stata操作命令-xtreg(7)

xtregpostestimation—Postestimationtoolsforxtreg469

Syntaxforpredict

Forallbutthepopulation-averagedmodel

????????????????

predicttypenewvarifin,statisticnooffsetPopulation-averagedmodel

????????????????

predicttypenewvarifin,PAstatisticnooffsetstatistic

Main

description

xbstdpue?

xbu?u?exjb,?ttedvalues;thedefaultstandarderrorofthe?ttedvaluesui+eit,thecombinedresidual

xjb+ui,predictionincludingeffectui,the?xed-orrandom-errorcomponenteit,theoverallerrorcomponent

Unstarredstatisticsareavailablebothinandoutofsample;typepredict...ife(sample)...ifwantedonlyfortheestimationsample.Starredstatisticsarecalculatedonlyfortheestimationsample,evenwhenife(sample)isnotspeci?ed.

PAstatisticMain

description

predictedprobabilityofdepvar;considerstheoffset()predictedprobabilityofdepvarlinearprediction

standarderrorofthelinearprediction

?rstderivativeoftheloglikelihoodwithrespecttoxjβ

muratexbstdpscoreThesestatisticsareavailablebothinandoutofsample;typepredictfortheestimationsample.

...ife(sample)...ifwantedonly

Menu

Statistics

>

Postestimation

>

Predictions,residuals,etc.

Optionsforpredict

￡￡Main

??

xbcalculatesthelinearprediction,thatis,a+bxit.Thisisthedefaultforallexceptthepopulation-averagedmodel.stdpcalculatesthestandarderrorofthelinearprediction.Forthe?xed-effectsmodel,thisexcludesthevarianceduetouncertaintyabouttheestimateofui.muandratebothcalculatethepredictedprobabilityofdepvar.mutakesintoaccounttheoffset(),andrateignoresthoseadjustments.muandrateareequivalentifyoudidnotspecifyoffset().muisthedefaultforthepopulation-averagedmodel.

470xtregpostestimation—Postestimationtoolsforxtreg

uecalculatesthepredictionofui+eit.

xbucalculatesthepredictionofa+bxit+ui,thepredictionincludingthe?xedorrandomcomponent.ucalculatesthepredictionofui,theestimated?xedorrandomeffect.ecalculatesthepredictionofeit.

scorecalculatestheequation-levelscore,uj=?lnLj(xjβ)/?(xjβ).

nooffsetisrelevantonlyifyouspeci?edoffset(varname)forxtreg,pa.Itmodi?esthecalculationsmadebypredictsothattheyignoretheoffsetvariable;thelinearpredictionistreatedasxitbratherthanxitb+offsetit.

Syntaxforxttest0

xttest0

Menu

Statistics

>

Longitudinal/paneldata

>

Linearmodels

>

Lagrangemultipliertestforrandomeffects

Remarks

Example1

Continuingwithourxtreg,reestimationexample(example4)inxtreg,wecanseethatxttest0willreportatestofνi=0.Incasewehaveanydoubts,wecouldtype

.usehttp://www.stata-press.com/data/r11/nlswork

(NationalLongitudinalSurvey.YoungWomen14-26yearsofagein1968).xtregln_wgradeagec.age#c.agettl_expc.ttl_exp#c.ttl_exp>tenurec.tenure#c.tenure2.racenot_smsasouth,retheta(outputomitted).xttest0

BreuschandPaganLagrangianmultipliertestforrandomeffects

ln_wage[idcode,t]=Xb+u[idcode]+e[idcode,t]

Estimatedresults:

Var

ln_wage

eu

Test:

Var(u)=0

chi2(1)=14779.98Prob>chi2=0.0000

.2283326

.0845038.066514

sd=sqrt(Var)

.4778416.2906954.2579031

xtregpostestimation—Postestimationtoolsforxtreg471

Example2

Moreimportantly,afterxtreg,reestimation,hausmanwillperformtheHausmanspeci?cationtest.Ifourmodeliscorrectlyspeci?ed,andifνiisuncorrelatedwithxit,the(subsetof)coef?cientsthatareestimatedbythe?xed-effectsestimatorandthesamecoef?cientsthatareestimatedhereshouldnotstatisticallydiffer:

.xtregln_wgradeagec.age#c.agettl_expc.ttl_exp#c.ttl_exp>tenurec.tenure#c.tenure2.racenot_smsasouth,re(outputomitted)

.estimatesstorerandom_effects

.xtregln_wgradeagec.age#c.agettl_expc.ttl_exp#c.ttl_exp>tenurec.tenure#c.tenure2.racenot_smsasouth,fe(outputomitted)

.hausman.random_effects

Coefficients(b)(B).random_eff~sage

c.age#c.age

ttl_expc.ttl_exp#~p

tenure

c.tenure#c~e

not_smsa

south

.0359987-.000723.0334668.0002163.0357539-.0019701-.0890108-.0606309

.036806-.0007133.0290207.0003049.039252-.0020035-.1308263-.0868927

(b-B)Difference-.0008073-9.68e-06.0044461-.0000886-.0034981.0000334.0418155.0262618

sqrt(diag(V_b-V_B))

S.E.

.0013177.0000184.001711.000053.0005797.0000373.0062745.0081346

Test:

b=consistentunderHoandHa;obtainedfromxtreg

B=inconsistentunderHa,efficientunderHo;obtainedfromxtregHo:differenceincoefficientsnotsystematic

chi2(8)=(b-B)’[(V_b-V_B)^(-1)](b-B)

=149.44

Prob>chi2=0.0000

Wecanrejectthehypothesisthatthecoef?cientsarethesame.Beforeturningtowhatthismeans,

notethathausmanlistedthecoef?cientsestimatedbythetwomodels.Itdidnot,however,listgradeand2.race.hausmandidnotmakeamistake;intheHausmantest,wecompareonlythecoef?cientsestimatedbybothtechniques.

Whatdoesthismean?Wehaveanunpleasantchoice:wecanadmitthatourmodelismisspeci?ed—thatwehavenotparameterizeditcorrectly—orwecanholdthatourspeci?ca-tioniscorrect,inwhichcasetheobserveddifferencesmustbeduetothezerocorrelationofνiandthexitassumption.

Technicalnote

Wecanalsomechanicallyexploretheunderpinningsofthetest’sdissatisfaction.Inthecomparisontablefromhausman,itisthecoef?cientsonnotsmsaandsouththatexhibitthelargestdifferences.Inequation(1??)of[XT]xtreg,weshowedhowtodecomposeamodelintowithinandbetweeneffects.Let’sdothatwiththesetwovariables,assumingthatchangesintheaveragehaveoneeffect,whereastransitionalchangeshaveanother:

472xtregpostestimation—Postestimationtoolsforxtreg

.egenavgnsmsa=mean(not_smsa),by(idcode).generatedevnsma=not_smsa-avgnsmsa(8missingvaluesgenerated)

.egenavgsouth=mean(south),by(idcode)

.generatedevsouth=south-avgsouth(8missingvaluesgenerated)

.xtregln_wgradeagec.age#c.agettl_expc.ttl_exp#c.ttl_exp>tenurec.tenure#c.tenure2.raceavgnsmdevnsmavgsoudevsouRandom-effectsGLSregressionNumberofobsGroupvariable:idcodeNumberofgroupsR-sq:within=0.1723Obspergroup:min

between=0.4809avgoverall=0.3737max

Randomeffectsu_i~GaussianWaldchi2(12)corr(u_i,X)=0(assumed)Prob>chi2

ln_wagegrade

age

c.age#c.age

ttl_expc.ttl_exp#c.ttl_exp

tenurec.tenure#c.tenure2.raceavgnsmsadevnsmaavgsouthdevsouth

_conssigma_usigma_e

rho

Coef..0631716.0375196-.0007248.0286542.0003222.0394424-.0020081-.0545938-.1833238-.0887596-.1011235-.0598538.268298.25791607.29069544.44046285

Std.Err..0017903.0031186.00005.0024207.0001162.001754.0001192.0102099.0109337.0095071.0098787.0109054.0495776

z35.2912.03-14.5011.842.7722.49-16.85-5.35-16.77-9.34-10.24-5.495.41

P>|z|0.0000.0000.0000.0000.0060.0000.0000.0000.0000.0000.0000.0000.000

=======280914697

16.0159319.690.0000

[95%Conf.Interval].0596627.0314072-.0008228.0239097.0000945.0360045-.0022417-.0746048-.2047533-.1073932-.1204855-.081228.1711277

.0666805.043632-.0006269.0333987.0005499.0428803-.0017746-.0345827-.1618942-.070126-.0817616-.0384796.3654683

(fractionofvarianceduetou_i)

Wewillleavethereinterpretationofthismodeltoyou,exceptthatifwewerereallygoingtosellthismodel,wewouldhavetoexplainwhythebetweenandwithineffectsaredifferent.Focusingonresidenceinanon-SMSA,wemighttellastoryaboutruralpeoplebeingpaidlessandcontinuingtogetpaidlesswhentheymovetotheSMSA.Givenourpaneldata,wecouldcreatevariablestomeasurethis(anindicatorformovedfromnon-SMSAtoSMSA)andtomeasuretheeffects.Inourassessmentofthismodel,weshouldthinkaboutwomeninthecitiesmovingtothecountryandtheirrelativeproductivityinabucolicsetting.

xtregpostestimation—Postestimationtoolsforxtreg473

Inanycase,theHausmantestnowis

.estimatesstorenew_random_effects

.xtregln_wgradeagec.age#c.agettl_expc.ttl_exp#c.ttl_exp>tenurec.tenure#c.tenure2.raceavgnsmdevnsmavgsoudevsou,fe(outputomitted)

.hausman.new_random_effects

Coefficients(b)(B)(b-B)sqrt(diag(V_b-V_B)).new_random~sDifferenceS.E.age

c.age#c.age

ttl_expc.ttl_exp#~p

tenure

c.tenure#c~e

devnsmadevsouth

.0359987-.000723.0334668.0002163.0357539-.0019701-.0890108-.0606309

.0375196-.0007248.0286542.0003222.0394424-.0020081-.0887596-.0598538

-.0015211.84e-06.0048126-.0001059-.0036885.000038-.0002512-.0007771

.0013198.0000184.0017127.0000531.0005839.0000377.0006826.0007612

Test:

b=consistentunderHoandHa;obtainedfromxtreg

B=inconsistentunderHa,efficientunderHo;obtainedfromxtregHo:differenceincoefficientsnotsystematic

chi2(8)=(b-B)’[(V_b-V_B)^(-1)](b-B)

=92.52

Prob>chi2=0.0000

Wehavemechanicallysucceededingreatlyreducingtheχ2,butnotbyenough.Themajordifferences

nowareintheage,experience,andtenureeffects.Wealreadyknewthisproblemexistedbecauseoftheever-increasingeffectofexperience.Morecarefulparameterizationworkratherthansimplyincludingsquaresneedstobedone.

Methodsandformulas

Allpostestimationcommandslistedaboveareimplementedasado-?les.xttest0

xttest0reportstheLagrangemultipliertestforrandomeffectsdevelopedbyBreuschandPagan(1980)andasmodi?edbyBaltagiandLi(1990).Themodel

yit=α+xitβ+νit

is?tviaOLS,andthenthequantity

λLM

iscalculated,where

(nT)2=

2

??

A2??21

(iTi)?nT??

??n??Ti

(t=1vit)2i=1????2A1=1?

itvit

474xtregpostestimation—Postestimationtoolsforxtreg

TheBaltagiandLimodi?cationallowsforunbalanceddataandreducestothestandardformula

λLM

nT=

2(T?1)????????2

2

(v)iti??t???12vitit

whenTi=T(balanceddata).Underthenullhypothesis,λLMisdistributedχ2(1).

References

Baltagi,B.H.,andQ.Li.1990.ALagrangemultipliertestfortheerrorcomponentsmodelwithincompletepanels.

EconometricReviews9:103–107.Breusch,T.S.,andA.R.Pagan.1980.TheLagrangemultipliertestanditsapplicationstomodelspeci?cationineconometrics.ReviewofEconomicStudies47:239–253.Hausman,J.A.1978.Speci?cationtestsineconometrics.Econometrica46:1251–1271.

Sosa-Escudero,W.,andA.K.Bera.2008.Testsforunbalancederror-componentsmodelsunderlocalmisspeci?cation.StataJournal8:68–78.

Alsosee

[XT]xtreg—Fixed-,between-,andrandom-effects,andpopulation-averagedlinearmodels[U]20Estimationandpostestimationcommands

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