Title
xtreg—Fixed-,between-,andrandom-effects,andpopulation-averagedlinearmodels
Syntax
GLSrandom-effects(RE)model
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xtregdepvarindepvarsifin,reREoptionsBetween-effects(BE)model
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xtregdepvarindepvarsifin,beBEoptions
Fixed-effects(FE)model
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xtregdepvarindepvarsifinweight,feFEoptionsMLrandom-effects(MLE)model
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xtregdepvarindepvarsifinweight,mleMLEoptionsPopulation-averaged(PA)model
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xtregdepvarindepvarsifinweight,paPAoptionsREoptions
Model
description
userandom-effectsestimator;thedefault
useSwamy–Aroraestimatorofthevariancecomponents
vcetypemaybeconventional,robust,clusterclustvar,bootstrap,orjackknife
setcon?dencelevel;defaultislevel(95)reportθ
controlspacinganddisplayofomittedvariablesandbaseandemptycells
displaycoef?cients’legendinsteadofcoef?cienttable
resa
SE/Robust
vce(vcetype)
Reporting
level(#)theta
displayoptions
?coeflegend?coeflegenddoesnotappearinthedialogbox.
439
440xtreg—Fixed-,between-,andrandom-effects,andpopulation-averagedlinearmodels
BEoptions
Model
description
usebetween-effectsestimatoruseweightedleastsquares
vcetypemaybeconventional,bootstrap,orjackknifesetcon?dencelevel;defaultislevel(95)
controlspacinganddisplayofomittedvariablesandbaseandemptycells
displaycoef?cients’legendinsteadofcoef?cienttable
bewls
SE
vce(vcetype)
Reporting
level(#)
displayoptions
?coeflegend?coeflegenddoesnotappearinthedialogbox.FEoptions
Model
description
use?xed-effectsestimator
vcetypemaybeconventional,robust,clusterclustvar,bootstrap,orjackknife
setcon?dencelevel;defaultislevel(95)
controlspacinganddisplayofomittedvariablesandbaseandemptycells
displaycoef?cients’legendinsteadofcoef?cienttable
fe
SE/Robust
vce(vcetype)
Reporting
level(#)
displayoptions
?coeflegend?coeflegenddoesnotappearinthedialogbox.
xtreg—Fixed-,between-,andrandom-effects,andpopulation-averagedlinearmodels441
MLEoptions
Model
description
suppressconstantterm
useMLrandom-effectsestimator
vcetypemaybeoim,bootstrap,orjackknife
setcon?dencelevel;defaultislevel(95)
controlspacinganddisplayofomittedvariablesandbaseandemptycells
controlthemaximizationprocess;seldomuseddisplaycoef?cients’legendinsteadofcoef?cienttable
noconstantmle
SE
vce(vcetype)
Reporting
level(#)
displayoptions
Maximization
maximizeoptions?coeflegend?coeflegenddoesnotappearinthedialogbox.
PAoptionsModel
description
suppressconstantterm
usepopulation-averagedestimator
includevarnameinmodelwithcoef?cientconstrainedto1within-groupcorrelationstructure
estimateevenifobservationsunequallyspacedintime
vcetypemaybeconventional,robust,bootstrap,orjackknifeusedivisorN?PinsteadofthedefaultN
multiplytherobustvarianceestimateby(N?1)/(N?P)
overridesthedefaultscaleparameter;parmmaybex2,dev,phi,or#setcon?dencelevel;defaultislevel(95)
controlspacinganddisplayofomittedvariablesandbaseandemptycells
controltheoptimizationprocess;seldomuseddisplaycoef?cients’legendinsteadofcoef?cienttable
noconstantpa
offset(varname)
Correlation
corr(correlation)force
SE/Robust
vce(vcetype)nmprgf
scale(parm)
Reporting
level(#)
displayoptions
Optimization
optimizeoptions
?coeflegend
?coeflegenddoesnotappearinthedialogbox.
442xtreg—Fixed-,between-,andrandom-effects,andpopulation-averagedlinearmodels
correlationexchangeableindependentunstructuredfixedmatnamear#
stationary#nonstationary#
description
exchangeableindependentunstructureduser-speci?ed
autoregressiveoforder#stationaryoforder#nonstationaryoforder#
Apanelvariablemustbespeci?ed.Forxtreg,pa,correlationstructuresotherthanexchangeableandindependentrequirethatatimevariablealsobespeci?ed.Usextset;see[XT]xtset.indepvarsmaycontainfactorvariables;see[U]11.4.3Factorvariables.
depvarandindepvarsmaycontaintime-seriesoperators;see[U]11.4.4Time-seriesvarlists.by,miestimate,andstatsbyareallowed;see[U]11.1.10Pre?xcommands.
vce(bootstrap)andvce(jackknife)arenotallowedwiththemiestimatepre?x.
aweights,fweights,andpweightsareallowedforthe?xed-effectsmodel.iweights,fweights,andpweightsareallowedforthepopulation-averagedmodel.iweightsareallowedforthemaximum-likelihoodrandom-effects(MLE)model.See[U]11.1.6weight.Weightsmustbeconstantwithinpanel.
See[U]20Estimationandpostestimationcommandsformorecapabilitiesofestimationcommands.
Menu
Statistics
>
Longitudinal/paneldata
>
Linearmodels
>
Linearregression(FE,RE,PA,BE)
Description
xtreg?tsregressionmodelstopaneldata.Inparticular,xtregwiththebeoption?tsrandom-effectsmodelsbyusingthebetweenregressionestimator;withthefeoption,it?ts?xed-effectsmodels(byusingthewithinregressionestimator);andwiththereoption,it?tsrandom-effectsmodelsbyusingtheGLSestimator(producingamatrix-weightedaverageofthebetweenandwithinresults).See[XT]xtdataforafasterwayto?t?xed-andrandom-effectsmodels.
OptionsforREmodel
￡￡Model
??
re,thedefault,requeststheGLSrandom-effectsestimator.
saspeci?esthatthesmall-sampleSwamy–Aroraestimatorindividual-levelvariancecomponentbeusedinsteadofthedefaultconsistentestimator.SeeMethodsandformulassectionfordetails.
￡￡SE/Robust
??
vce(vcetype)speci?esthetypeofstandarderrorreported,whichincludestypesthatarederivedfromasymptotictheory,thatarerobusttosomekindsofmisspeci?cation,thatallowforintragroupcorrelation,andthatusebootstraporjackknifemethods;see[XT]vceoptions.vce(conventional),thedefault,usestheconventionallyderivedvarianceestimatorforgeneralizedleast-squaresregression.
Specifyingvce(robust)isequivalenttospecifyingvce(clusterpanelvar);seextreg,reinMethodsandformulas.
xtreg—Fixed-,between-,andrandom-effects,andpopulation-averagedlinearmodels443
￡￡Reporting
??
level(#);see[R]estimationoptions.
theta,usedwithxtreg,reonly,speci?esthattheoutputincludetheestimatedvalueofθusedincombiningthebetweenand?xedestimators.Forbalanceddata,thisisaconstant,andforunbalanceddata,asummaryofthevaluesispresentedintheheaderoftheoutput.displayoptions:noomitted,vsquish,noemptycells,baselevels,allbaselevels;see[R]es-timationoptions.Thefollowingoptionisavailablewithxtregbutisnotshowninthedialogbox:coeflegend;see[R]estimationoptions.
OptionsforBEmodel
￡￡Model
??
berequeststhebetweenregressionestimator.
wlsspeci?esthat,forunbalanceddata,weightedleastsquaresbeusedratherthanthedefaultOLS.Bothmethodsproduceconsistentestimates.Thetruevarianceofthebetween-effectsresidualis2222σν+Tiσ??(seeMethodsandformulasbelow).WLSproducesa“stabilized”varianceofσν/Ti+σ??,whichisalsonotconstant.ThusthechoicebetweenOLSandWLSamountstowhichismorestable.Comment:xtreg,beisrarelyusedanyway,butbetweenestimatesareaningredientintherandom-effectsestimate.Ourimplementationofxtreg,reusestheOLSestimatesforthisingredient,
22
inmostmodels.Formally,onlyaconsistentislargerelativetoσ??basedonourjudgmentthatσν
estimateofthebetweenestimatesisrequired.
￡￡SE
??
vce(vcetype)speci?esthetypeofstandarderrorreported,whichincludestypesthatarederivedfromasymptotictheoryandthatusebootstraporjackknifemethods;see[XT]vceoptions.vce(conventional),thedefault,usestheconventionallyderivedvarianceestimatorforgeneralizedleast-squaresregression.
￡￡Reporting
??
level(#);see[R]estimationoptions.
displayoptions:noomitted,vsquish,noemptycells,baselevels,allbaselevels;see[R]es-timationoptions.Thefollowingoptionisavailablewithxtregbutisnotshowninthedialogbox:coeflegend;see[R]estimationoptions.
OptionsforFEmodel
￡￡Model
??
ferequeststhe?xed-effects(within)regressionestimator.
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