工具变量法地Stata命令及实例.doc

工具变量法地Stata命令及实例标准实用文案工具变量法的 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：.sumVariableObsMeanStd.Dev.MinMaxrns758.2691293.443800101rns80758.292876.455382501mrt758.5145119.500119401mrt80758.8984169.302298801smsa758.7044855.45657501smsa80758.7124011.45294201med75810.910292.74112018iq758103.856213.6186754145kww75836.573887.3022471256year75869.031662.6317946673age75821.835092.9817561630age8075833.011873.0855042838s75813.405012.231828918s8075813.707122.214693918expr7581.7354292.105542011.444expr8075811.394264.210745.69222.045tenure7581.8311351.67363010tenure807587.3627975.05024022lw7585.686739.42894944.6057.051lw807586.826555.40992684.7498.032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）。

文档标准实用文案作为一个参考系，先进行OLS回归，并使用稳健标准差：.reglwsexprtenurernssmsa,rLinearregressionNumberofobs=758F(5,752)=84.05Prob>F=0.0000R-squared=0.3521RootMSE=.34641RobustlwCoef. Std.Err.t P>|t| [95%Conf.Interval]s .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.其中expr,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）。

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：文档标准实用文案.reglwsiqexprtenurernssmsa,rLinearregressionNumberofobs=758F(6,751)=71.89Prob>F=0.0000R-squared=0.3600RootMSE=.34454RobustlwCoef.Std.Err.tP>|t|[95%Conf.Interval]s.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_cons3.895172.115928633.600.0003.6675894.122754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：文档标准实用文案.ivregress2slslwsexprtenurernssmsa(iq=medkwwmrtage),rInstrumentalvariables(2SLS)regressionNumberofobs=758Waldchi2(6)=355.73Prob>chi2=0.0000R-squared=0.2002RootMSE=.38336RobustlwCoef.Std.Err.zP>|z|[95%Conf.Interval]iq-.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-.1176984.0359582-3.270.001-.1881751-.0472216smsa.149983.03222764.650.000.0868182.2131479_cons4.837875.379943212.730.0004.09325.58255Instrumented: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,kww）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：文档标准实用文案.ivregress2slslwsexprtenurernssmsa(iq=medkww),rfirstFirst-stageregressionsNumberofobs=758F(7,750)=47.74Prob>F=0.0000R-squared=0.3066AdjR-squared=0.3001RootMSE=11.3931RobustiqCoef. Std.Err.t P>|t|[95%Conf.Interval]s 2.467021.232775510.600.0002.0100522.92399expr-.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.3081811.06467944.760.000.1812068.4351553_cons56.671223.07695518.420.00050.6307562.71169Instrumentalvariables(2SLS)regressionNumberofobs=758Waldchi2(6)=370.04Prob>chi2=0.0000R-squared=0.2775RootMSE=.36436RobustlwCoef.Std.Err.zP>|z|[95%Conf.Interval]iq.0139284.00603932.310.021.0020916.0257653s.0607803.01895053.210.001.023638.0979227expr.0433237.00741185.850.000.0287968.0578505tenure.0296442.0083173.560.000.0133432.0459452rns-.0435271.0344779-1.260.207-.111。