工具變量法的Stata命令和實(shí)例

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.MinMaxrns758.2691293.443800101rns80758.292876.455382501mrt758.5145119.500119401mrt80758.8984169.302298801smsa758.7044855.45657501smsa80758.7124011.45294201med75810.910292.74112018iq758103.856213.6186754145kww75836.573887.3022471256year75869.031662.6317946673age75821.835092.9817561630age8075833.011873.0855042838s75813.405012.231828918s8075813.707122.214693918expr7581.7354292.105542011.444expr8075811.394264.210745.69222.045tenure7581.8311351.67363010tenure807587.3627975.05024022Iw7585.686739.42894944.6057.051lw807586.826555.40992684.7498.032?考察智商與受教育年限的相關(guān)關(guān)系：.corriqs(obs=758)iqsiq1.0000s0.51311.0000上表顯示?智商（在一定程度上可以視為能力的代理變量）與受教育年限具有強(qiáng)烈的正相關(guān)關(guān)系（相關(guān)系數(shù)為0?51）。?作為一個(gè)參考系?先進(jìn)行0LS回歸?并使用穩(wěn)健標(biāo)準(zhǔn)差:Linearregression75884.05Linearregression75884.050.0000F(5,752)Prob>FR-squared = 0.3521RootMSE = .34641lwCoef.RobustStd.Err.tP>lt|[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)似乎太高了?？赡艿脑蚴?由于遺漏變量“能力”與受教育正相關(guān).故能力”對(duì)工資的貢獻(xiàn)也被納入教育的貢獻(xiàn).因此高估了教育的回報(bào)率。引入智商iq作為能力的代理變量?再進(jìn)行OLS回歸:Linearregression75871.89Linearregression75871.890.0000F(6,751)Prob>FR-squared = 0.3600RootMSE = .34454lwCoef.RobustStd.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雖然教育的投資回報(bào)率有所下降.但是依然很高。由于用iq作為能力的代理變量有測(cè)量誤差?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(jī)）、mrt（婚姻虛擬變量.已婚=1）age（年齡））作為iq的工具變量?進(jìn)行2SLS回歸?并使用穩(wěn)健的標(biāo)準(zhǔn)差：Instrumentalvariables(2SLS)regressionNumberofobs=758Waldchi2(6) = 355.73Prob>chi2 = 0.0000R-squared = 0.2002RootMSE = .38336lwCoef.RobustStd.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回歸中?教育回報(bào)率反而上升到13.73%.而iq對(duì)工資的貢獻(xiàn)居然為負(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(guò)度識(shí)別檢驗(yàn).考察是否所有的工具變量均外生即與擾動(dòng)項(xiàng)不相關(guān)：.estatoveridTestofoveridentifyingrestrictions:Scorechi2(3)=51.5449(p=0.0000)結(jié)果強(qiáng)烈拒絕所有工具變量均外生的原假設(shè)。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結(jié)果：First-stageregressionsNumberofobsF(7,750)Prob>FR-squaredAdjR-squaredRootMSE75847.740.00000.3066NumberofobsF(7,750)Prob>FR-squaredAdjR-squaredRootMSE75847.740.00000.30660.300111.3931iqCoef.RobustStd.Err.tP>|t|[95%Conf.Interval]s2.467021.232775510.600.0002.0100522.92399expr-.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)regressionNumberofobsWaldchi2(6)Prob>chi2R-squared758370.040.00000.2775RootMSE=.36436lwCoef.RobustStd.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-.1111026.0240483smsa.1272224.02974144.280.000.0689303.1855146_cons3.218043.39836838.080.0002.4372563.998831Instrumented:iqInstruments: sexprtenurernssmsamedkww上表顯示.教育的回報(bào)率為6.08%.較為合理.再次進(jìn)行過(guò)度識(shí)別檢驗(yàn)：.estatoveridTestofoveridentifyingrestrictions:Scorechi2(1)=.151451(p=0.6972)接受原假設(shè)?認(rèn)為(med?kww)外生?與擾動(dòng)項(xiàng)不相關(guān)。進(jìn)一步考察有效工具變量的第二個(gè)條件.即工具變量與內(nèi)生變量的相關(guān)性。從第一階段的回歸結(jié)果可以看出?工具變量對(duì)內(nèi)生變量具有較好的解釋力。更正式的檢驗(yàn)如下：.estatfirststage,allforcenonrobustFirst-stageregressionsummarystatisticsVariableR-sq.AdjustedR-sq.PartialR-sq.RobustF(2,750)Prob>Fiq0.30660.30010.038213.4028 0.0000Shea'spartialR-squaredShea'sShea'sVariablePartialR-sq. Adj.PartialR-sq.iq0.03820.0305Minimumeigenvaluestatistic=14.9058CriticalValuesHo:Instrumentsareweak2SLSrelativebias#ofendogenousregressors: CriticalValuesHo:Instrumentsareweak2SLSrelativebias#ofexcludedinstruments: 25% 10% 20% 30%(notavailable)2SLSSizeofnominal5%WaldtestLIMLSizeofnominal2SLSSizeofnominal5%WaldtestLIMLSizeofnominal5%Waldtest10% 15% 20%19.93 11.59 8.758.68 5.33 4.4225%7.253.92從以上結(jié)果可以看出?雖然Shea'spartialR"2不到0.04?但是F統(tǒng)計(jì)量為13.40>10。我們知道.雖然2SLS是一致的?但卻是有偏的?故使用2SLS會(huì)帶來(lái)“顯著性水平扭曲”(sizedistortion)?而且這種扭曲隨著弱工具變量而增大。上表的最后部分顯示.如果在結(jié)構(gòu)方程中對(duì)內(nèi)生解釋變量的顯著性進(jìn)行“名義顯著性水平”(nominalsize)為5%的沃爾德檢驗(yàn)?加入可以接受的“真實(shí)顯著性水平”(truesize)不超過(guò)15%?則可以拒絕“弱工具變量”的原假設(shè)?因?yàn)樽钚√卣髦到y(tǒng)計(jì)量為14?91?大于臨界值11?59?？傊覀冇欣碛烧J(rèn)為不存在弱工具變量。但為了穩(wěn)健起見(jiàn)?下面使用對(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) = 369.62Prob>chi2 = 0.0000R-squared = 0.2768RootMSE = .36454lwCoef.RobustStd.Err.zP>|z|[95%Conf.Interval]iq.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.1271796.02975994.270.000.0688512.185508_cons3.214994.40014928.030.0002.4307163.999272Instrumented:iqInstruments: sexprtenurernssmsamedkww結(jié)果發(fā)現(xiàn).LIML的系數(shù)估計(jì)值與2SLS非常接近?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)生解釋變量?為此須進(jìn)行豪斯曼檢驗(yàn)?其原假設(shè)是“所有的解釋變量均為外生”

.estimatesstoreols.quiivregress2slslwsexprtenurernssmsa(iq=medkww).estimatesstoreiv.hausmanivols,constantsigmamore―fficients⑹―fficients⑹iv(B)olsiq.0139284.0032792s.0607803.0927874expr.0433237.0393443tenure.0296442.034209rns-.0435271-.0745325smsa.1272224.1367369_cons3.2180433.895172Coefficients(b-B)Differencesqrt(diag(V_b-V_B))S.E..0106493.0054318-.032007.0163254.0039794.0020297-.0045648.0023283.0310054.0158145-.0095145.0048529-.6771285.3453751Note:therankofthedifferencedvariancematrix(1)doesnotequalthenumberofcoefficientsbeingtested(7);besurethisiswhatyouexpect,ortheremaybeproblemscomputingthetest.Examinetheoutputofyourestimatorsforanythingunexpectedandpossiblyconsiderscalingyourvariablessothatthecoefficientsareonasimilarscale.b=consistentunderHoandHa;obtainedfromivregressB=inconsistentunderHa,efficientunderHo;obtainedfromregressTest:Ho:differenceincoefficientsnotsystematicchi2(1)(b-B)'[(V_b-V_B廠(-1)](b-B)3.84Prob>chi20.0499(V_b-V_Bisnotpositivedefinite)上表顯示.可以在5%的顯著性水平下拒絕“所有解釋變量均外生的原假設(shè)”?即認(rèn)為存在內(nèi)生解釋變量iq。由于傳統(tǒng)的豪斯曼檢驗(yàn)建立在同方差的前提下.故在上述回歸中均沒(méi)有使用穩(wěn)健標(biāo)準(zhǔn)差。由于傳統(tǒng)的豪斯曼檢驗(yàn)在異方差的情形下不成立.下面使用異方差穩(wěn)健的DWH檢驗(yàn)：.estatendogenousTestsofendogeneityHo:variablesareexogenousDurbin(score)chi2(1) =3.87962(p=0.0489)Wu-HausmanF(1,750) =3.85842(p=0.0499)據(jù)此可認(rèn)為iq為內(nèi)生解釋變量。?如果存在異方差?則GMM比2SLS更有效。為此進(jìn)行如下的最優(yōu)GMM估計(jì)：.ivregressgmmlwsexprtenurernssmsa(iq=medkww)Instrumentalvariables(GMM)regressionGMMweightmatrix:RobustNumberofobsInstrumentalvariables(GMM)regressionGMMweightmatrix:RobustNumberofobs=758Waldchi2(6)=372.75Prob>chi2=0.0000R-squared=0.2750RootMSE=.36499lwCoef.RobustStd.Err.zP>|z|[95%Conf.Interval]iq.0140888.00603572.330.020.0022591.0259185s.0603672.01895453.180.001.0232171.0975174expr.0431117.00741125.820.000.0285861.0576373tenure.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(guò)度識(shí)別檢驗(yàn)：.estatoveridTestofoveridentifyingrestriction:Hansen'sJchi2(1)=.151451(p=0.6972)?由于p值為0.70?故認(rèn)為所有的工具變量均為外生?？紤]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-07Instrumentalvariables(GMM)regressionNumberofobs758Waldchi2(6)372.73Prob>chi20.0000R-squared0.2750GMMweightmatrix:RobustRootMSE.36499RobustIwCoef.Std.Err.zP>|z|[95%Conf.Interval]iq.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.1267399.02976374.260.000.0684041.1850757cons3.207224.39808788.060.0002.4269863.987462Instrumented:iqInstruments:sexprtenurernssmsamedkww如果希望將以上各種估計(jì)法的系數(shù)估計(jì)值及其標(biāo)準(zhǔn)差列在同一張表中.可使用如下命令：.