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Interview with Lars Peter Hansen InterviewWith Lars PeterHansen 1.Eric Ghysels and Alastair Hall (Editors): How did you aspredictors of future spot rates. When the forward cometo be interested in estimation based on moment contractinterval exceeds the sampling interval, tem- conditions? poraldependence is induced.Given the serial correla- tionin thedisturbance term, many applied researchers LarsPeter Hansen (L.P .H.): As agraduatestu- atthe time thought the right thing to do was touse a dentat the University of Minnesota, I hadthe opportu- standardgeneralized least squares (GLS)-type correc- nityto take classes from ChrisSims andT omSargent. tion.In fact, while least squares remains consistent, Bothemphasized the idea that dynamic econometric thelack of strictexogeneity of theregressors prevents modelsshould be viewed as restrictions on stochas- GLS from beingconsistent. This tripped up several ticprocesses. Sims’ s classroomdevelopment of large- researchersand was theimpetus for myoriginal least sampleeconometrics broke with the more conventional squarespaper. In addition to the Brown and Maital viewof thetime of focusingon modelswith exogenous paper,which with Sims’ s inuence proceeded cor- regressorsor instrumentalvariables (IVs). His workon rectly,Hodrick quickly informed authors of thepapers causalityhad emphasized the testable restrictions on submittedto the Journalof PoliticalEconomy that the stochasticprocesses of thenotion of strictexogeneity. GLS stylecorrection that they had used was invalid. Theidea of embedding estimation and testing prob- Myleast squares paper was rejectedat Economet- lemswith a stochasticprocess framework provedto be rica becauseit failed to be ambitious enough. This averyuseful starting point. Although this is common irritatedme and made me restructure the arguments ineconometrics today, it was notat the time I was a inmuch greater generality. I hadseen recent lecture graduatestudent. notesof Sims thatdescribed a familyof generalized Iwas exposedto nonlinear estimation and testing methodof moments (GMM) estimators,indexed by a problemsin Sims’ s graduatecourse. Sims loved to matrixthat selected which moment conditions to use experimentwith new material and proofs in class, and inestimation. Sims treatedtime series applications, Ilearnedmuch from llingin details and some holes butwith a focuson martingaledifference disturbances. inlecture notes. His nonconventionalteaching style Iadoptedthis formulation to present a moregeneral was valuablefor me. centrallimit approximation for estimatorswith Sims’ s WhileI was workingon my dissertation on encouragement.I learnedsubsequently from areferee exhaustibleresources, I becameinterested in central thatthe selection matrix idea had been used by Sargan limittheory for temporallydependent processes. This (1958,1959) in studies of linear and nonlinear instru- interestpredated the excellent book by Halland Heyde mentalvariables estimators. I was abitembarrassed (1980).Sims hadmade reference to work by Scott thatI hadnot cited the very nice Sargan (1958) paper (1973),but the central paper for mewas thatof Gordin inmy original submission. This paper provided the (1969).(Scott indeed cites Gordin, which is how I impetusfor myanalysis of the limiting distribution becamefamiliar with that work.) Gordin showed how ofsample moment conditions evaluated at parameter toconstruct a martingaleapproximation to a wide estimators. classof stationary ergodic processes. It thus extended Sinceprevious referees complainedabout my casual theapplicability of earliermartingale central limit the- treatmentof consistency, I addedsome speci city by oryby Billingsley (1961) and others to processeswith usinga quadraticform constructionas in the statis- arichtemporal dependence structure. ticsliterature on minimumchi-squared estimation and 2. Editors: Withhindsight, it can be seen that your paper inAmemiya’ s (1974,1977) treatments of nonlinear (Hansen1982) has had considerable in uence on the two-and three-stage least squares. While developing practiceof econometrics. What was your perspective on consistencyresults, I becameinterested in the role of thework at thetime? Can you also tell us aboutthe initial compactnessin consistency arguments and explored reactionof others(including referees!) to yourpaper? alternativeways of justifying consistency based on tail characterizationsof the objective functions. L.P.H.: Ioriginallywrote a paperon least squares estimationwith temporally dependent disturbances. 3. Editors: Yourpapers with Ken Singleton in Economet- Themotivation for thispaper was simple.As an rica(Hansen and Singleton 1982) and Bob Hodrick in editor of Econometrica ,Sims was handlinga paper theJournal of P oliticalEconomy (Hansen and Hodrick 1980)were very in uential in demonstrating the poten- byBrown and Maital (1981) on assessing the ef - tialpower of GMM inapplications. Can you tell us how ciencyof multiperiod forecasts. The multiperiod thesecollaborations came about? natureinduced temporal dependence in the distur- banceterm. Sims urgedme to proceed quickly to get somethingwritten up as a paperthat could be cited © 2002 American StatisticalAssociation andused. Hodrick (my colleague at Carnegie Mellon Journal of Business &Economic Statistics atthe time) made me aware ofsimilar problems in October2002, Vol.20, No.4 theliterature on the study for forward exchangerates DOI10.1198/ 073500102288618577 442 InterviewWith Lars PeterHansen 443 L.P.H.: BobHodrick and I beganour discussion 5. Editors: Inthe mid-1980s, you worked on the problem ofeconometric issues when I describedto him the ofcharacterizing the optimal instrument in generalized pitfallsin applying GLS ineconometric equations IV estimation.What led you to work on thisproblem and thatcome from multiperiodforecasting problems. He whatis your perspective on this literature today? immediatelyshowed me working papers in the liter- L.P.H.: Iworkedon this problem because many atureon forward exchangerates in which GLS was applicationsof GMM estimation were motivatedby appliedas aremedyfor serialcorrelation. At thesame conditionalmoment restrictions or had the following timehe was educatingpeople in international nance, timeseries structure. Any time an IV existed,lags of heand I beganworking on our own analysis of for- theIVs were alsovalid instruments. As inmy other ward exchangerates by applying least squares and work,I was particularlyinterested in time series prob- adjustingthe standard errors. lems.Strict exogeneity of IVs alsoallows for leading BobHodrick was atCarnegie Mellon when I arrived valuesof IVs tobe valid instruments, but this orthog- there.Ken Singleton came to Carnegie Mellon after onalitywas notin my econometric formulation. Prior me,and after I hadwritten my GMM paper. Both of tomyGMMpaper, Robert Shiller (1972) had empha- usknew Hall’ s workon consumption(Hall 1978), and sizedthat in rational expectations models, omission of Kencame back from aconferenceafter hearing an conditioninginformation gave rise to orthogonal dis- underappreciatedpaper by Grossman and Shiller .A turbance.In a timeseries problem, this Shiller notion stripped-downversion of this paper was subsequently ofan error termoften had the feature that this error publishedin the AmericanEconomic Review (Gross- termwas orthogonalto arbitrary past values of vari- manand Shiller 1981). Singleton suggested that the ablesin a conditioninginformation set used by an consumptionEuler equation could be fruitfully posed econometrician.This same argument will not work for asa conditionalmoment restriction and our collabora- arbitraryleading values of the conditioning informa- tionbegan. After Iarrivedat Chicago, Jim Heckman tion,because economic agents will not have seen these showedme MaCurdy’ s microeconomiccounterpart to values. Hall’s paper(MaCurdy 1978). Ken’ s andmy second Myinitial work in this area (Hansen 1985) used (andempirically more interesting) paper published in martingaleapproximations to give lower bounds on the Journalof PoliticalEconomy (Hansenand Single- theef ciency of a classof feasible GMM problems. ton1983) came about by our construction of a maxi- Informulating this problem, I hadto extend the selec- mumlikelihood counterpart to the GMM estimation in tionapproach of Sargan, Sims, and others to cases in our Econometrica paper.Given the more transparent whichthe number of underlying moment conditions natureof howpredictability had implications measur- isin nite. This is a naturalframework withinwhich ingand assessing risk aversion, this project became tothink about estimation problems in which nonlin- moreambitious and took on a lifeof its own. earfunctions of IVs arevalid IVs andparticularly for 4. Editors: Whatis yourperspective on howGMM tsinto timeseries problems in which lagged values of IVs thewider literature on statistical estimation? remainvalid instruments. This gave rise to an explic- itlyin nite-dimensional family of GMM estimators. L.P.H.: Ispentsome time on this question in Attainingthis ef ciency, especially in a timeseries myrecent contribution to the Encyclopediaof the problem,is moreproblematic. There is aneedasymp- Socialand Behavioral Sciences (Hansen2002). The toticallyto useinformation arbitrarily far intothe past. quadratic-formcriterion that I usedto formulate con- WhileI was workingin this area, I becameaware sistencycertainly has its origins in the minimum chi- ofclosely related work in engineering aiming to con- squaredestimators used to produce estimators that structonline estimators that are easy to compute (see, arestatistically
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