工具變量法的Stata命令及實(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)特征：.sumVariableOpsMea nStd. Dev.Minrns7582691293.44380010rn s8075 3.292876.45538250mrt, 7585145119.50011940mrt8075 3.8984169.30229880smsa75 8.7044855.4565750smsa807 58 .7124011.4529420med75 810.910292.741120iq, 758103.856213.6186754kww175 836.573887.3

2、0224712year,75869.031662.63179466age75821.835092.98175616age8075 833.011873.08550428s75813.405012.2318289s801 75813.707122.2146939expr7581.7354292.1055420expr8075 811.394264.210745.692ten ure75 31.8311351.673630tenu re807 587.3627975.050240lw7585.68673942894944.605lw80175816.826555.40992684.749Max11

3、11111814556733038181811.44422.04510227.0518.032考察智商與受教育年限的相關(guān)關(guān)系:.corriq 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(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OLS回歸，并使用穩(wěn)健標(biāo)準(zhǔn)差:.reg lw s expr tenure rns smsa,rLin ear regressiNumber of obs =758onF(5, 752)=84.05Prob F =0.0000R-squared= 0.3521R

4、oot MSE=.34641Robustlw Coef. Std. Err.t P|t|95% Conf.Intervals .102643 .006209916.53 0.000.0904523.1148338expr .0381189 .00661445.76 0.000.025134.0511038ten ure .0356*46 .00799884.45 0.000.0199118.0513173rns -.0840797.029533-2.85 0.005-.1420566 -.0261029smsa .1396666 .028056 4.98 0.000 .0845893 .194

5、744cons 4.103675 .0876665 46.81 0.000 3.931575 4.275775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。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(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 :.reg Iw s iq expr tenure rns smsa,rLin ear regressi on Number of obs

6、 =758F(6, 751)=71.89Prob F =0.0000R-squared= 0.3600Root MSE=.34454RobustIw Coef. Std. Err. t P|t|95% Con f. I ntervals.0927874.006976313.30 0.000.0790921.1064826iq.0032792.0011321 .2.90 0.004.0010567.0055016expr03934 43.00666035.91 0.000.0262692.0524193tenure.0342 09.00789574.33 0.000.0187088.049709

7、2rns-.0745325 .0299772-2.49 0.013-.1333815-.0156834smsa.1367369 .02777124.92 0.000.0822186.1912553cons3.895172 .115928633.60 0.0003.6675894.122754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 knowledgeof the World of Work”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

8、量，進(jìn)行2SLS回歸，并使用穩(wěn)健的標(biāo)準(zhǔn)差 :In strume ntal variables (2SLS) regressi onNumber of obs = 758Wald chi2(6) =355.73Prob chi2 =0.0000R-squared= 0.2002Root MSE= .38336RobustlwCoef.Std. Err. zP|z95% Conf. In terval|0.041iq -. 0115468 .0056376-2.05.0225962-.0004974s.1373477 .01749897.850.0001030506.1716449expr.033

9、8041 .00748444.520.000.019135.0484732ten ure5.04064 .00958484.230.000.0217781.05935rnsX .0359582-3.27 0.001-.1881751 -.0472216-.11769smsa8.14983 .03222764.650.000.0868182.2131479_cons 94.837375 . 379943212.73 0.0004.09325.58255,In strume nted: iqIn strume nts: s expr tenure rns smsa med kww mrt age在

10、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) :.estat overidTest of overide ntify ing restrict ions:Score chi2(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-stage regressionsNumber of ob

11、s =758F( 7,750)=47.74Prob F0.0000R-squared0.3066Adj R-squared0.3001Root MSE=11.3931Robustiq Coef. Std. Err. t P|t| ntervals2.467021 .2327755expr-.4501353 .2391647tenure.2059531.269562rns-2.689831 .8921335.2627416.9465309smsa.34701 33.1681356med.3081811.0646794kww56.671223.076955cons95% Con f. I10.60

12、0.0002.0100522.92399-1.880.060-.9196471.01937660.76 0.445-.3232327.7351388-3.020.003-4.441207-.9384550.280.781-1.5954242.1209072.060.039.0169409.67708574.760.000.1812068.435155318.42 0.00050.6307562.71169Instrumental variables(2SLS) regressionNumber of obs =758Wald chi2 (6)=370.04Prob chi2=0.0000R-squared=0.2775Root MSE=.36436Robustlw Coef. Std. Err. z P|z| ntervali.0139284 .0060393q.0607803.0189505s.04332：exprtenure37 .0074118.0296442.008317rns-.0435271 .0344779smsa.1272224.0297414cons3.218043.398368395% Con f. I2.31 0.021.0020916.02576533.21 0.001023638.09792275.850.000.028796