工具變量法Stata命令實(shí)例

1、工具變量法的Stata命令及實(shí)例本實(shí)例使用數(shù)據(jù)集“grilic.dta”。先看一下數(shù)據(jù)集的統(tǒng)計(jì)特點(diǎn)：.sumVariableObsMeanStd.Dev.MinMaxrns758.2691293.443800101rns80758.292876.455382501mrt758.5145119.500119401mrt80758.8984169.302298801smsa758.7044855.45657501smsa80758.7124011.45294201med75810.910292.74112018iq758103.856213.6186754145kww75836.573887.30

2、22471256year75869.031662.6317946673age75821.835092.9817561630age8075833.011873.0855042838s75813.405012.231828918s8075813.707122.214693918expr7581.7354292.105542011.444expr8075811.394264.210745.69222.045tenure7581.8311351.67363010tenure807587.3627975.05024022lw7585.686739.42894944.6057.051lw807586.82

3、6555.40992684.7498.032觀察智商與受教育年限的有關(guān)關(guān)系：.corriqs(obs=758)iqsiq1.0000s0.51311.0000上表顯示.智商（在必定程度上能夠視為能力的代理變量）與受教育年限擁有激烈的正有關(guān)關(guān)系（有關(guān)系數(shù)為0.51）。作為一個(gè)參照系.先進(jìn)行OLS回歸.并使用穩(wěn)重標(biāo)準(zhǔn)差：.reglwsexprtenurernssmsa,rLinearregressionNumberofobs=758F(5,752)=84.05ProbF=0.0000R-squared=0.3521RootMSE=.34641RobustlwCoef.Std.Err.tP|t|95

4、%Conf.Interval.102643.006209916.530.000.0904523.1148338expr.0381189.00661445.760.000.025134.0511038tenure.0356146.00799884.450.000.0199118.0513173rns-.0840797.029533-2.850.005-.1420566-.0261029smsa.1396666.0280564.980.000.0845893.194744_cons4.103675.087666546.810.0003.9315754.275775.此中expr,tenure,rn

5、s,smsa均為控制變量.而我們主要感興趣的是變量受教育年限（s）?；貧w的結(jié)果顯示.教育投資的年回報(bào)率為10.26%.這個(gè)仿佛太高了?？赡艿脑墒?因?yàn)檫z漏變量“能力”與受教育正有關(guān).故“能力”對(duì)薪資的貢獻(xiàn)也被歸入教育的貢獻(xiàn).所以高估了教育的回報(bào)率。引入智商iq作為能力的代理變量.再進(jìn)行OLS回歸：.reglwsiqexprtenurernssmsa,rLinearregressionNumberofobs=758F(6,751)=71.89ProbF=0.0000R-squared=0.3600RootMSE=.34454RobustlwCoef.Std.Err.tP|t|95%Conf.I

6、ntervals.0927874.006976313.300.000.0790921.1064826iq.0032792.00113212.900.004.0010567.0055016expr.0393443.00666035.910.000.0262692.0524193tenure.034209.00789574.330.000.0187088.0497092rns-.0745325.0299772-2.490.013-.1333815-.0156834smsa.1367369.02777124.920.000.0822186.1912553_cons3.895172.115928633

7、.600.0003.6675894.122754固然教育的投資回報(bào)率有所降落.可是依舊很高。因?yàn)橛胕q作為能力的代理變量有丈量偏差.故iq是內(nèi)生變量.考慮使用變量（med（母親的受教育年限）、kww（在“knowledgeoftheWorldofWork”中的成績）、mrt（婚姻虛構(gòu)變量.已婚=1）age（年紀(jì)）作為iq的工具變量.進(jìn)行2SLS回歸.并使用穩(wěn)重的標(biāo)準(zhǔn)差：.ivregress2slslwsexprtenurernssmsa(iq=medkwwmrtage),rInstrumentalvariables(2SLS)regressionNumberofobs=758Waldchi2(

8、6)=355.73Probchi2=0.0000R-squared=0.2002RootMSE=.38336RobustlwCoef.Std.Err.zP|z|95%Conf.Intervaliq-.0115468.0056376-2.050.041-.0225962-.0004974s.1373477.01749897.850.000.1030506.1716449expr.0338041.00748444.520.000.019135.0484732tenure.040564.00958484.230.000.0217781.05935rns-.1176984.0359582-3.270.

9、001-.1881751-.0472216smsa.149983.03222764.650.000.0868182.2131479_cons4.837875.379943212.730.0004.09325.58255Instrumented:iqInstruments:sexprtenurernssmsamedkwwmrtage在此2SLS回歸中.教育回報(bào)率反而上漲到13.73%.而iq對(duì)薪資的貢獻(xiàn)竟然為負(fù)值。使用工具變量的前提是工具變量的有效性。為此.進(jìn)行過分辨別查驗(yàn).觀察能否全部的工具變量均外生.即與擾動(dòng)項(xiàng)不有關(guān)：.estatoveridTestofoveridentifyingrest

10、rictions:Scorechi2(3)=51.5449(p=0.0000)結(jié)果激烈拒絕全部工具變量均外生的原假定。考慮僅使用變量（med,kww）作為iq的工具變量.再次進(jìn)行2SLS回歸.同時(shí)顯示第一階段的回歸納果：.ivregress2slslwsexprtenurernssmsa(iq=medkww),rfirstFirst-stageregressionsNumberofobs=758F(7,750)=47.74ProbF=0.0000R-squared=0.3066AdjR-squared=0.3001RootMSE=11.3931RobustiqCoef.Std.Err.tP|t

11、|95%Conf.Intervals2.467021.232775510.600.0002.0100522.92399expr-.4501353.2391647-1.880.060-.9196471.0193766tenure.2059531.2695620.760.445-.3232327.7351388rns-2.689831.8921335-3.020.003-4.441207-.938455smsa.2627416.94653090.280.781-1.5954242.120907med.3470133.16813562.060.039.0169409.6770857kww.30818

12、11.06467944.760.000.1812068.4351553_cons56.671223.07695518.420.00050.6307562.71169Instrumentalvariables(2SLS)regressionNumberofobs=758Waldchi2(6)=370.04Probchi2=0.0000R-squared=0.2775RootMSE=.36436RobustlwCoef.Std.Err.zP|z|95%Conf.Intervaliq.0139284.00603932.310.021.0020916.0257653s.0607803.01895053

13、.210.001.023638.0979227expr.0433237.00741185.850.000.0287968.0578505tenure.0296442.0083173.560.000.0133432.0459452rns-.0435271.0344779-1.260.207-.1111026.0240483smsa.1272224.02974144.280.000.0689303.1855146_cons3.218043.39836838.080.0002.4372563.998831Instrumented:iqInstruments:sexprtenurernssmsamed

14、kww上表顯示.教育的回報(bào)率為6.08%.較為合理.再次進(jìn)行過分辨別查驗(yàn)：.estatoveridTestofoveridentifyingrestrictions:Scorechi2(1)=.151451(p=0.6972)接受原假定.以為（med.kww）外生.與擾動(dòng)項(xiàng)不有關(guān)。進(jìn)一步觀察有效工具變量的第二個(gè)條件.即工具變量與內(nèi)生變量的有關(guān)性。從第一階段的回歸納果能夠看出.工具變量對(duì)內(nèi)生變量擁有較好的解說力。改正式的查驗(yàn)以下：.estatfirststage,allforcenonrobustFirst-stageregressionsummarystatisticsAdjustedPart

15、ialRobustVariableR-sq.R-sq.R-sq.F(2,750)ProbFiq0.30660.30010.038213.40280.0000SheaspartialR-squaredSheasSheasVariablePartialR-sq.Adj.PartialR-sq.iq0.03820.0305Minimumeigenvaluestatistic=14.9058CriticalValues#ofendogenousregressors:1Ho:Instrumentsareweak#ofexcludedinstruments:25%10%20%30%2SLSrelative

16、bias(notavailable)10%15%20%25%2SLSSizeofnominal5%Waldtest19.9311.598.757.25LIMLSizeofnominal5%Waldtest8.685.334.423.92從以上結(jié)果能夠看出.固然SheaspartialR2不到0.04.可是F統(tǒng)計(jì)量為13.4010。.我們知道.固然2SLS是一致的.但倒是有偏的.故使用2SLS會(huì)帶來“明顯性水平歪曲”（sizedistortion）.并且這類歪曲跟著弱工具變量而增大。上表的最后部分顯示.假如在構(gòu)造方程中對(duì)內(nèi)生解說變量的明顯性進(jìn)行“名義明顯性水平”（nominalsize）為5%的

17、沃爾德查驗(yàn).加入能夠接受的“真切明顯性水平”（truesize）不超出15%.則能夠拒絕“弱工具變量”的原假定.因?yàn)樽钚√攸c(diǎn)值統(tǒng)計(jì)量為14.91.大于臨界值11.59?？傊覀冇性梢詾椴淮嬖谌豕ぞ咦兞?。但為了穩(wěn)重起見.下邊使用對(duì)弱工具變量更不敏感的有限信息最大似然法（LIML）:.ivregresslimllwsexprtenurernssmsa(iq=medkww),rInstrumentalvariables(LIML)regressionNumberofobs=758Waldchi2(6)=369.62Probchi2=0.0000R-squared=0.2768RootMSE=.36

18、454RobustlwCoef.Std.Err.zP|z|95%Conf.Intervaliq.0139764.00606812.300.021.0020831.0258697s.0606362.0190343.190.001.0233303.0979421expr.0433416.00741855.840.000.0288016.0578816tenure.0296237.0083233.560.000.0133109.0459364rns-.0433875.034529-1.260.209-.1110631.0242881smsa.1271796.02975994.270.000.0688

19、512.185508_cons3.214994.40014928.030.0002.4307163.999272Instrumented:iqInstruments:sexprtenurernssmsamedkww結(jié)果發(fā)現(xiàn).LIML的系數(shù)預(yù)計(jì)值與2SLS特別靠近.這也從側(cè)面印證了“不存在弱工具變量”。使用工具變量法的前提是存在內(nèi)生解說變量.為此須進(jìn)行豪斯曼查驗(yàn).其原假定是“全部的解說變量均為外生”：.quireglwiqsexprtenurernssmsa.estimatesstoreols.quiivregress2slslwsexprtenurernssmsa(iq=medkww).est

20、imatesstoreiv.hausmanivols,constantsigmamoreNote:therankofthedifferencedvariancematrix(1)doesnotequalthenumberofcoefficientsbeingtested(7);besurethisiswhatyouexpect,ortheremaybeproblemscomputingthetest.Examinetheoutputofyourestimatorsforanythingunexpectedandpossiblyconsiderscalingyourvariablessothat

21、thecoefficientsareonasimilarscale.Coefficients(b)(B)(b-B)sqrt(diag(V_b-V_B)ivolsDifferenceS.E.iq.0139284.0032792.0106493.0054318s.0607803.0927874-.032007.0163254expr.0433237.0393443.0039794.0020297tenure.0296442.034209-.0045648.0023283rns-.0435271-.0745325.0310054.0158145smsa.1272224.1367369-.009514

22、5.0048529_cons3.2180433.895172-.6771285.3453751b=consistentunderHoandHa;obtainedfromivregressB=inconsistentunderHa,efficientunderHo;obtainedfromregressTest:Ho:differenceincoefficientsnotsystematicchi2(1)=(b-B)(V_b-V_B)(-1)(b-B)3.84Probchi2=0.0499(V_b-V_Bisnotpositivedefinite).上表顯示.能夠在5%的明顯性水平下拒絕“全部解

23、說變量均外生的原假定”.即以為存在內(nèi)生解說變量iq。因?yàn)閭鹘y(tǒng)的豪斯曼檢驗(yàn)成立在同方差的前提下.故在上述回歸中均沒有使用穩(wěn)重標(biāo)準(zhǔn)差。因?yàn)閭鹘y(tǒng)的豪斯曼查驗(yàn)在異方差的情況下不可立.下邊使用異方差穩(wěn)重的DWH查驗(yàn)：.estatendogenousTestsofendogeneityHo:variablesareexogenousDurbin(score)chi2(1)=3.87962(p=0.0489)Wu-HausmanF(1,750)=3.85842(p=0.0499)據(jù)此可以為iq為內(nèi)生解說變量。假如存在異方差.則GMM比2SLS更有效。為此進(jìn)行以下的最優(yōu)GMM預(yù)計(jì)：.ivregressgmml

24、wsexprtenurernssmsa(iq=medkww)Instrumentalvariables(GMM)regressionNumberofobs=758Waldchi2(6)=372.75Probchi2=0.0000R-squared=0.2750GMMweightmatrix:RobustRootMSE=.36499RobustlwCoef.Std.Err.zP|z|95%Conf.Intervaliq.0140888.00603572.330.020.0022591.0259185s.0603672.01895453.180.001.0232171.0975174expr.04

25、31117.00741125.820.000.0285861.0576373tenure.0299764.00827283.620.000.013762.0461908rns-.044516.0344404-1.290.196-.1120179.0229859smsa.1267368.02976334.260.000.0684018.1850718_cons3.207298.3980838.060.0002.4270693.987526Instrumented:iqInstruments:sexprtenurernssmsamedkww.進(jìn)行過分辨別查驗(yàn)：.estatoveridTestofo

26、veridentifyingrestriction:HansensJchi2(1)=.151451(p=0.6972)因?yàn)閜值為0.70.故以為全部的工具變量均為外生。考慮迭代GMM：.ivregressgmmlwsexprtenurernssmsa(iq=medkww),igmmIteration1:changeinbeta=1.753e-05changeinW=1.100e-02Iteration2:changeinbeta=4.872e-08changeinW=7.880e-05Iteration3:changeinbeta=2.495e-10changeinW=2.304e-07Ins

27、trumentalvariables(GMM)regressionNumberofobs=758Waldchi2(6)=372.73Probchi2=0.0000R-squared=0.2750GMMweightmatrix:RobustRootMSE=.36499RobustlwCoef.Std.Err.zP|z|95%Conf.Intervaliq.0140901.00603572.330.020.0022603.02592s.0603629.01895483.180.001.0232122.0975135expr.0431101.00741135.820.000.0285841.057636tenure.0299752.00827293.620.000.0137606.0461898rns-.0445114.0344408-1.290.196-.1120142.0229913smsa.1267399.02976374.260.000.0684041.1850757_cons3.207224.39808788.060.0002.4269863.987462Instrumented:iqInstruments:sexprtenurernssmsamedkww假如希望將以上各樣預(yù)計(jì)法的系數(shù)預(yù)