第7講 面板數(shù)據(jù)

面板數(shù)據(jù)24-124-2AgendaPanelDataPanelDataDGP’sFixedEffectsRandomEffectsExample:ProductionFunctionsTheHausmanTest24-3PanelDataPotentialunobservedheterogeneityisaformofomittedvariablesbias.“Unobservedheterogeneity”referstoomittedvariablesthatarefixedforanindividual(atleastoveralongperiodoftime).Aperson’supbringing,familycharacteristics,innateability,anddemographics(exceptage)donotchange.24-4PanelData(cont.)Withcross-sectionaldata,thereisnoparticularreasontodifferentiatebetweenomittedvariablesthatare

fixedovertimeandomittedvariablesthatarechanging.However,whenanomittedvariableisfixedovertime,paneldataoffersanothertoolforeliminatingthebias.24-5PanelData(cont.)PanelDataisdatainwhichwe

observerepeatedcross-sectionsofthe

sameindividuals.Examples:AnnualunemploymentratesofeachstateoverseveralyearsQuarterlysalesofindividualstoresover

severalquartersWagesforthesameworker,workingatseveraldifferentjobs24-6PanelData(cont.)Someofthemostvaluabledatasetsineconomicsarepaneldatasets.Longitudinalsurveysreturnyearafteryeartothesameindividuals,trackingthemovertime.7什么是面板數(shù)據(jù)經(jīng)典計量經(jīng)濟學(xué)模型使用的或者是時序序列數(shù)據(jù)（timeseriesdata)，或者是截面數(shù)據(jù)(crossssectiondata)。面板數(shù)據(jù)模型是將時間序列和截面數(shù)據(jù)聯(lián)合使用建立的模型。可以增大樣本數(shù)量可以增大變量的變異程度可以分析不同觀察對象之間的差異可以分析不同時期之間的差異可以分析跨時期的因果關(guān)系（動態(tài)模型）概括而言，聯(lián)合使用時間序列和截面混合數(shù)據(jù)(Pooleddata)增加了信息含量，這不僅有利于改善模型估計結(jié)果，而且可以探討單純用時間序列數(shù)據(jù)或截面數(shù)據(jù)無法分析的問題。面板數(shù)據(jù)有哪些來源在現(xiàn)實生活中，有大量的公開統(tǒng)計數(shù)據(jù)屬于時間序列和截面混合數(shù)據(jù)。歷年分行政區(qū)的統(tǒng)計數(shù)據(jù)上市企業(yè)報表國家統(tǒng)計局居民收支調(diào)查(定期輪換)農(nóng)產(chǎn)品成本調(diào)查數(shù)據(jù)農(nóng)業(yè)部農(nóng)村經(jīng)濟研究中心固定觀察點調(diào)查資料…89處理時間序列和截面混合數(shù)據(jù)的方法處理時間序列和截面混合數(shù)據(jù)有以下兩種做法：混合數(shù)據(jù)模型：將針對不同時期、不同對象的觀察結(jié)果（指標(biāo)）看作是隨機抽取的觀察值。處理方法最為簡便，但由樣本提取的信息不夠充分。面板數(shù)據(jù)模型(Paneldata)：將針對不同時期、不同對象的觀察結(jié)果看作是與時期或截面相關(guān)聯(lián)的現(xiàn)象。處理方法較復(fù)雜，但能夠更充分地利用樣本信息?；旌蠑?shù)據(jù)模型可以被看作是處理面板數(shù)據(jù)的一種特例。在應(yīng)用工作中，可以將面板數(shù)據(jù)分為：平衡的面板數(shù)據(jù)（樣本量=N*T）非平衡的面板數(shù)據(jù)（樣本量=）面板數(shù)據(jù)的優(yōu)點控制個體異質(zhì)性Eg.香煙消費對滯后消費，價格和收入Zi:宗教、教育程度Wt：廣告Deaton1995.reg單產(chǎn)onland,labor,fertilizer,farmer’seducation等小農(nóng)戶單產(chǎn)更高？24-10面板數(shù)據(jù)的優(yōu)點解釋：不確定下，小農(nóng)戶追求更高單產(chǎn)家庭農(nóng)場監(jiān)督成本低土地質(zhì)量差異：小農(nóng)戶土地質(zhì)量高24-11面板數(shù)據(jù)的優(yōu)點面板數(shù)據(jù)提供更多信息，更多變化，更少共線性，更多自由度，更有效面板數(shù)據(jù)可以更好分析動態(tài)調(diào)整更好分析時間序列、橫截面數(shù)據(jù)無法分析的效應(yīng)Eg婦女勞動參與率、滿意度分析24-12面板數(shù)據(jù)的優(yōu)點面板數(shù)據(jù)可以更好估計和檢驗復(fù)雜行為模型Eg.技術(shù)效率24-1314例1：供給行為模型在生產(chǎn)函數(shù)分析中，人們長期關(guān)注的一個問題是如何分離規(guī)模經(jīng)濟和技術(shù)進(jìn)步產(chǎn)生的效果。就我國農(nóng)村情況而言，這類研究有助于回答是否應(yīng)鼓勵擴大農(nóng)戶經(jīng)營規(guī)模這一政策問題。截面數(shù)據(jù)可以反映規(guī)模差異的影響，但無法考慮技術(shù)進(jìn)步。時間序列數(shù)據(jù)將兩者的影響混合在一起而難以分離。15例2：需求行為模型對需求行為分析造成困擾的一個難題是如何分離收入變化的影響和價格變化的影響。兩者的動態(tài)變化模式常常表現(xiàn)出高度相關(guān)，因而利用時間序列數(shù)據(jù)建立模型面臨嚴(yán)重的多重共線。利用Panel數(shù)據(jù)可以增大價格和收入的變異程度，降低其相關(guān)程度，從而改善模型參數(shù)的估計結(jié)果。此外Panel數(shù)據(jù)樣本量較大，因而允許引入更多的其他影響因素（例如人口學(xué)變量）。Panel模型結(jié)果可以幫助識別觀察對象間的差別及消費行為隨時間的變化模式，這些信息有助于決策制定。面板數(shù)據(jù)的缺點數(shù)據(jù)收集問題測量誤差問題選擇性偏誤、不響應(yīng)、耗損較短的時間序列24-16面板數(shù)據(jù)模型考慮以下利用混合數(shù)據(jù)建立的模型（2N個待估計參數(shù)）此表達(dá)式意味著為每個截面單獨建立模型。是否可行（樣本容量）是否必要（研究目的）簡化假定1：有共同的斜率（N+1個待估計參數(shù)）上述情況屬于截面固定效應(yīng)模型(Fixedeffectmodel)。簡化假定2：有共同的常數(shù)項和斜率（2個待估計參數(shù)）1724-18APanelDataDGP24-19PanelDataDGPsNoticethatwhenwehavepaneldata,weindexobservationswithbothiandt.Paycloseattentiontothesubscripts

onvariables.Somevariablesvaryonlyacrosstimeoracrossindividual.24-20PanelDataDGP’s(cont.)24-21PanelDataDGP’s(cont.)24-22PanelDataDGP’s(cont.)InthisDGP,theb0i

arefixedacrosssamples.Theunmeasuredheterogeneityisthesame

ineverysample.ThisDGPiscalledthe“Distinct

Intercepts”DGP.Itissuitableforpanelsofstatesorcountries,wherethesameindividualswouldbeselectedineachsample.24-23PanelDataDGP’s(cont.)Withlongitudinaldataonindividualworkersorconsumers,wedrawadifferentsetofindividualsfromthepopulationeachtimewecollect

asample.Eachindividualhashis/herownsetoffixedomittedvariables.Wecannotfixeachindividualintercept.24-24AnotherPanelDataDGP24-25PanelDataDGP’sInthisDGP,wereturntoamodelwithasingleinterceptforalldatapoints,b0However,webreaktheerrortermintotwocomponents:Whenwedrawanindividuali,wedrawonevithatisfixedforthatindividualinalltimeperiods.viincludesallfixedomittedvariables.24-26PanelDataDGP’s(cont.)IntheDistinctInterceptsDGP,theunobservedheterogeneityisabsorbedintotheindividual-specificinterceptb0iInthesecondDGP,theunobservedheterogeneityisabsorbedintotheindividualfixedcomponentoftheerrorterm,viThisDGPisan“ErrorComponentsModel誤差成分模型.”24-27PanelDataDGP’s(cont.)TheErrorComponentsDGPcomesintwoflavors,dependingon .If ,thentheunobservedheterogeneityisuncorrelatedwith

theexplanators.OLSisunbiasedandconsistent.24-28PanelDataDGP’s(cont.)If ,thentheunobservedheterogeneityIScorrelatedwith

theexplanators.OLSisBIASEDandINCONSISTENT.24-29PanelDataDGP’s(cont.)PaneldataismostusefulinthesecondErrorComponentscase.When ,OLSisinconsistent.Usingpaneldata,wecancreateaconsistentestimator:FixedEffects.24-30FixedEffectsTheFixedEffectsEstimatorUsedwithEITHERthedistinctinterceptsDGPORtheerrorcomponentsDGP

withBasicIdea:estimateaseparateinterceptforeachindividual24-31FixedEffects(cont.)Thesimplestwaytoestimateseparateinterceptsforeachindividualistousedummyvariables.Thismethodiscalledtheleastsquaresdummyvariableestimator(最小二乘虛擬變量估計量）.24-32FixedEffects(cont.)Wehavealreadyseenthatwecanusedummyvariablestoestimateseparateinterceptsfordifferentgroups.Withpaneldata,wehavemultipleobservationsforeachindividual.Wecangrouptheseobservations.24-33FixedEffects(cont.)LeastSquaresDummyVariableEstimator:Createasetofndummyvariables,

Dj,suchthatDj=1ifi=j.RegressYitagainstallthedummies,

Xt,andXitvariables(youmustomit

Xivariablesandtheconstant).24-34FixedEffects(cont.)TheLSDVestimatorisconceptuallyquitesimple.Inpractice,thetrickypartsare:CreatingthedummyvariablesEnteringtheregressionintothecomputerReportingresults24-35FixedEffects(cont.)Supposewehavealongitudinaldatasetwith300workersover10years.n=300Wemustcreate300dummyvariablesandthenspecifyaregressionwith

300+explanators.Howdowedothisinoursoftwarepackage?24-36FixedEffects(cont.)Ourregressionoutputincludes

300intercepts.Usually,wearenotinterestedintheinterceptsthemselves.Weincludethedummyvariablestocontrolforheterogeneity.24-37FixedEffects(cont.)Inreportingyourregressionoutput,

itispreferabletonotethatyouhaveincluded“individualfixedeffects.”Thenomitthedummyvariablecoefficientsfromyourtableofresults.24-38FixedEffects(cont.)Atsomepoint,nbecomestoolarge

forthecomputertohandleeasily.ModerncomputerscanimplementLSDVforeverlargerdatasets,buteventuallyLSDVbecomescomputationallyintractable.雙重固定效應(yīng)截面和時間都設(shè)虛擬變量檢驗pool還是固定效應(yīng)24-3924-40FixedEffects(cont.)AcomputationallyconvenientalternativeiscalledtheFixedEffectsEstimator.Technically,onlythisstrategyis

“FixedEffects;”usingdummyvariablesisLSDV.Inpractice,econometricianstendtorefertoeithermethodasFixedEffects.24-41FixedEffects(cont.)TheinitialinsightfortheFixedEffectsestimator:ifweDIFFERENCEobservationsforthesameindividual,thevicancelsout.24-42FixedEffects(cont.)24-43FixedEffects(cont.)Whenwedifference,theheterogeneitytermvidropsout.(Inthedistinctinterceptsmodel,theb0iwoulddropout).Byassumption,themitareuncorrelatedwiththeXitOLSwouldbeaconsistentestimator

ofb124-44FixedEffects(cont.)IfT=2,thenwehaveonly2observationsforeachindividual

(asintheGibbonsandKatzexample).Differencingthe2observations

isefficient.IfT>2,thendifferencingany2observationsignoresvaluableinformationintheotherobservations

foreachindividual.24-45FixedEffects(cont.)Wecanusealltheobservations

foreachindividualifwesubtract

theindividual-specificmeanfrom

eachobservation.24-46FixedEffects(cont.)24-47FixedEffects(cont.)24-48FixedEffects(cont.)TheFixedEffectsandDVLSestimatorsprovideexactlyidenticalestimates.Then-T-ktermoftheFixedEffectse.s.e.’smustbeadjustedtoaccountfortheextrandegreesoffreedomthathavebeenused.Thecomputercanmakethisadjustment.24-49FixedEffects(cont.)Demeaningeachobservationbytheindividual-specificmeaneliminatestheneedtocreatendummyvariables.FEiscomputationallymuchsimpler.24-50FixedEffects(cont.)FixedEffects(howeverestimated)discardsallvariationbetweenindividuals.FixedEffectsusesonlyvariationovertimewithinanindividual.FEissometimescalledthe“within”estimator.24-51FixedEffects(cont.)FixedEffectsdiscardsagreatdealofvariationintheexplanators(allvariationbetweenindividuals).FixedEffectsusesndegrees

offreedom.FixedEffectsisnotefficientifCouldweuseOLS?24-52CheckingUnderstanding(cont.)24-53CheckingUnderstanding(cont.)BecauseXisuncorrelatedwitheither

vorm,OLSisconsistentintheuncorrelatedversionoftheerrorcomponentsDGP.Theerrortermsarehomoskedatic.24-54CheckingUnderstanding(cont.)However,thecovariancebetweendisturbancesforagivenindividualis24-55CheckingUnderstanding(cont.)Inthepresenceofserialcorrelation,OLSisinefficient.24-56RandomEffectsWhenunobservedheterogeneityisuncorrelatedwithexplanators,paneldatatechniquesarenotneededtoproduceaconsistentestimator.However,wedoneedtocorrectforserialcorrelationbetweenobservationsofthesameindividual.24-57RandomEffects(cont.)When ,paneldataprovides

avaluabletoolforeliminatingomittedvariablesbias.WeuseFixedEffectstogainthebenefitsofpaneldata.When ,paneldatadoesnotofferspecialbenefits.WeuseRandomEffectstoovercometheserialcorrelationofpaneldata.24-58RandomEffects(cont.)Thekeyideaofrandomeffects:Estimatesv2andsm2Usetheseestimatestoconstructefficientweightsofpaneldataobservations（GLS）24-59RandomEffects(cont.)24-60RandomEffects(cont.)Oncewehaveestimatesofsv2and

sm2,wecanre-weighttheobservationsoptimally.Thesecalculationsarecomplicated,

butmostcomputerpackagescanimplementthem.24-61Example:ProductionFunctions

Wehavedatafrom625firmsfrom

16countriesfor8years.WewishtoestimateaCobb–Douglasproductionfunction:Takinglogs:Weestimateusingrandomeffects.24-62TABLE16.1RandomEffectsEstimation

ofaCobb–DouglasProductionFunction

foraSampleofManufacturingFirms24-63Example:ProductionFunctionsTheestimatedcoefficientsof0.30forcapitaland0.69forlaboraresimilartoestimatesusingUSdata.Wealsogetsimilarresultsusingfixedeffectsestimation.TABLE16.2FixedEffectsEstimationofaCobb–DouglasProductionFunctionforaSampleofManufacturingFirms24-6424-65Example:ProductionFunctionsWearriveatsimilarestimatesusingeitherrandomeffectsorfixedeffects.Becauseonlyfixedeffectscontrols

forunobservedheterogeneitythatiscorrelatedwiththeexplanators,thesimilaritybetweenthetwoestimatessuggeststhatunobservedheterogeneityisnotcreatingalargebiasin

thissample.24-66Example:ProductionFunctions(cont.)Thefixedeffectsestimatordiscardsallvariationbetweenfirms,andmustuse

624moredegreesoffreedomthan

randomeffects.MovingfromREtoFEincreasesthee.s.e.

oncapitalfrom0.0116to0.0145Thee.s.e.onlabormovesfrom0.0118

to0.013224-67Example:ProductionFunctions(cont.)TheREestimatorprovidesmore

preciseestimatesWewouldprefertouseREinsteadofFE.However,REmightbeinconsistentifWeneedatesttohelpdeterminewhether

itissafetouseRE.固定效應(yīng)模型與隨機效應(yīng)模型固定效應(yīng)模型優(yōu)點不需要事先假定固定效應(yīng)與X無關(guān)；估計系數(shù)具有一致性；固定效應(yīng)可能含有有用的信息。缺點自由度損失大，不適合用于觀察對象眾多的情況。隨機效應(yīng)模型優(yōu)點自由度損失小，適用于處理觀察對象多的情況。缺點固定效應(yīng)與X無關(guān)的假定不一定成立，因而有可能出現(xiàn)遺漏重要解釋變量錯誤，此時無法保證估計系數(shù)的無偏性和一致性。6824-69TheHausmanTestHausman’sspecificationtestforerrorcomponentsDGPsprovidesguidanceonwhetherThekeyidea:if ,thentheinconsistentREestimatorandtheconsistentFEestimatorconvergetodifferentestimates.24-70TheHausmanTest(cont.)If ,thentheunobservedheterogeneityisuncorrelatedwith

X

anddoesnotcreateabias.REandFEarebothconsistent.Fortwoconsistentestimatorstoprovidesignificantlydifferentestimateswouldbesurprising.24-71TheHausmanTest(cont.)WeknowtheFEestimatorisconsistentevenwhenTheproblemwithFEisitsinef