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

2、573887.3022471256year75869.031662.6317946673age75821.835092.9817561630age8075833.011873.0855042838s75813.405012.231828918s8075813.707122.214693918expr7581.7354292.105542011.444expr8075811.394264.210745.69222.045tenure7581.8311351.67363010tenure807587.3627975.05024022lw7585.686739.42894944.6057.051lw

3、807586.826555.40992684.7498.032考察智商與受教育年限的相關(guān)關(guān)系：. corr iq s(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烈的正相關(guān)關(guān)系相關(guān)系數(shù)為0.51 。作為一個參考系 . 先進展 OLS回歸 . 并使用穩(wěn)健標準差：專業(yè)資料整理WORD格式.專業(yè)資料整理WORD格式. reg lw s expr tenure rns smsa,rLinear regressionNumber of obs =758F(5, 752)=84.05Prob > F=0.000

4、0R-squared=0.3521Root MSE=.34641RobustlwCoef.Std. Err.tP>|t|95% Conf. Intervals .102643 .0062099 16.53 0.000 .0904523 .1148338 expr .0381189 .0066144 5.76 0.000 .025134 .0511038tenure.0356146.00799884.450.000.0199118.0513173rns-.0840797 .029533 -2.85 0.005 -.1420566 -.0261029smsa.1396666.0280564.

5、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。回歸的結(jié)果顯示 . 教育投資的年回報率為 10.26%. 這個似乎太高了。可能的原因是 . 由于遺漏變量“能力與受教育正相關(guān) . 故“能力對工資的奉獻也被納入教育的奉獻 . 因此高估了教育的回報率。引入智商 iq 作為能力的代理變量 . 再進展 OLS回歸：專業(yè)資料整理WORD格式.專業(yè)資料整理WORD格式. reg lw s iq expr ten

6、ure rns smsa,rLinear regressionNumber of obs =758F(6, 751)=71.89Prob > F=0.0000R-squared=0.3600Root MSE=.34454RobustlwCoef. Std. Err.tP>|t|95% Conf. Intervals.0927874.006976313.300.000.0790921.1064826iq.0032792.00113212.90 0.004.0010567 .0055016expr.0393443.00666035.910.000.0262692.0524193tenu

7、re.034209.00789574.330.000.0187088.0497092rns-.0745325.0299772-2.490.013-.1333815-.0156834smsa.1367369.02777124.920.000.0822186.1912553_cons3.895172.115928633.60 0.0003.6675894.122754雖然教育的投資回報率有所下降. 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“ knowledge of the World of Work

8、中的成績、 mrt 婚姻虛擬變量 . 已婚 =1age年齡作為 iq 的工具變量 . 進展 2SLS回歸 . 并使用穩(wěn)健的標準差：專業(yè)資料整理WORD格式.專業(yè)資料整理WORD格式. ivregress 2sls lw s expr tenure rns smsa (iq=med kww mrt age),rInstrumental variables (2SLS) regressionNumber of obs =758Wald chi2(6)=355.73Prob > chi2=0.0000R-squared=0.2002Root MSE=.38336RobustlwCoef. St

9、d. Err.zP>|z|95% Conf. Intervaliq-.0115468.0056376-2.050.041-.0225962-.0004974s.1373477.01749897.85 0.000.1030506.1716449expr.0338041.00748444.520.000.019135.0484732tenure.040564.00958484.230.000.0217781.05935rns-.1176984.0359582-3.270.001-.1881751-.0472216smsa.149983.03222764.650.000.0868182.213

10、1479_cons4.837875 .379943212.73 0.0004.09325.58255Instrumented: iqInstruments:s expr tenure rns smsa med kww mrt age在此 2SLS回歸中 . 教育回報率反而上升到 13.73%. 而 iq 對工資的奉獻居然為負值。使用工具變量的前提是工具變量的有效性。為此. 進展過度識別檢驗 . 考察是否所有的工具變量均外生 . 即與擾動項不相關(guān)：. estat overidTest of overidentifying restrictions:Score chi2(3)= 51.5449 (

11、p = 0.0000)結(jié)果強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 . 再次進展 2SLS 回歸 . 同時顯示第一階段的回歸結(jié)果：專業(yè)資料整理WORD格式.專業(yè)資料整理WORD格式. ivregress 2sls lw s expr tenure rns smsa (iq=med kww),r firstFirst-stage regressionsNumber of obs=758F( 7, 750)=47.74Prob > F=0.0000R-squared=0.3066Adj R-squared=0.3001Root MSE=11.

12、3931RobustiqCoef.Std. Err.tP>|t|95% Conf. Intervals 2.467021 .2327755 10.60 0.000 2.010052 2.92399 expr -.4501353 .2391647 -1.88 0.060 -.9196471 .0193766tenure.2059531.2695620.760.445-.3232327.7351388rns-2.689831 .8921335 -3.02 0.003 -4.441207 -.938455smsa.2627416.94653090.280.781-1.5954242.12090

13、7med.3470133.16813562.060.039.0169409.6770857kww.3081811.06467944.760.000.1812068.4351553_cons56.671223.07695518.420.00050.6307562.71169Instrumental variables (2SLS) regressionNumber of obs =758Wald chi2(6)=370.04Prob > chi2=0.0000R-squared=0.2775Root MSE=.36436RobustlwCoef.Std. Err.zP>|z|95%

14、Conf. Intervaliq.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 -1.26 0.207 -.1111026 .0240483smsa.1272224.02974144.280.000.0689303.1855146_cons3.218043

15、.39836838.080.0002.4372563.998831Instrumented: iqInstruments:s expr tenure rns smsa med kww上表顯示 . 教育的回報率為6.08%. 較為合理 . 再次進展過度識別檢驗：專業(yè)資料整理WORD格式.專業(yè)資料整理WORD格式. estat overidTest of overidentifying restrictions:Score chi2(1)= .151451 (p = 0.6972)承受原假設(shè) . 認為 med.kww外生 . 與擾動項不相關(guān)。進一步考察有效工具變量的第二個條件 . 即工具變量與內(nèi)生

16、變量的相關(guān)性。從第一階段的回歸結(jié)果可以看出 . 工具變量對內(nèi)生變量具有較好的解釋力。更正式的檢驗如下：. estat firststage,all forcenonrobustFirst-stage regression summary statisticsAdjustedPartialRobustVariable R-sq.R-sq.R-sq.F(2,750)Prob > Fiq0.30660.30010.038213.40280.0000Shea's partial R-squaredShea'sShea'sVariablePartial R-sq.Adj.

17、Partial R-sq.iq0.03820.0305Minimum eigenvalue statistic = 14.9058Critical Values# of endogenous regressors:1Ho: Instruments are weak# of excluded instruments: 25%10%20%30%2SLS relative bias(not available)10%15%20%25%2SLS Size of nominal 5% Wald test19.9311.598.757.25LIML Size of nominal 5% Wald test

18、8.685.334.423.92從以上結(jié)果可以看出 . 雖然 Sheas partial R2 不到 0.04. 但是 F 統(tǒng)計量為 13.40>10 。專業(yè)資料整理WORD格式.專業(yè)資料整理WORD格式我們知道 . 雖然 2SLS是一致的 . 但卻是有偏的 . 故使用 2SLS會帶來“顯著性水平扭曲size distortion . 而且這種扭曲隨著弱工具變量而增大。上表的最后局部顯示 . 如果在構(gòu)造方程中對內(nèi)生解釋變量的顯著性進展“名義顯著性水平nominal size 為 5%的沃爾德檢驗 . 參加可以承受的“真實顯著性水平true size 不超過 15%.那么可以拒絕“弱工具變

19、量的原假設(shè) . 因為最小特征值統(tǒng)計量為 14.91. 大于臨界值 11.59 。總之我們有理由認為不存在弱工具變量。但為了穩(wěn)健起見. 下面使用對弱工具變量更不敏感的有限信息最大似然法LIML :. ivregress liml lw s expr tenure rns smsa (iq=med kww),rInstrumental variables (LIML) regressionNumber of obs =758Wald chi2(6)=369.62Prob > chi2=0.0000R-squared=0.2768Root MSE=.36454RobustlwCoef.Std.

20、 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 -1.26 0.209 -.1110631 .0242881smsa.1271796.02975994.270.000.0688512.185

21、508_cons3.214994.40014928.030.0002.4307163.999272Instrumented: iqInstruments:s expr tenure rns smsa med kww結(jié)果發(fā)現(xiàn) .LIML 的系數(shù)估計值與 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 . 為此須進展豪斯曼檢驗 . 其原假設(shè)是“所有的解釋變量均為外生 ：專業(yè)資料整理WORD格式.專業(yè)資料整理WORD格式. qui reg lw iq s expr tenure rns smsa. estimates store ols. qui

22、ivregress 2sls lw s expr tenure rns smsa (iq=med kww). estimates store iv. hausman iv ols, constant sigmamoreNote: the rank of the differenced variance matrix (1) does not equal the number of coefficients being tested (7); be sure this is what you expect, or theremay be problems computing the test.

23、Examine the output of your estimators for anything unexpected and possibly consider scaling your variables so that the coefficients are on a similar scale.Coefficients(b)(B)(b-B)sqrt(diag(V_b-V_B)ivolsDifferenceS.E.iq.0139284.0032792.0106493.0054318s.0607803.0927874-.032007.0163254expr.0433237.03934

24、43.0039794.0020297tenure.0296442.034209-.0045648.0023283rns-.0435271-.0745325.0310054.0158145smsa.1272224.1367369-.0095145.0048529_cons3.2180433.895172-.6771285.3453751b = consistent under Ho and Ha; obtained from ivregressB = inconsistent under Ha, efficient under Ho; obtained from regressTest: Ho:

25、 difference in coefficients not systematicchi2(1) = (b-B)'(V_b-V_B)(-1)(b-B)= 3.84Prob>chi2 =0.0499(V_b-V_B is not positive definite).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) . 即認為存在內(nèi)生解釋變量 iq 。由于傳統(tǒng)的豪斯曼檢驗建立在同方差的前提下 . 故在上述回歸中均沒有使用穩(wěn)健標準差。由于傳統(tǒng)的豪斯曼檢驗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：專業(yè)資料整理WORD格式.專業(yè)資料整理WOR

26、D格式. estat endogenousTests of endogeneityHo: variables are exogenousDurbin (score) chi2(1)= 3.87962 (p = 0.0489)Wu-Hausman F(1,750)= 3.85842 (p = 0.0499)據(jù)此可認為 iq為內(nèi)生解釋變量。如果存在異方差 . 那么 GMM比 2SLS更有效。為此進展如下的最優(yōu) GMM 估計：. ivregress gmm lw s expr tenure rns smsa (iq=med kww)Instrumental variables (GMM) regre

27、ssionNumber of obs=758Wald chi2(6) =372.75Prob > chi2=0.0000R-squared=0.2750GMM weight matrix: RobustRoot MSE=.36499RobustlwCoef.Std. Err. zP>|z|95% Conf. Intervaliq.0140888.00603572.330.020.0022591.0259185s.0603672.01895453.180.001.0232171.0975174expr.0431117.00741125.820.000.0285861.0576373t

28、enure.0299764.00827283.620.000.013762.0461908rns-.044516 .0344404 -1.29 0.196 -.1120219 .0229859smsa.1267368.02976334.260.000.0684018.1850718_cons3.207298.3980838.060.0002.4270693.987526Instrumented: iqInstruments:s expr tenure rns smsa med kww.進展過度識別檢驗：. estat overidTest of overidentifying restrict

29、ion:Hansen's J chi2(1) = .151451 (p = 0.6972)由于 p 值為 0.70. 故認為所有的工具變量均為外生。 考慮迭代 GMM：專業(yè)資料整理WORD格式.專業(yè)資料整理WORD格式. ivregress gmm lw s expr tenure rns smsa (iq=med kww),igmmIteration 1: change in beta =1.753e-05change in W =1.100e-02Iteration 2: change in beta =4.872e-08change in W =7.880e-05Iteratio

30、n 3: change in beta =2.495e-10change in W =2.304e-07Instrumental variables (GMM) regressionNumber of obs=758Wald chi2(6) =372.73Prob > chi2=0.0000R-squared=0.2750GMM weight matrix: RobustRoot MSE=.36499RobustlwCoef.Std. Err. zP>|z|95% Conf. Intervaliq.0140901.00603572.330.020.0022603.02592s.06

31、03629.01895483.180.001.0232122.0975135expr.0431101.00741135.820.000.0285841.057636tenure.0299752.00827293.620.000.0137606.0461898rns-.0445114 .0344408 -1.29 0.196 -.1120212 .0229913smsa.1267399.02976374.260.000.0684041.1850757_cons3.207224.39808788.060.0002.4269863.987462Instrumented: iqInstruments:

32、s expr tenure rns smsa med kww如果希望將以上各種估計法的系數(shù)估計值及其標準差列在同一X表中 . 可使用如下命令：專業(yè)資料整理WORD格式.專業(yè)資料整理WORD格式. qui reg lw s expr tenure rns smsa,r. estimates store ols_no_iq. qui reg lw s expr tenure rns smsa iq,r. estimates store ols_with_iq. qui ivregress 2sls lw s expr tenure rns smsa (iq=med kww),r. estimates store tsls. qui ivregress liml l