内生性与工具变量估计方法一 一元模型的 IV 估计采用MROZ数据，进行练习。 估计教育对工资收入的回报：log( wage ) = B + B educ + 卩01为了便于比较首先得到 OLS 估计结果，在命令窗口输入 smpl 1 428equation eq01.ls log(wage) c educDependent Variable: LOG(WAGE Method: LeastSquaresate: 11/23/10 Time: 10:47Sample: 1 428Included observations: 428CoefficientStd. Errort-StatisticProb.C-0.1851970.185226-0.999S4S0.3180EDUC0.1006490.0144-007.5451250.0000R-squared0.117833血mn depends nt 灿1.190173Adjusted R-squared0.115012S.D. dependent var0.723198S.E. of regression0.630032Akaike info criterion2.071309Sum squared resid197.0010Schwarz criterion2.090276Log likelihood-441.2600Hannan-Quinn criter.2.07SS00F-statistic56.92091 urbin-Watso n stat1.904707Prob(F-statistic)0.000000教育的系数估计值表明，每多接受一年教育可得到月 11%的回报。接下来，我们用父亲的受教育程度(fatheduc)作为educ的工具变量。我们必须认为fatheduc 与u不相关；第二个要求是educ与fatheduc相关。为了验证第二点，作一个educ对fatheduc 的回归。equation eq02.ls educ c fatheducDependent Variable: EDUC Method: Least Squares ate: 11/29/10 Time: 08:14 Sample: 1 428Included observations: 428CoefficientStd. Errort-StatisticProb.C10.237050.27593637.099330.0000FATHEDUC0.2694-420.0285869.4255380.0000R-squared0.172560Memn dependent var12.65888Adjusted R-squared0.170617S.D. dependent var2.285376S.E. of regression2.081302Akaike info criterion4.300526Sum squared resid1345354Schwarz criterion4-327494Log likelihood-920.0246Hannan-duinn uite.4316017F-statistic83.04076Durbin-Watson stat1.918691Prob(F-statistic0.000000可以看出，educ与fatheduc之间存在统计显著的正相关。采用fatheduc作为educ的工具变量，进行工具变量回归。equation eq03.tsls log(wage) c educ fatheduc ependentVariable: LOGfWAGE) Method: Two-Stage Least Squares Date: 11/29/10 Time: 03:28 Sample: 1 428Included observations: 428 Instrument list FATHEDUCCoefficientStd. Errort-StatisticProb.C0 4411030.4461020.9887950.3233EDUC0.0591730.0351421.6838500.0929R-squared0.093433Mean dlependEnt var1.190173Adjusted R-squared0.091310S.D. dependent var0.723198S.E. of regression0.609390Sum squared resid202.4601F-statistic2.335351Durbi n-Wmtson stat1.968194ProbF-statistic)0.092943Second-Stage SSR221.9799IV估计量的标准误是OLS标准误的2.5倍，这在我们的意料之中。二多元模型的IV估计采用card数据，进行练习。估计教育对工资收入的回报：log( wage ) = B B educ + B Control var iables + 卩0 1 2为了便于对照，先做 OLS 回归Smpl 1 3010Equation eq01.ls log(wage) c educ exper expersq black smsa south smsa66 reg662 reg663 reg664 reg665 reg666 reg667 reg668 reg669ependentVariable: LOG(WAGE) Method: Least Squares ate: 11/28/10 Time: 11:13 Sample (adjusted): 1 3010 Included observations: 3010 after adjustmentsCoefficientStd. Errort-StatisticProb.C4.6208070.07423362.247560.0000EDUC0.0746930.00349821351020.0000EXP ER0.0043320.00662412.806340.0000EXPERSQ-0.0022870.000317-7.2231570.0000BLACK-0.1990120.018243-10.905800.0000SMSA0.1363350.0201006.7851430.0000SOUTH-0.1479550.025900-5.6949030.0000SMSA660.0262420.0194-481 3493490.T773REG6 620.0963670.035898Z68447B0.0073REG66S0.1445400.035124411150850.0000REG6 640.0550760.04-1657-13221-100.1862REG6650.1200250.0413393.0599050.0022REG6660.1405170.0452473.1055670.0019REG 6 670.1179810.0440022.6333590.0005REG 6 63-0.0564360.051253-1.1010220.2710REG6690.-11857000388303.0535560.0023R-squared0.299836Mean dependent var6.261 S32Adjusted R-squared0.296329S.D. dependent var0.443798S.E. of re口ession0.372280Akaike info criterion0.866961Sum squared resid414.9461Schwarz criterion0.898907Log likelihood-1238.777Hannan-Quinn criter.0.878450F-statistic85.47627Durbin-Watson stat1.880434ProbfF-statistic)0.000000在这个例子中，受教育程度的工具变量是标志着一个人是否在一所四年制大学附 近成长的虚拟变量(n earc4)。为了验证受教育程度与该虚拟变量的偏相关性，先做educ对nearc4以及其他所 有外生变量的回归：Equation eq02.ls educ c nearc4 exper expersq black smsa south smsa66 reg662 reg663 reg664 reg665 reg666 reg667 reg668 reg669Dependent Variable: EDUCM eth o d: Le ast Sq u aresDate: 11/28/10 Time: 11:16Sample (adjusted): 1 3010Included observations: 3010 after adjustmentsCoefficientStd Errort-StatisticProb.C16.63S250.24063069.144630.0000NEARC40.3190990.0870643.640050O.OOflOEXPER-0 4125330.033700-12.24U90.0000EXPERSO0.0000690.0016500.5262070.5987BLACK-0.9355290.0937S5-9.9005960.0000SMSA0.4021820.1048113.8372080.0001SOUTH-0.0516130.135428-0.3311060.7032SMSA660.0254810.1057690.2409070.8096REG662-0.0736360.137115-0.4202560.6743REG663-0.0279390.133375-01523600.8739REG6640.1171820.2172530.5383800.5397REG665-0.2726160.21B420-1.2401270.2121REG666-0.3023150.237071-1.2773150.2016REG667-0.2163180.234388-0.92503303550REG663