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HandbookofComputationalEconometrics
HandbookofComputational Econometrics
Editedby DavidA.Belsley
BostonCollege,USA
ErricosJohnKontoghiorghes
UniversityofCyprusandQueenMary,UniversityofLondon,UK
A John Wiley and Sons, Ltd., Publication
Thiseditionfirstpublished2009 2009,JohnWiley&Sons,Ltd
Registeredoffice
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Handbookofcomputationaleconometrics/editedbyDavidA.Belsley,ErricosKontoghiorghes. p.cm.
Includesbibliographicalreferencesandindex.
Summary:“HandbookofComputationalEconometricsexaminesthestateoftheartofcomputationaleconometrics andprovidesexemplarystudiesdealingwithcomputationalissuesarisingfromawidespectrumofeconometricfields includingsuchtopicsasbootstrapping,theevaluationofeconometricsoftware,andalgorithmsforcontrol,optimization, andestimation.Eachtopicisfullyintroducedbeforeproceedingtoamorein-depthexaminationoftherelevant methodologiesandvaluableillustrations.Thisbook:Providesself-containedtreatmentsofissuesincomputational econometricswithillustrationsandinvaluablebibliographies.Bringstogethercontributionsfromleadingresearchers. Developsthetechniquesneededtocarryoutcomputationaleconometrics.Featuresnetworkstudies,non-parametric estimation,optimizationtechniques,Bayesianestimationandinference,testingmethods,time-seriesanalysis,linearand nonlinearmethods,VARanalysis,bootstrappingdevelopments,signalextraction,softwarehistoryandevaluation.
Thisbookwillappealtoeconometricians,financialstatisticians,econometricresearchersandstudentsof econometricsatbothgraduateandadvancedundergraduatelevels”–Providedbypublisher.
Summary:“Thisproject’smainfocusistoprovideahandbookonallareasofcomputingthathaveamajorimpact, eitherdirectlyorindirectly,oneconometrictechniquesandmodelling.Thebooksetsouttointroduceeachtopicalong withamorein-depthlookatmethodologiesusedincomputationaleconometrics,toincludeuseofeconometricsoftware andevaluation,bootstraptesting,algorithmsforcontrolandoptimizationandlooksatrecentcomputational advances”–Providedbypublisher.
ISBN978-0-470-74385-0
1.Econometrics–Computerprograms.2.Economics–Statisticalmethods.3. Econometrics–Dataprocessing.I.Belsley,DavidA.II.Kontoghiorghes,ErricosJohn. HB143.5.H3572009 330.0285’555–dc22
2009025907
AcataloguerecordforthisbookisavailablefromtheBritishLibrary.
ISBN:978-0-470-74385-0
TypeSetin10/12ptTimesbyLaserwordsPrivateLimited,Chennai,India PrintedandboundinGreatBritainbyAntonyRowe,Ltd,Chippenham,Wiltshire.
Toourfamilies
2.4.2Statisticaldistributions
ManfredGilliandPeterWinker
3.1Traditionalnumericalversusheuristicoptimizationmethods
3.1.1Optimizationineconometrics
3.1.2Optimizationheuristics
3.1.3Anincompletecollectionofapplicationsofoptimization heuristicsineconometrics
3.1.4Structureandinstructionsforuseofthechapter
3.3.1Optimizationasstochasticmapping
3.3.2Convergenceofheuristics
3.3.3Convergenceofoptimization-basedestimators
PanosParpasandBer¸cRustem 4.1Introduction
4.2.1Subgradientof (x) andbasiciteration
4.2.3Choiceof c and µ
4.4.1Analgorithmforexpectedvalueoptimization
4.5Evaluationframeworkforminimaxrobustpoliciesandexpected
5Nonparametricestimation
RandR.Wilcox
5.1Introduction
5.3Nonparametricregression
5.3.1Anillustration
5.3.2Multiplepredictors
5.3.3Someillustrations
5.3.4Estimatingconditionalassociations
5.4.1Somemotivatingexamples
5.4.2Abootstrap-t method
5.4.3Thepercentilebootstrapmethod
5.4.4Simpleordinaryleastsquaresregression
5.4.5Regressionwithmultiplepredictors
6Bootstraphypothesistesting
JamesG.MacKinnon
6.1Introduction
6.2BootstrapandMonteCarlotests
6.3Finite-samplepropertiesofbootstraptests
6.5.1Resamplingandthepairsbootstrap
6.5.2Theresidualbootstrap
6.5.3Thewildbootstrap
6.5.4BootstrapDGPsformultivariateregressionmodels
6.5.5BootstrapDGPsfordependentdata
6.6Multipleteststatistics
6.6.1Testsforstructuralchange
6.6.2Point-optimaltests
6.6.3Non-nestedhypothesistests
6.7Finite-samplepropertiesofbootstrapsupF tests
7Simulation-basedBayesianeconometricinference:principles andsomerecentcomputationaladvances215 LennartF.Hoogerheide,HermanK.vanDijkandRutgerD.vanOest
7.1Introduction
7.2AprimeronBayesianinference
7.2.1MotivationforBayesianinference
7.2.2Bayes’theoremasalearningdevice
7.2.3Modelevaluationandmodelselection
7.2.4ComparisonofBayesianinferenceandfrequentistapproach232
7.3Aprimeronsimulationmethods
7.3.1Motivationforusingsimulationtechniques
7.3.2Directsamplingmethods
7.3.3Indirectsamplingmethodsyieldingindependentdraws236
7.3.4MarkovchainMonteCarlo:indirectsamplingmethods yieldingdependentdraws 249
7.4Somerecentlydevelopedsimulationmethods
7.4.1Adaptiveradial-baseddirectionsampling
7.4.2Adaptivemixturesof t
8Econometricanalysiswithvectorautoregressivemodels
HelmutL¨utkepohl
8.1Introduction
8.1.1Integratedvariables
8.2.1ThelevelsVARrepresentation
8.3.1EstimationofunrestrictedVARs
8.3.2EstimationofVECMs
8.3.3Estimationwithlinearrestrictions
8.3.4BayesianestimationofVARs
8.4.1Choosingthelagorder
8.4.2ChoosingthecointegratingrankofaVECM
8.5.1Testsforresidualautocorrelation
8.5.2Testsfornon-normality
8.5.3ARCHtests
8.5.4Stabilityanalysis
8.6.1Knownprocesses
8.7.1Intuitionandtheory
8.7.2TestingforGranger-causality
8.8StructuralVARsandimpulseresponseanalysis
8.8.1LevelsVARs
8.8.2StructuralVECMs
8.8.3Estimatingimpulseresponses
8.8.4Forecasterrorvariancedecompositions
9.4Theconceptsofthefrequencydomain
9.4.1Theperiodogram
9.4.2Filteringandthefrequencydomain
9.4.3AliasingandtheShannon–Nyquistsamplingtheorem
10.3.1Weakwhitenoiseandstrongwhitenoisetesting
10.3.2Testinglinearityagainstaspecificnonlinearmodel
10.3.3Testinglinearitywhenthemodelisnotidentifiedunderthenull392 10.4Probabilistictools
10.4.1Astrictstationaritycondition
10.4.2Second-orderstationarityandexistenceofmoments
10.4.3Mixingcoefficients
10.5.2AsymptoticdistributionoftheQMLE
10.5.3Identificationandmodeladequacy
10.6.1Forecastgeneration
10.6.2Intervalanddensityforecasts
11.3.1Transportationnetworkequilibriumwithtraveldisutility functions
11.3.2Elasticdemandtransportationnetworkproblemswithknown traveldemandfunctions
11.6.1Theclassicaloligopolyproblem
11.7.2Theprojecteddynamicalsystem
11.8Dynamictransportationnetworks
11.8.1Thepathchoiceadjustmentprocess
11.8.2Stabilityanalysis
11.8.3Discrete-timealgorithms
11.8.4Adynamicspatialpricemodel
11.9Supernetworks:applicationstotelecommutingdecisionmaking andteleshoppingdecisionmaking
ListofContributors
AlessandraAmendola,DiSES,UniversityofSalerno,84084Fisciano(SA),Italy
ChristianFrancq,EQUIPPE-GREMARS,Universit ´ edeLille,BP60149,59653
Villeneuved’Ascq,France
ManfredGilli,DepartmentofEconometrics,UniversityofGenevaandSwissFinance Institute,BdduPontd’Arve40,1211Geneva4,Switzerland
LennartF.Hoogerheide,CenterforOperationsResearchandEconometrics,Universit ´ e CatholiquedeLouvain,VoieduRomanPays34,1348Louvain-la-Neuve,Belgiumand EconometricandTinbergenInstitutes,ErasmusUniversityRotterdam,Burg.Oudlaan50, 3062PARotterdam,TheNetherlands
HelmutLutkepohl,EconomicsDepartment,EuropeanUniversityInstitute,VillaSan Paolo,ViadellaPiazzuola,43,I-50133Firenze,Italy
JamesG.MacKinnon,DepartmentofEconomics,Queen’sUniversity,Kingston,Ontario, K7L3N6,Canada
B.D.McCullough,DepartmentofEconomics,LeBowCollegeofBusiness,DrexelUniversity,Philadelphia,PA19104,USA
AnnaNagurney,DepartmentofFinanceandOperationsManagement,IsenbergSchool ofManagement,UniversityofMassachusetts,Amherst,MA01003,USA
PanosParpas,DepartmentofComputing,ImperialCollegeofScience,Technology& Medicine,180Queen’sGate,LondonSW72AZ,UK
D.StephenG.Pollock,DepartmentofEconomics,UniversityofLeicester,LeicesterLE1 7RH,UK, and 12GladsmuirRoad,LondonN193JX,UK
CharlesG.Renfro,AlphametricsCorporation,11EastPrincetonRoad,BalaCynwyd, PA19004,USA, and 601West113thStreet,#12GNewYork,NY10025,USA
Berc¸Rustem,DepartmentofComputing,ImperialCollegeofScience,Technology& Medicine,180Queen’sGate,LondonSW72AZ,UK
HermanK.vanDijk,EconometricandTinbergenInstitutes,ErasmusUniversity Rotterdam,Burg.Oudlaan50,3062PARotterdam,TheNetherlands
RutgerD.vanOest,DepartmentofMarketing,TilburgUniversity,Warandelaan2,5000 LETilburg,TheNetherlands
RandR.Wilcox,DepartmentofPsychology,UniversityofSouthernCalifornia,Los Angeles,CA90089-1061,USA
PeterWinker,FacultyofEconomicsandBusinessAdministration,UniversityofGiessen, LicherStrasse64,35394Giessen,Germany
Preface
Thisvolumecompriseselevenchaptersdealingwithavarietyofaspectsofcomputational econometrics.Computationaleconometricsisadisciplinethat,tothosewhodoit,is easilyunderstood,but,tothewiderfield,appearstobedifficulttodefine.Many(most) top-leveleconometricsjournalsignorethesubjectaltogether,andmosteconometrics textbooksgiveitshortshrift,providing,atbest,practicallyuselesstreatments.Yetits substanceistheveryheartandsoulofappliedeconometricpractice,theessentialmeans bywhichmosteconometricstudiestakeplace.Theresult,asismadeclearinseveralof thechaptersinthishandbook,isthatthecomputationaltoolscommonlymadeavailable tocarryouteconometricstudiescanbefarfromcuttingedge,and,worse,quiteillsuited forproducingthedesiredresults.Amajorgoalofthishandbook,then,istoexaminethe stateoftheartofcomputationaleconometricsandtoprovideexemplarystudiesdealing withcomputationalissuesarisinginawidespectrumofeconometricfields.
Econometricshas,byitsverynature,alargestatisticalcomponent.Buteconometriciansdifferfromstatisticiansinatleastoneimportantaspect:statisticiansareessentially mathematiciansdealingwithprobabilisticphenomenanotnecessarilyrelatedtoanyspecificdiscipline,whereaseconometriciansaretrainedinbothstatistics and thediscipline ofeconomics.Theybringtothetable,therefore,aparticularpointofviewthatshapes thekindsofstudiestheyfindofinterestandthekindsoftoolstheyfindappropriateto useandtodevelop.Thishasresultedinadisciplinewithaflavourofitsown,aflavour thatisinheritedbythoseengagedinthecomputationalaspectsofeconometrics.
Computationaleconometricshasseveralmainsubfields,allrepresentedinthishandbook.Theseinclude:thedevelopmentofcomputationaltechniquesforcarryingout econometrics,suchasestimationornumericalmethods;studiesinwhichthecomputeris thecentralplayingfield,suchasMonteCarloexperiments,geneticalgorithms,network studies,orestimationmethodslikesimulatedannealing;studiesinwhichthecomputer doesthenecessaryheavylifting,suchasnonlinearestimationoflarge-scalesystemsor massivesimulations;andthedevelopmentofcomputationalenvironmentsinwhichto conducteconometricstudies,suchasGAMSorStata.Allsuchpotentiallydiversestudies fallintotherubricofcomputationaleconometrics,andthatisperhapsthereasonthefield issodifficulttodefine.Thishandbookcontainsstudiesinallthesecategories.Allattempt
toprovideaself-containedoverviewoftheirsubjectand,whererelevant,anaccessible technicaldevelopmentalongwithexamplesorillustrations.Theyshouldbeofvalueto thoselearningaswellastothosewellversedinthefield.
Econometricsoftware
CharlesG.Renfro
1.1Introduction
TheproductionanduseofeconometricsoftwarebeganattheUniversityofCambridge intheearly1950sasaconsequenceoftheavailabilitythereofthefirstoperative stored-programelectroniccomputer,theEDSAC(ElectronicDelayStorageAutomatic Calculator).Thismachinebecameavailableforacademicresearchstartinginorabout 1951[214,248,249].AmongthefirsttouseitweremembersoftheDepartmentof AppliedEconomics(DAE),someofwhomhadbeeninvitedtoCambridgebytheDirector,RichardStone.Fromthebeginning,theyemployedtheEDSACtoproducework thatremainswellregarded[8,77,124,195].Theyalsoappeartohavebeenthefirstto describeinprinttheworkadayprocessofusingastored-programcomputer[36].There, LucySlater,workingwithMichaelFarrell,wrotethefirstdistinguishableeconometric softwarepackage,aregressionprogram[14,224,225].However,theseeconomistswere notaloneintheirearlyadoptionofemergingcomputingtechnologies,forpreviously,in 1947,atoneofthefirstgatheringsofcomputerdesigners,theSymposiumonLarge-Scale DigitalCalculatingMachinery,WassilyLeontief[153]hadpresentedsomeofhisthen currentworkoninter-industryrelationshipstoprovideanexampleofachallengingcomputationalproblem.Heusedtheexistingelectromechanical‘MarkI’AutomaticSequence ControlCalculatoratHarvard,which,althoughnotactuallyastored-programelectronic computer,cannonethelessbedescribedasthefirst‘automaticdigitalcomputer’[248]. TheMarkIalsorepresentsIBM’sstartinabusinessitwaslatertodominate.
Atthetime,worldwide,thesemachinesweretheonlyautomaticcomputing devicesgenerallyavailableforresearch.Consequently,othercomputationallyinclined
economists,includingLawrenceKlein,ArthurGoldberger,andtheircolleaguesatthe UniversityofMichigan[87],stillusedelectromechanicaldesktopcalculators.However, in1954,thesemi-electronicIBMCardProgrammedCalculator(CPC)becameavailable tothemandwasfirstusedtoestimatemomentsinpreparationfortheestimationofthe parametersoftheKlein–Goldbergermodel[138].Afewyearslater,in1958–59,at whatwouldbecometheLawrenceLivermoreLaboratory,FrankandIrmaAdelmanwere thefirsttosolveaneconometricmodelusingacomputer,employinganIBM650[6, 7,139].Contemporaneously,possiblyattheIBMScientificCenterinNewYork,Harry Eisenpresswrotethefirstprogramtoperformlimitedinformationmaximumlikelihood estimation[60].Afewyearsearlier,withJuliusShiskininWashington,DC[218],he hadcreatedtheCensusX-11seasonaladjustmentmethodusingaUNIVAC(UNIVersal AutomaticComputer),anearrelativetotheEDSAC[214].ThisUNIVAC,firstinstalled attheUSBureauoftheCensusin1951,wasthefirststored-programcomputertobe soldcommercially.
Thisdescriptionof1950scomputerusebyeconomistspossiblyreadslikeaseriesof selectivelychosenexhibits,butactuallyitappearstobethecompleteearlyrecord,with theexceptionofworkbyothersattheDAE[14,15,44,195]andthestartofRobertSummers’MonteCarlostudyofestimatorproperties[235].Throughoutthe1950s,computers werescarce.Theywerealsoexpensivetouse–anhourofmachinetimecouldcostliterallytriplethemonthlysalaryoftheeconomistusingit[7].Itwasonlyduringthenext twodecades,startingintheearly1960s,thattheybegantoproliferateandeconomists morecommonlybecameusers[30,52].Anumberofeconometricfirstsoccurredduringthe1960s,includingtheimplementationofavarietyofincreasinglycomputationally complextechniques,amongthemtwo-andthree-stageleastsquares,seeminglyunrelatedregressionequations,andfullinformationmaximumlikelihood[204].Inaddition, beginninginabout1964,economistscreatedsomeoftheearliestlarge-scalecomputer databases,togetherwiththesoftwaretomanagethem[160–162].However,progress wasneitheruniformnoruniversal:eveninthemid-1960s,theWhartonmodel,adirect descendentoftheKlein–Goldbergermodel[31,127],wasstillbeingsolvedbyusingan electromechanicaldesktopcalculator[203,216].Itwasonlyduringthenextfewyears thateconomistsattheUniversityofPennsylvaniafirstusedanelectroniccomputerto solvemacroeconometricmodelsasnonlinearsimultaneousequationsystems[52,68,69, 216].
Asindicated,thelevelofsophisticationprogressivelyincreasedduringthisdecade. Muchofthisworkrepresentstheeffortsofindividuals,althoughfrequentlyinthecontext offormalresearchprojects[57,58,68,69,159,197].Ittypicallybeganwiththecreationofsinglepurposeprogramstoestimateparameters,managedatasets,andlatersolve macroeconometricmodels.However,towardstheendofthe1960s,withtheadventof time-sharingcomputers,thefirstnetwork-residentinteractiveeconometricsoftwaresystemsbegantobecreated[203,207],animportantstepinthedevelopmentofthemodern econometriccomputationalenvironment.Intheearly1970scameattemptstofocusthis research:inparticular,attheMITCenterforComputationalResearchinEconomicsand ManagementScience,economistsbegantodevoteconsiderableefforttothestudyof relevantcomputeralgorithms[29,48–50,120,147–150]andcloselyrelatedregression diagnostics[19,21,22].Followingtheseadvances,the1970ssawthedevelopmentof wide-areaonlinetelecommunications-linkedeconomicdatabase,analysis,andeconometricmodelingsystems,which,bytheendofthedecade,becameusedworldwide[3,4,
56,205,206].Asaresult,atthebeginningofthe1980s,economistswerereadyto adoptthethenemergingmicrocomputerand,bythemiddleofthatdecade,hadbegunto useitastheprimarylocusforanalyticalprocessing,includingby1985thesolutionof econometricmodelsof600andmoreequations[209].However,itwasonlyinlate1984 thatitbegantobecomecommonforeconometricmodelstobemountedonmorethana singlecomputer[203].
Buildinguponthesefoundationslaidinthe1960sandearly1970s,economistshave sincecreatednotonlysophisticated,targetedapplicationsbutalsospecializedeconometric modelingandprogramminglanguages,aswellasgenerallyapplicableeconometricsoftwareforparameterestimationandhypothesistestingthatcanbeusedwithtime-series, cross-section,andpaneldata.Ateachstage,thisworkhasaffectedthedisciplinary progressofeconomicsandeconometrics.Simultaneously,someofthisworkfedback intothemoregeneraldevelopmentofsoftware,includingoperatingsystems,spreadsheet packages(suchasVisiCalcandLotus1-2-3specifically),andavarietyofotherapplications[204].Last,butcertainlynotleast,becauseofthesubjectmatterofeconomics, econometricsoftwarehasplayedacriticalpartinthemanagementoftheperformance oftheworld’seconomies,initseffectbothonthetimelydisseminationofeconomic informationandonthedevelopmentofthemoderntoolsofappliedeconomics.Ofall disciplines,economicshasbeenoneofthosemostaffectedbytheuseoftheelectronic computer,andinturn,innosmallmeasure,thisusehashelpedtoenablethebroadly consistentexpansionanddevelopmentofbothindustriesandeconomies.
Fromthefirstavailabilityoftheelectroniccomputer,economistswereobviously primedtobecomeusers,raisingthequestion:Why?AreflectivecommentmadebyKlein in1950suggestsareason[134,p.12].ReferringtotheseminalCowlesCommissionwork andthemethodologicalprogressofthe1940s–andseeminglyunawareofwhatwould occurwithinthenextdecade–heratherpessimisticallyobservedthat:
Anannoyingproblemthatariseswiththenewmethodsisthelaboriousness andcomplexityofcomputation.Veryeconomicaltechniquesofdealingwith multiplecorrelationproblemshavebeenperfected,buttheycannolongerbe usedexceptinspecialcases wherethesystemisjustidentified.Unlesswe developmoreeconomicalcomputationalmethodsormoreefficientcomputing machines,theproblemswillremainbeyondthereachofindividualresearch workers.
Wereitnotforsuchpreservedcommentary,itmightnowbedifficulttoimaginethat itappearedatleasttosomeeconomistsatthebeginningofthe1950sthateconometric methodologyfacedaseriouscomputationalroadblock.Thesenseofinevitabilitythat hindsightprovidesmakesiteasytooverlooktheimportanceofthetimingoftheadoption oftheelectroniccomputerbyeconomists.Thedistancebetweenthattimeandoursis accentuatedbythewatershedeffectofthecreationofARPANET,theprecursornetwork totheInternet,inabout1970andtheequallypotentconsequenceoftheintroductionof thefirstmicrocomputersinthemid-1970s.
Oneofthemostsignificantdifferencesbetweenthenandnowisthat,inthoseearlier times,especiallyintheyearspriorto1975,itwasalmostrequisiteforanycomputer usertobeginbywritingsomecode,andthiswascertainlytrueinthoseinstancesin whichanapplicationmightinvolvenewtechniques.Thentherewassomuchaneedto
program,andcomparativelysomuchlesscomputerusethantoday,thatpracticallyany econometricsoftwarewrittenpriorto1975involvessomeaspectthatcanbedeclared a‘first,’oratminimumviewedasinvolvingsometypeofpioneeringeffort.Although therewerecertainlyinstancesofsharedsoftwareuseby(comparativelysmallgroupsof) economistsduringtheperiodbetween1960and1980[33,35,89,115,131,160,196, 222,223],itwasusualneverthelessthatanintendinghands-onusergenerallyneeded tolearntoprogram,atleasttosomedegree,butoftenataratherfundamentallevel. Untilatleastthemid-1970s,anappliedeconomistwishingtoemployacomputerwould commonlyeitherneedtostartfromscratch,or,atbest,beprovidedaboxofcards(or, sometimes,apapertape),ontowhichwerepunchedthesourcecodestatementsfora program–evenifby1975,perhapsearlier,itwasnotunusualforthe‘boxofcards’to havebeenreplacedbyamachine-readablecardimagefile.Specificcodechangeswere oftennecessary,atminimumtopermitdatatransformations.Forcalculationsassociated withaparticularapplication,asubstantialamountofnewcodingmightberequired. Today,incontrast,itisonlysomeoneoperatingatthedevelopmentalleadingedgeof econometricswhomayneedtobeproficientatprogramming,buteventhennotalways intheuseofacomputerlanguagesuchasAssembly,C++,C#,orFortran,orinsuch awaythatmightrequireunderstandingofthecomputer’soperatingsystemandspecific hardwareprotocols.
However,todeclarethebeginningofanewepochisnottosaythatalltheheavy liftinghasbeendone.Theyearofthefilm 2001:ASpaceOdyssey hascomeandgone, butwedonotyetconversecasuallywitharticulate,seeminglyintelligentcomputers,like HAL,norsimplydeclareinbroadoutline,viathekeyboardorsomeotherinterface,what wewishtodoandthenhaveitdone,automatically,effortlessly,andappropriately.In importantrespects,thecomputerstillremainsanewtechnology.Topresentareliable assessmentofthecurrentstateoftheart,itisthereforenecessarytoproceedcarefully, aswellastobeginbyestablishingaproperframework,soastobeabletodescribeand evaluatecurrentprogress.Forinstance,thereisausefuldistinctiontobemadebetween creatingsoftwaredesignedtoperformaspecifictaskversusdevelopingaprogramfora moregenerallydefinedpurpose,possiblyintendedforusebyothers.Aroutinemightbe writtenspecificallytocalculateanddisplayasetofparameterestimates.Alternatively, thegoalmightbetocreateaprogramtobeusedtobuilda‘model,’oraclassofmodels, orsomeothercomposite,possiblyquitecomplex,undertaking.Thefirstofthesecases involvesapurecomputationalproblem,thesuccessofwhichmightbeassessedbythe degreetowhichtheindividualcalculationsareaccurately,efficiently,andevenelegantly orperhapsquicklyperformed.Thisqualitativeevaluationcanalsoincludeadetermination ofthedegreetowhichtheresultsareinformativelyandevenattractivelydisplayed.Inthe second,moregeneral,case,whatisrequiredispotentiallymuchmoreelaboratecomputer codetoperformanintegratedseriesoftasks,notallofwhicharepurelycomputational problems.Thesetasksmightalsoincorporateoperationsnotlikelytobeimmediately classifiedaseithereconomicallyoreconometricallyrelevant.Suchoperations,which canincludethestorage,retrieval,andmanagementofdata,aswellasthedevelopment ofthehumaninterfaceofaprogram,areneverthelessasmuchapartofeconometric softwarecreationasistheprogrammingofanestimator.Furthermore,whetherornot theseelementsareindividuallyconsideredtobeeconometricallyinteresting,thefuture developmentofeconomicsandeconometricsmaydependuponasuccessfulsolutionto theproblemeachofthemposes.
Aperspectiveontheunderlyingissuescanbeobtainedbyconsideringtheusageof thecontrastingterms,‘computationaleconometrics’and‘econometriccomputing.’Achim Zeileis[252,p.2988]hasrecentlysuggestedthatthefirstoftheseistopically‘mainly about[mathematicalorstatistical]methodsthatrequiresubstantialcomputations’whereas thesecondinvolvesthealgorithmictranslationof‘econometricideasintosoftware.’Initially,economistsbegantousethecomputerasameanstoanend,simplytomake necessarycalculationsmorerapidlythancouldbedonemanually,withoutagreatdeal ofintrospection.Thislackofintrospectionhaslingered.Ageneralappreciationthatthe executionofthesecomputationscanhavedisciplinarilysignificantimplicationshasbeen slowtoemerge:‘simplycomputational’remainsacommonwave-of-the-handexpression usedtosuggesttheexistenceofonlyafewremaining,possiblylaborious,butessentiallystraightforwarddemonstrativesteps.Perhapsasaconsequence,theself-conscious considerationofsoftwareasadisciplinaryresearchtopichasbeenresistedalmostreflexively,evenwhilethecomplexityofeconometricideashasincreasedovertheyears. Economistsseemtofeelinstinctivelythatthespecificalgorithmicaspectsofeconometric softwaremostproperlyshouldbeconsideredfromtheperspectivesofcomputerscience oroperationsresearch,leavingtotheeconomicspecialist,theeconometrician,onlythe taskofspecifyingtheparticularformulastobeimplementedalgorithmically,butnotthe assessmentorevaluationoftheendresultnorthemannerofitsimplementation.What maybemostindicativeofthetendencyofeconomiststoregardeconometriccomputing aslogicallyseparableisthatbothtextbooksandthemoregeneraleconometricliteraturetypicallyonlyrefertotheexistenceofsoftware,withoutconsideringitsparticular aspectsandnature.Thespecificissuesofsoftwarecreation,includingeventhosemost obviously‘econometric’incontent,haveseldombeenconsideredandevaluatedpubliclybyeconomists.Itisthereforenotsurprisingthatmosteconomicsandeconometrics journalsexcludediscussionofthesematters.Indeed,economicjournalsnormallyreject asnotgermanearticlesthatfocustooobviouslyonspecificcomputationalissues,even whencriticaltotheevaluationofthepublishedfindings.Apossibleexceptiontothisis numericalaccuracy[175,253],butonlyrecentlyandstillintokenform[34,38,154,167, 169,170,172,174,219,229,231,232].Todate,economistsdealwithcomputational issuesatafullarm’slengthanddependuponothers,oftenstatisticiansandthestatistics literature,toprobethedetails[10,122,155,220,239],evenifsomerelatedissueshave beenconsideredwithintheboundsofeconometrics[16,17,21,22].Mosteconomistsare awareofJohnvonNeumann’sroleinthedevelopmentofgametheory,butcomparatively fewknowthathealsowrotethefirstcomputerprogramandparticipatedinthedesign ofthefirststored-programcomputer[140].Oftheseseveralendeavors,whichintheend willprovethemostseminalisaninterestingquestion.
1.2Thenatureofeconometricsoftware
Thephrase‘econometricsoftware’isactuallyacomparativelynewtermintheeconomics literature.ItsnewnesscanbeassessedusingJSTOR,thefull-text-searchableonlinejournalsarchive.Aqueryofthe52economicsandeconometricsjournalsidentifiedthereas ‘economicsjournals’revealsthat,since1950,only182articleshavebeenpublishedthat includetheterm‘econometricsoftware.’Thefirstuseofthisterminprintappearsto havebeenbyRobertShillerina1973 Econometrica article[217].Itappearsinonly14
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