工具变量法地Stata命令及实例

1、工具变量法的Stata命令及实例本实例使用数据集“grilic.dta先看一下数据集的统计特征：.sumVariableOpsMeanStd.Dev.MinMaxrns7582691293.443800101rns80758.292876.455382501mrt758.5145119.500119401mrt80758.8984169.302298801smsa758.7044855.45657501smsa80758.7124011.45294201med75810.910292.74112018iq758103.856213.6186754145kww75836.573887.30224

2、71256year75869.031662.6317946673age75821.835092.9817561630age8075833.011873.0855042838s75813.405012.231828918s8075813.707122.214693918expr7581.7354292.105542011.444expr8075811.394264.210745.69222.045tenure7581.8311351.67363010tenure807587.3627975.05024022lw7585.686739.42894944.6057.051lw8075816.8265

3、55.40992684.7498.032考察智商与受教育年限的相关关系：.corriqs(obs=758)iqsiq1.0000s0.51311.0000上表显示，智商（在一定程度上可以视为能力的代理变量）与受教育年限具有强烈的正相关关系（相关系数为0.51）。作为一个参考系，先进行OLS回归，并使用稳健标准差：文档大全.reglwsexprtenurernssmsa,rLinearregression758Numberofobs=F(5,752)=84.05Prob>F=0.0000R-squared=0.3521RootMSE=.34641RobustlwCoef.Std.Err.t

4、P>|t|95%Conf.Intervals.102643.006209916.530.000.0904523.1148338expr.0381189.00661445.760.000.025134.0511038tenure.0356146.00799884.450.000.0199118.0513173rns-.08407$)7.029533-2.850.005-.1420566-.0261029smsa.1396i666.0280564.980.000.0845893.194744_cons4.103i675.087666546.810.0003.9315754.275775其中e

5、xpr,tenure,rns,smsa均为控制变量，而我们主要感兴趣的是变量受教育年限（s）o回归的结果显示，教育投资的年回报率为10.26%,这个似乎太高了。可能的原因是，由于遗漏变量“能力”与受教育正相关，故“能力”对工资的贡献也被纳入教育的贡献，因此高估了教育的回报率。引入智商iq作为能力的代理变量，再进行OLS回归：实用标准Linearregression758.reglwsiqexprtenurernssmsa,rNumberofobs=F(6,751)=71.89Prob>F=0.0000R-squared=0.3600RootMSE=.34454RobustlwCoef.S

6、td.Err.tP>|t|95%Conf.Intervals.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.1367：369.02777124.920.000.0822186.1912

7、553_cons3.895172.115928633.600.0003.6675894.122754虽然教育的投资回报率有所下降，但是依然很高。由于用iq作为能力的代理变量有测量误差，故iq是内生变量，考虑使用变量（med（母亲的受教育年限）、kww（在“knowledgeoftheWorldofWork”中的成绩）、mrt（婚姻虚拟变量，已婚=1）age（年龄）作为iq的工具变量，进行2SLS回归，并使用稳健的标准差：实用标准.ivregress2slslwsexprtenurernssmsa(iq=medkwwmrtage),rInstrumentalvariables(2SLS)regr

8、essionNumberofobs=758Waldchi2(6)=355.73Prob>chi2=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.040564.00958484.230.000.02

9、17781.05935rns-.1176984.0359582-3.270.001-.1881751-.0472216smsa.149983.03222764.650.000.0868182.2131479_cons4.8371875.379943212.730.0004.09325.58255Instrumented:iqInstruments:sexprtenurernssmsamedkwwmrtage在此2SLS回归中，教育回报率反而上升到13.73%,而iq对工资的贡献居然为负值。使用工具变量的前提是工具变量的有效性。为此，进行过度识别检验，考察是否所有的工具变量均外生，即与扰动项不相

10、关：.estatoveridTestofoveridentifyingrestrictions:Scorechi2(3)=51.5449(p=0.0000)结果强烈拒绝所有工具变量均外生的原假设。考虑仅使用变量(med,kwv作为iq的工具变量，再次进行2SLS回归，同时显示第一阶段的回归结果：实用标准.ivregress2slslwsexprtenurernssmsa(iq=medkww),rfirstFirst-stageregressionsNumberofobs=758F(7,750)=47.74Prob>F=0.0000R-squared=0.3066AdjR-squared=

11、0.3001RootMSE=11.3931iqRCoef.obustStd.Err.tP>|t|95%Conf.Intervals2.467021.232775510.600.0002.0100522.92399expr-.4501353.2391647-1.880.060-.9196471.0193766tenure.2059(；31.2695620.760.445-.3232327.7351388rns-2.6898：8921335-3.020.003-4.441207-.938455smsa.2627416.94653090.280.781-1.5954242.120907med.

12、3470133.16813562.060.039.0169409.6770857kww.30818111.06467944.760.000.1812068.4351553_cons56.671223.07695518.420.00050.6307562.71169Instrumentalvariables(2SLS)regressionWaldchi2(6)Prob>chi2R-squaredRootMSENumberofobs=758=370.04=0.0000=0.2775=.36436RobustlwCoef.Std.Err.zP>|z|95%Conf.Intervaliq.

13、0139284.00603932.310.021.0020916.0257653s.0607803.01895053.210.001.023638.0979227expr.0433237.00741185.850.000.0287968.0578505tenure.0296142.0083173.560.000.0133432.0459452rns-.043527'1.0344779-1.260.207-.1111026.0240483smsa.1272：224.02974144.280.000.0689303.1855146_cons3.218)43.39836838.080.000

14、2.4372563.998831Instrumented:iqInstruments:sexprtenurernssmsamedkww上表显示，教育的回报率为6.08%,较为合理，再次进行过度识.estatoveridTestofoveridentifyingrestrictions:Scorechi2(1)=.151451(p=0.6972)接受原假设，认为(meetkwv外生，与扰动项不相关。进一步考察有效工具变量的第二个条件，即工具变量与内生变量的相关性。从第一阶段的回归结果可以看出，工具变量对内生变量具有较好的解释力。更正式的检验如下：.estatfirststage,allforce

15、nonrobustFirst-stageregressionsummarystatisticsAdjuVariableR-sq.>tedR-sqPartialRobustR-sq.F(2,750)Prob>Fiq0.30660.30010.038213.40280.0000Shea'spartialR-squaredVariableShea'sPartialF:-sq.Shea'sAdj.PartialR-sq.iq0.03820.0305Minimumeigenvaluestatistic=14.9058CriticalValues#ofendogenou

16、sregressors:1Ho:Instrumentsareweak#ofexcludedinstruments:25%10%20%30%2SLSrelativebias(notavailable)10%15%20%25%2SLSSizeofnominal5%Waldtest19.9311.59LIMLSizeofnominal5%Waldtest8.685.338.757.254.423.92从以上结果可以看出，虽然Shea'spartialR2不到0.04,但实用标准是F统计量为13.40>10o我们知道，虽然2SLS是一致的，但却是有偏的，故使用2SLS会带来“显著性水平扭

17、曲”(sizedistortion),而且这种扭曲随着弱工具变量而增大。上表的最后部分显示，如果在结构方程中对内生解释变量的显著性进行“名义显著性水平”(nominalsize)为5%勺沃尔德检验，加入可以接受的“真实显著性水平”(truesize)不超过15%则可以拒绝“弱工具变量”的原假设，因为最小特征值统计量为14.91,大于临界值11.59。总之我们有理由认为不存在弱工具变量。但为了稳健起见，下面使用对弱工具变量更不敏感的有限信息最大似然法(LIML):.ivregresslimllwsexprtenurernssmsa(iq=medkww),rNumberofobs=369.62=0

18、.0000=0.2768=.36454758Instrumentalvariables(LIML)regressionWaldchi2(6)Prob>chi2R-squaredRootMSERobustlwCoef.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.02962>37.0083233.

19、560.000.0133109.0459364rns-.043387'5.034529-1.260.209-.1110631.0242881smsa.1271796.02975994.270.000.0688512.185508_cons3.2141994.40014928.030.0002.4307163.999272Instrumented:iqInstruments:sexprtenurernssmsamedkww结果发现，LIML的系数估计值与2SLS非常接近，这也从侧面印证了“不存在弱工具变量”。使用工具变量法的前提是存在内生解释变量，为此须进行豪斯曼检验，其原假设是“所有的

20、解释变量均为外生”：.quireglwiqsexprtenurernssmsa.estimatesstoreols.quiivregress2slslwsexprtenurernssmsa(iq=medkww).estimatesstoreiv.hausmanivols,constantsigmamoreNote:therankofthedifferencedvariancematrix(1)doesnotequalthenumberofcoefficientsbeingtested(7);besurethisiswhatyouexpect,ortheremaybeproblemscomput

21、ingthetest.Examinetheoutputofyourestimatorsforanythingunexpectedandpossiblyconsiderscalingyourvariablessothatthecoefficientsareonasimilarscale.Coefficients(b)(B)(b-B)sqrt(diag(V_b-V_B)ivolsDifferenceS.E.iq.0139284.0032792s.06078()3.0927874expr.04332>37.0393443tenure.0296442.034209rns-.0435271-.07

22、45325smsa.1272224.1367369_cons3.2180433.895172.0106493-.032007.0039794-.0045648.0310054-.0095145-.6771285.0054318.0163254.0020297.0023283.0158145.0048529.3453751b=consistentunderHoandHa;obtainedfromivregressB=inconsistentunderHa,efficientunderHo;obtainedfromregressTest:Ho:differenceincoefficientsnot

23、systematicchi2(1)=(b-B)'(V_b-V_B)A(-1)(b-B)=3.84Prob>chi2=0.0499(V_b-V_Bisnotpositivedefinite)上表显示，可以在5%勺显著性水平下拒绝“所有解释变量均外生的原假设”，即认为存在内生解释变量iq。由于传统的豪斯曼检验建立在同方差的前提下，故在上述回归中均没有使用稳健标准差。由于传统的豪斯曼检验在异方差的情形下不成立，下面使用异方差稳健的DWK验：.estatendogenousTestsofendogeneityHo:variablesareexogenousDurbin(score)chi

24、2(1)=3.87962(p=0.0489)Wu-HausmanF(1,750)=3.85842(p=0.0499)据此可认为iq为内生解释变量。如果存在异方差，则GMM匕2SLS更有效。为此进行如下的最优GMMfr计：.ivregressgmmlwsexprtenurernssmsa(iq=medkww)Instrumentalvariables(GMM)regressionNumberofobs=758Waldchi2(6)=372.75Prob>chi2=0.0000R-squared=0.2750GMMweightmatrix:RobustRootMSE=.36499lwRCoe

25、f.obustStd.Err.zP>|z|95%Conf.Intervaliq.0140888.00603572.330.020.0022591.0259185s.0603672.01895453.180.001.0232171.0975174expr.0431117.00741125.820.000.0285861.0576373tenure.02997'64.00827283.620.000.013762.0461908rns-.044516.0344404-1.290.196-.1120179.0229859smsa.1267：368.02976334.260.000.06

26、84018.1850718_cons3.207298.3980838.060.0002.4270693.987526Instrumented:iqInstruments:sexprtenurernssmsamedkww进行过度识别检验:.estatoveridTestofoveridentifyingrestriction:Hansen'sJchi2(1)=.151451(p=0.6972)由于p值为0.70,故认为所有的工具变量均为外生。考虑迭代GMM.ivregressgmmlwsexprtenurernssmsa(iq=medkww),igmmIteration1:changei

27、nbeta=1.753e-05changeinW=1.100e-02Iteration2:changeinbeta=4.872e-08changeinW=7.880e-05Iteration3:changeinbeta=2.495e-10changeinW=2.304e-07Instrumentalvariables(GMM)regressionNumberofobs=758Waldchi2(6)=372.73Prob>chi2=0.0000R-squared=0.2750GMMweightmatrix:RobustRootMSE=.36499RobustlwCoef.Std.Err.z

28、P>|z|95%Conf.Intervaliq.0140901.00603572.330.020.0022603.02592s.0603629.01895483.180.001.0232122.0975135expr.0431101.00741135.820.000.0285841.057636tenure.02997'52.00827293.620.000.0137606.0461898rns-.0445114.0344408-1.290.196-.1120142.0229913smsa.1267：399.02976374.260.000.0684041.1850757_cons3.207224.39808788.060.0002.4269863.987462Instrumented:iqInstruments:sexprtenurernssmsamedkww如果希望将以上各种