopricesincorporateinformation?Andwhatinstitutionalstructuresfacilitatethat?Howlongdoesittake?Howefficientaremarkets,anyway?Essentiallywhatmarketmicrostructurerecognizesisthatagentsarecontinuouslydoinganinferenceproblem,tryingtofigureoutwhatthepriceoughttobegivenwhattheyseearoundthem.Whattheyseearoundthemaretrades.Peoplebuying,peopleselling,aswellaspublicinformation,andsotheeconometricianhasthesameinformationtheagentshave,oratleastanappreciablesubsetofit,andhecantrytofigureouthowthisinferenceproblemreallyworks.So,bythetimewegettomarketmicrostructure,we’rebackinanarenawhichisalittleclosertothemacroeconomicarenawetalkedaboutearlier,wherepricesdon’tyetreflectourinformation.Thereispredictabilityinprices,butit’spredictabilityonlyoverhoursorminutesorevenseconds,andtheinterestingquestionishowquicklywemovetothenewequilibrium.FXD:You’veworkedondurationmodelslately,inparticularmodelsofdurationsbetweentrades,estimatedusingtransactionsdata.Whatisyourviewonthelinksbetweenthosedurationmodelsandvariousmarketmicrostructuremodels?Inparticular,whatistheabilityofthosemodelstoilluminateaspectsofmarketmicrostructurethatmightbeeconomicallyimportant?RFE:Well,thedata,ofcourse,areirregularlyspacedandsotheeconometricianhastodosomethingaboutthat,andtherearevarioussolutions,butitseemstometheidealsolutionistousealltheinformationandnottoaggregateitout,whichforcestheeconometriciantosomehowestimateamodelwithirregularlyspacedtimingintervals.Now,thismightbethoughtofasjustanuisance,andsomemodelstreatitasjustanuisance,butIthinkthatoneofthethingsthatweseeintheresearchisthatinfacttheinformationavailableinthesedurations,whichisavailablenotonlytousbuttomarketparticipants,tellssomethingaboutthestateofthemarket.Andsothedurationsbetweentradesactuallyinformpeopleofwhat’shappening.Thatis,ifyoupicturetheNewYorkStockExchangeandthepeopleclusteredallaroundthespecialist,jumping,shouting,screamingandraisingtheirhands,whatyou’regoingtoseeonthetapeisalotoftradesallclusteredtogether,andthemarketbehavesratherdifferentlywhenthetrades15 areclosetogetherthanwhenthey’respreadout.Andsothatbylookingatthetimingoftradesyoulearnsomethingaboutthestateofthemarket;whenthetradesareclosetogetherthere’sinformationflow,whetherpublicorprivate,andalotofagentsarelookingateachothertryingtofigureoutwhattodo.Andassoonasyouseethiskindofherdingbehaviorthemarketbehavesinsortofanilliquidwayandvolatilityishigh,bidaskspreadstendtobehigh,andIthinkthemarkettendstohavehighcostsofdoingbusinessatthosetimes,badexecution.FXD:ThisisveryreminiscentofPeterClark’swork,intermsofinformationflow,linkstovolatility,andsoon.RFE:That’sright.PeterClarkcertainlyproposedthisgeneralclassofmodels.Hedidn’treallyhaveawayoftyingittoobservables.Itwasmoreofatheoreticalconstruct,butIthinktheasymmetricinformationmodelsdotieuptotradesinaveryniceway.Forexample,intheEasleyandO’Haramodel,intervalsbetweentradesgetveryshortwithinformationflow,becauseanyinformedtraderwhogetsthechancetotradewilltrade,whereaswhenthereisnoinformationflowinformedtradersfindthatit’snotprofitabletotrade.Soyou’vegottimesbetweentradeschangingendogenouslybasedonoptimization;thisisinfactalsoawaythatinformedtraderscanbesortofsingleminded,becausethey’rereallytryingtotradeasfastastheycan.FXD:ContinuingwiththeClarkthemebutfromavolatilityasopposedtodurationmodelingperspective,onceoneallowsforseriallycorrelatedinformationarrival,onearrivesatthestochasticvolatilitymodel.WhatareyouviewsonGARCHvs.stochasticvolatility?RFE:InaGARCHmodel,thevarianceismeasurablewithrespecttoobservedinformation,whereasinastochasticvolatilitymodelit’sdrivenbyalatentvariableandimmeasurablewithrespecttoobservedinformation.Andsomehoweconomists,andpossiblystatisticiansaswell,seemtofeelthattheunmeasurableonesaremorenaturalandmorestructural,whichisactuallyafeelingthatI’veneverunderstood.Measurabilitywithrespecttoalatentvariabledoesn’tsuggestthatthey’remorenatural,anddoesn’tsuggestthattheyfitthedata,andreallydoesn’tsuggestanything.Thefeelingseemstobethatstochasticvolatilitymodelsaremorenaturalbecausethey’rediscrete-timeanalogsofdiffusionmodels,buttheanalogyissuperficialanddoesn’tensurethatstochasticvolatilitymodelsareinanysense“good.”FXD:Whatdoyouthinkabouttheemergenceoffinancialeconometrics.Hasitemerged?Ifsowhynowandnotthirtyyearsago,andwherewillwebetenyearsfromnow?Andifithasemerged,whyhasitemerged?Whatisfinancialeconometrics?RFE:Well,Ithinkfinancialeconometricshasdefinitelyemerged,itisaveryrapidlygrowingareaofeconometricsandIguessthereareacoupleofreasonsforit.Oneisthatfinancialtheoriesareverypreciseandverymuchamendabletotesting.Anotherreasonisthatthedataareveryhighquality,especiallycomparedtothedataweareusedtoinmacro,laborandsomeoftheotherareaswherethereisalotmoreconcernaboutthedataquality.Andthethirdreasonisthattherearealotofrewardstopeoplewhostudyit.Therearelucrativejobopportunitiesforpeoplewhodecidenottobeacademics,soitmakesitagoodtopicfordissertationsbypeoplewhoarenotcertainthattheywanttogointoacademics.Thequestionofwhydidn’tfinancialeconometricsdidn’temergethirtyyearsagoisreallyinteresting.AndIamnotsurethatitreallydidn’t.Butitdidn’treallyattracttheattentionofeconometricianssoearly.Buttherewasalotofworkbeingdone.Alotofitwasdoneonthestreet.Alotofstockselectionmodelsweresetupandalotofportfoliomodelsweresetup.Theyprobablywerenotassophisticatedastoday’smodels,buttheyservedthefunction.Ithinkfromanacademicpointofviewfinancialeconometricswasviewedastryingtobeatthemarket,whichinfactwasataskwhichblewimmediately16 intothefaceoffinancialtheoryandthereforeitwaskindofdisreputable.Bystudyingandturningourattentiontoriskandportfolios,derivativesandallthesekindsofthings,allofasuddenitisnowconsistentwiththeoryasopposedtobeinginconflictwithit.FXD:Whatdoyouthinkofthejournalsandcollectionsthathaveemerged,suchastheJournalofEmpiricalFinance,theJournalofFinancialEconometrics,theHandbookofFinancialEconometrics,andsoon?RFE:Ithinkthereisroomforthesejournals,andtheyclearlyreflectthecongealingandmaturationofthefield.Ithinkthereisfinancialeconometricswhichismorecomplicatedormoreabstractthanwhatisanaturalcandidateforthemainfinancejournals.Ontheotherhand,Ithinkalotoffinancialeconometricsendsupappearingineconomicsandeconometricsjournalsratherthaninthefinanceorfinancialeconometricsjournals.FXD:Whatdoyouthinkaboutthecommunicationingeneralbetweenwhatyoumightcallfinancialeconometriciansandthebroaderempiricalfinancecommunity?RFE:Ithinkthereisabiggap.FXD:Why,andwhatcanwedotonarrowit?RFE:Well,thereisprobablyagapbecausethecultureisdifferent.Empiricalfinancepeopletypicallycomefromfinancedepartmentsandeconometricianstypicallycomefromeconomicsdepartments,andeachseestheotherasrelativelyunsophisticated.Empiricalfinancepeopleseetheeconometriciansastremendouslyunsophisticatedpeople,becausetheydon’tknowhowthemarketsworkandhowthedataisconstructedandwhataretheimportantquestions.Ithinkcross-fertilizationistremendouslyvaluable.That’swhyIhadconferencesinSanDiegoquiteafewtimeswhereItriedtogethalfoftheaudiencetobefinancepeopleandhalfoftheaudiencetobeeconometricians,andtogetthemtotalktoeachother.FXD:Threeofthepillarsofmodernfinancialeconometricsareassetpricing,portfolioallocationandriskmanagement.Whatdoyouthinkaretheinterestingquestionsforfutureresearchinthoseareas?RFE:IguessIthinkofyourthreepillarsasallbeingassetpricing,becauseassetpricesaredeterminedbysometradeoffbetweenriskandreturns,nomatterwhatkindofmodelyouhaveinmind.Ithinkassetpricingisanareathatappealstoeconometricians,becausethedataisverygood,andthetheoriesmakestrongpredictions.SoIthinkthatthosearedifferentwaysoflookingattheassetpricingproblemandIthinktheyareallveryinteresting.Ithinkthatriskmanagementhasprovidedgreatimpetustofinancialeconometrics,becauseitisarealproblemthatpeopletrytosolveeveryday,andIthinkitsextensionstocreditriskandliquidityriskarealsoveryfruitfulareasforfinancialeconometricresearchwhichremainunderdeveloped.17 VI.NewYorkUniversityandNewYorkCityFXD:YourecentlymovedtotheSternSchoolofBusinessatNewYorkUniversity.Howdoyoufindtheresearchenvironmentinabusinessschoolasopposedtoaneconomicsdepartment?RFE:Oneofthefascinatingthingsforme,nowbeingintheSternSchoolatNYU,istohaveallthesefinancecolleagues.Itreallygivesyouadifferentperspectiveontheinterestingquestionsandthequalityofthedataandwhatarethekindsofissuesyouhavetodevelopyourmodelsfor.FXD:Whatdoyouthinkabouttheenvironmentfortraininggraduatestudents,ingeneral,ineconomicsdepartmentsversusbusinessschools?RFE:Idon’tknowenoughbusinessschoolstomakeageneralstatement,butitseemsthatmostbusinessschoolsareclearlymuchmorefocusedontheMBAprogramthanonthePh.D.program,whereasthemissionofeconomicsdepartmentsthatIknowofistypicallynotatallfocusedonmasterstudentsbutonPh.D.students.SoitseemstomethatPh.D.traininghappensverylargelyineconomicsdepartmentsasopposedtobusinessschools.Thatbeingsaid,sometoppeopledocomefrombusinessschools.FXD:ThereisarealissuethatPh.D.studentshavetofacenow,muchmoresothantwentyyearsago--Ph.D.studentsineconometricsandfinancialeconometricsinparticular--whichiswhethertheywantjobsinbusinessschoolsorineconomicsdepartments.Whatdoyouseeastherelevantaspectsofthesituationandhowshouldstudentsdecide?RFE:ThisisverymuchrelatedtowhatIwastalkingaboutbefore,whichisthedifficultyofbridgingthegapbetweenthefinancecommunityandtheeconometricscommunity.AndIthinkthatisanissuethatgraduatestudentsaregoingtoface.IftheygettheirPh.D.ineconometrics,theymightverywellendupfindingajobinabusinessschool.But,itisnotaneasystep,somebusinessschoolsareveryreticenttohirenon-businessschooltrainedPh.D’sbecauseofexactlythisdividethatwe’vebeentalkingabout.IfindthatmanyofmyPh.D.studentsnowworkinginabusinessschoolsinitiallygotajobinaneconomicsdepartmentandthenafteracoupleofyearsmovedtoabusinessschool.Sotheywoulddoitsidewaysbutnotstraightahead.SowhenItalktoaPh.D.student,Itypicallyaskthem,aretheyinterestedinajobinabusinessschoolorinaneconomicsdepartment?Tosomeextentthatshapestheirdissertationtopic.Idon’tthinkthatisunreasonable,andIthinktherearemanydissertationtopicswhichwouldgobothways,althoughtherearecertainlyquiteafewtopicsthatwouldonlybeinterestinginabusinessschoolsorwouldonlybeinterestinginaneconomicsdepartment.FXD:ThestatisticsdepartmentatNYUisinthebusinessschool.Whatdoyouthinkistheroleofastatisticsdepartmentinabusinessschoolasopposedtoastatisticsdepartmentelsewhereintheuniversity?Forexample,atbothNYUandPennthe(only)statisticsdepartmentisinthebusinessschool.Shouldstatisticsdepartmentsinsuchsituationseffectivelybeeconometricsdepartments?RFE:Statdepartmentshavealwaysbeenpoliticalandhencethequestionisverycomplicated.Sometimesstatdepartmentsareinmathdepartments,inwhichcasetheybecomeverytheoreticalandnotveryuseful.Butassoonastheymoveintothesubjectareas,thentheyareincompetitionwiththesubjectarea.ButcertainlyIthinkitmakessenseforstatisticiansinbusinessschoolstobeinvolvedinfinancialeconometrics.Thentheycanmaintaintheirmissionasstatdepartments,andalsodosomethingusefulforthebusinessschool.FXD:Let’smovefromNYUtoNYC.NewYorkandLondonarethefinancialcapitalsoftheworld.DoesthataspectofbeinginNewYorkinfluenceyourresearch?18 RFE:ItypicallydoresearchonproblemsIthinkareinterestingandwherethereareintellectualpayoffs,butIammotivatedinmypayoffsbyproblemsthatIthinkpeoplewouldreallywanttosolve.OverthelastfiveorsoyearsI’vedonealotofworkinmarketmicrostructure,andI’veneverfoundanybodyinthefinancialmarketswhoisveryinterestedinit.ButinNewYorkI’vediscoveredthatwithinthecitytherearealotofpeoplewhoaretryingtosolveexactlytheproblemsthatIthinkareinteresting,whereasinotherplacespeopledon’treadilyseethat.Theydon’tworkonthetimescaleofmarketmicrostructure,theydon’tworkontheactualvolumescaleofthemarketmaker.AndsoreallyNewYorkisuniqueinbeingabletoprovideasettingwheresomeofmyresearchactuallyfindsitsnaturalplace.So,Iamhavingagreattimehere,Imustsay.FXD:Whatdoyouthinkoftheinteractionbetweenconsultingandresearch,andhowdoesNewYorkfactorintothat?RFE:Ithinkthatresearchthathasnoapplicationissortofboring.Andyet,ifyoudotoomuchconsultingwithnoresearchimplications,thatisboringtoo.SoIthinkthereisreallyanicebalancethatyoucan,ifyouarelucky,maintainwhereyourresearchinformsyourconsultingandyourconsultinginformsyourresearch.AndsoIamalwaysmuchmoreenthusiasticaboutconsultingwhenpublicationoftheresultsisanaturaloutcome.Itissurprisinghowmanyconsultingprojectswantexactlythat.Theywanttobringinanacademic,becausetheywanttopublicizewhatthey’vefoundandwhattheyareinterestedin.Thatismyfirstchoiceinconsulting.Ithinkthatactuallyenrichesbothacademicandconsultingarrangements.FXD:We’redrawingtoaclose.Arethereanyconcludingremarksthatyouwouldliketoadd?RFE:JustthatIthinkitisanexcitingtimetobestudyingfinancialeconometrics.Oneofthethingsinfinancialmarketsthatmakesitevenmoreinterestingtostudyeconometricsisspeed.Financialmarketsaregettingmoreandmorecomputeroriented,theyaremovingfasterandfasteranditisgettingtobeimpossibleforanindividualtokeepup.Anindividualtraderormarketmakercan’tactuallysurveyallthepossibilitiesandmakeoptimaldecisions.Thatforcesyoutogotothecomputeranddostatisticalthings.So,myfeelingisthat,inthefuture,financialeconometricsisgoingtosetupautomatedmarketmakersandautomatedbrokersandtraderswhoinfacthavestrategieswhicharedesignedtoaccomplishwell-definedobjectives,inwell-definedmarketenvironments.FXD:Whenyousayautomatedmarketmakers,thisbasicallymeanselectronicmarketsusingalgorithmstomatchbuyersandsellers?RFE:Right,butifyouplaceyourorderwithanelectronicbroker,heneedstobeabletosurveymarketsallovertheworld,someofwhichareopen,someofwhichareclosed.Andheneedstobeabletoassessdifferentwaysofpurchasingaparticularcommodity,forexampleasanADRorasindexfutures.Andanindividualbrokerdoesn’treallyhaveaccesstothat.Thescreensimplycan’tconveyallthatinformation.SoIthinkthereisscopeforstatisticaloptimizing,whichwillworkprettywell.It’sreallynotaquestionofdesigningabetterchessplayer;rather,it’saquestionofrecognizingwhattheuncertaintiesareandmakingthebestdecisionsgiventheuncertainties.19 VII.TheFutureofEconometricsFXD:What’syourviewontheinteractionbetweentheoryanddataintheadvancementofscience?RFE:Ithinkit’sthebestpartofourprofession.Theideathatyoucanbuildmodelsfromtheoryandthatyoucanbuildmodelsfromdataandworktomakethemmeshisreallywhateveryeconometrician’ssupposedtodo,andIthinkit’swhatourprofession’saboutandIthinkit’stoobadifyoutakeeitherofthoseingredientsoutofit.Manypeoplewouldthinkthatmyworkwaseithernotgroundedenoughintheoryormaybenotgroundedenoughindata,butIreallythinkthatit’sthatsubtlebalancebetweenthetwothatmakestheimportantcontributions.FXD:Iagree.Butitoftenseemstomethateconometriciansroutinelyviewpartofwhatthey’resupposedtodoaspayingattentiontotheory,forgoodreason,butthatveryfewtheoristsviewpartofwhatthey’resupposedtodoaspayingattentiontothedata.Whatdoyouthinkofthatassertion?RFE:I’vebeenaskedbytheorists“What’stheempiricalevidenceonthisquestionorthatquestion?”ButImustadmit,notveryoften.Ithinkthatthebesttheorymusthavedataandstylizedfactstosupportitsimportancejustlikethebesteconometricworkhasgottohavetheorytosupportit.Iamskepticalofempiricalworkthatspendsalotoftimederivingthemodelfromtheoryandthendoesn’ttesttoseewhetheritactuallyfitsthedata.Ithinkthatyou’veonlystartedtheresearchatthatpoint.AlmosteverytimeI’vedoneanempiricalprojectI’vefoundthatthedatahadsomethingsurprisinginitandIthinkthatthebestworkisworkthatlooksatthatsurprisinginformation,figuresoutwhethertotakeitseriously,andthenaltersthetheoryinsomewaytobeconsistentwiththeempiricalresults.Amodelpurelybornoftheorydoesn’thavethatstrength.FXD:SanDiegoisobviouslyakeycurrentcenterofeconometricsresearch.Whatotherpocketsofintellectualactivityintrigueyou,andwilltheybestableinthelongrun?RFE:BerkeleyandYaleareverystrongtoo.WewereveryluckyactuallyatSanDiegobecausewehadalotofstability,reallyexcellentfaculty,excellentgraduatestudents,andtremendoussupportbytheadministrationinbringingingoodgraduatestudentswhowanttodoeconometricsandsupportingtheeconometricsprogramandnotthinkingofitasbeingsomethingthat’stoobigortoopowerfulorsomethinglikethat.IthinkthesamethinghashappenedatYale.Idon’twanttocompareitwithSanDiego,butIthinkYalehasthemoststimulatingtimeseriesprograminthecountry.Therearealotofotherplaceswithgoodgroupsdoingcross-sectionalmodelingandnon-parametrics,andthatwholeclassoftoolsusedinlaborandindustrialorganization.IthinktheCambridgeareawithHarvard/MITreallyisexcellentinthatareaofeconometrics.FXD:Andwhatofthefutureofeconometricsitself?Thetime-serieshalfoftheHandbookofEconometricsthatyouandDanMcFaddeneditedwasagreatdistillationofthe‘80sand’90s.Butwherewillwebetenyearsfromnow?RFE:IthinkthatanawfullotoftheeconometricsIthinkwe’reworkingonthesedaysandinthefuturewillconcernnonlinearityofonesortoranother.ButIthinkthattheclassofnonlinearmodelsissogeneral,thatgeneraltreatmentsareboring;insteadIprefernonlinearmodelstailoredtoparticularsituations.AndIthinkthemostcommontypes,themostsuccessfultypes,ofnonlinearitiesarewhenthenonlinearityisactuallyassociatedwiththedependentvariable.OneinterpretationoftheARCHmodelsisthatitisassociatedwithdependantvariable,asamodelforsquaredreturns.Otherimportantnonlinearmodelslikethatarelogit,probitandrelatedmodels,whichareclearlynonlinearbecausethedependantvariableisdiscreteorcensored.Durationarealsonaturallymodelednonlinearly,soIthinkthattherewill20 beagrowingcollectionofnonlinearmodels,butIwon’tbetoosurprisedifwefindthatthey’remorefocusedondifferenttypesofdataandanalysis.AndIwouldalsothinkthattherearelotsofinterestinggeneralizationsofMarkov-switchingmodelsthatcouldbeusefullyentertained.FXD:Whataboutthefutureoffinancialeconometricsvs.macro-econometrics?Acolleaguejokedtometheotherdaythattime-serieseconometricianshavewonfinancebutlostmacro.Doyouagree?RFE:Ithinkthatthedeclineofempiricalmacroistemporary.Imean,Ithinkthere’snosubstituteforempiricalmacroeconomicsandmaybethemodelsinthepastweretoosimple,butIjustcan’tbelievethatyoucanhaveaviablemacroeconomicprofessionwithoutseriousempiricaltimeserieseconometricanalysis,soIthinkthatempiricalmacrowillbeback.FXD:Thankyou,Rob.RFE:Thankyou,Frank.21