“众里寻他千百度”——工具变量法（IV）的Stata操作
数据说明
Replication Data for: Ting Chen, James Kai-sing Kung, Chicheng Ma. Long Live Keju ! The Persistent Effects of China’s Civil Examination System[J]. The Economic Journal, 2020, 130 (631) : 2030–2064.
识别策略
lneduyearlnjinshipopbprvdistlnnightlight、到海岸线的距离lncoastdist、地形崎岖程度tri、农业产量suitability 、人口密度lnpopdensity、城市化率urbanrates和省级固定效应Stata操作
ivregress命令和ivreg2命令。ivregress命令
ivregress命令是Stata自带的命令，支持两阶段最小二乘（2SLS）、广义矩估计（GMM）和有限信息最大似然估计（LIML）三种工具变量估计方法，我们最常使用的是两阶段最小二乘法（2SLS），因为2SLS最能体现工具变量的实质，并且在球形扰动项的情况下，2SLS是最有效率的工具变量法。ivregress后面加上2sls即可，然后将内生解释变量lnjinshipop和工具变量bprvdist放在一个小括号中，用=号连接。选项first表示报告第一阶段回归结果，选项cluster()表示使用聚类稳健的标准误。ivregress 2sls lneduyear (lnjinshipop=bprvdist) lnnightlight lncoastdist tri suitability lnpopdensity urbanrates i.provid , first cluster(provid)
第一阶段回归结果
First-stage regressions-----------------------
Number of obs = 274 No. of clusters = 28 F( 7, 239) = 85.27 Prob > F = 0.0000 R-squared = 0.6487 Adj R-squared = 0.5988 Root MSE = 0.4442
------------------------------------------------------------------------------ | Robust lnjinshipop | Coef. Std. Err. t P>|t| [95% Conf. Interval]-------------+----------------------------------------------------------------lnnightlight | .183385 .0682506 2.69 0.008 .0489354 .3178346 lncoastdist | .0350333 .077158 0.45 0.650 -.1169634 .1870299 tri | 1.06676 .5637082 1.89 0.060 -.0437105 2.177231 suitability | -.0769726 .0549697 -1.40 0.163 -.1852596 .0313144lnpopdensity | .196144 .0843727 2.32 0.021 .0299349 .3623532 urbanrates | 3.352916 1.687109 1.99 0.048 .029414 6.676419 | provid | 12 | .2051006 .0551604 3.72 0.000 .096438 .3137632 13 | -1.890425 .0951146 -19.88 0.000 -2.077795 -1.703055...... 64 | -1.301895 .1581021 -8.23 0.000 -1.613346 -.9904433 | bprvdist | -.0846917 .0107859 -7.85 0.000 -.1059393 -.0634441 _cons | 2.126233 .9791046 2.17 0.031 .1974567 4.05501------------------------------------------------------------------------------bprvdist的系数为-0.085，标准误为0.011，在1%的水平上显著。第二阶段回归结果
Instrumental variables (2SLS) regression Number of obs = 274
Wald chi2(34) = 13.62
Prob > chi2 = 0.9993
R-squared = 0.7874
Root MSE = .05434
(Std. Err. adjusted for 28 clusters in provid)
------------------------------------------------------------------------------
| Robust
lneduyear | Coef. Std. Err. z P>|z| [95% Conf. Interval]
-------------+----------------------------------------------------------------
lnjinshipop | .0834221 .0116773 7.14 0.000 .060535 .1063092
lnnightlight | .0592777 .0102138 5.80 0.000 .0392589 .0792964
lncoastdist | .0093399 .0118791 0.79 0.432 -.0139426 .0326224
tri | -.1044346 .063917 -1.63 0.102 -.2297097 .0208404
suitability | -.0008944 .0125824 -0.07 0.943 -.0255555 .0237666
lnpopdensity | -.0472648 .0115102 -4.11 0.000 -.0698245 -.0247051
urbanrates | -.0353689 .1784687 -0.20 0.843 -.3851612 .3144233
|
provid |
12 | -.10732 .0088755 -12.09 0.000 -.1247157 -.0899243
13 | .0244675 .0276005 0.89 0.375 -.0296284 .0785634
......
64 | -.0740796 .0350354 -2.11 0.034 -.1427477 -.0054116
|
_cons | 2.014146 .1490819 13.51 0.000 1.721951 2.306341
------------------------------------------------------------------------------
lnjinshipop的系数为0.083，标准误为0.012，在1%的水平上显著。弱工具变量检验
estat firststage命令对第一阶段的结果进行分析，以判断是否存在弱工具变量问题。. estat firststage,forcenonrobust
First-stage regression summary statistics -------------------------------------------------------------------------- | Adjusted Partial Robust Variable | R-sq. R-sq. R-sq. F(1,27) Prob > F -------------+------------------------------------------------------------ lnjinshipop | 0.6487 0.5988 0.3276 61.914 0.0000 -------------------------------------------------------------------------- (F statistic adjusted for 28 clusters in provid)
Minimum eigenvalue statistic = 116.419
Critical Values # of endogenous regressors: 1 Ho: Instruments are weak # of excluded instruments: 1 --------------------------------------------------------------------- | 5% 10% 20% 30% 2SLS relative bias | (not available) -----------------------------------+--------------------------------- | 10% 15% 20% 25% 2SLS Size of nominal 5% Wald test | 16.38 8.96 6.66 5.53 LIML Size of nominal 5% Wald test | 16.38 8.96 6.66 5.53 ---------------------------------------------------------------------bprvdist对内生变量lnjinshipop有很强的解释力度。F统计量=61.914>10，根据经验准则可以判断，我们的工具变量不是一个弱工具变量。除此之外，estat firststage命令还会报告一个最小特征值统计量（Minimum eigenvalue statistic），一般大于2SLS Size of nominal 5% Wald test中10%对应的临界值就表明不存在弱工具变量问题。ivreg2命令
ivreg2命令是对ivregress命令的改进和优化，功能更加强大，支持的估计方法更多（默认使用2SLS），并且会直接报告工具变量的几个统计检验结果，陈婷、龚启圣和马驰骋三位老师使用的就是ivreg2命令。ivreg2命令是一个外部命令，所以使用之前需要安装（ssc install ivreg2）。它的语法格式和ivregress基本一致：ivreg2 lneduyear (lnjinshipop=bprvdist) lnnightlight lncoastdist tri suitability lnpopdensity urbanrates i.provid , first cluster(provid)
第一阶段回归结果
First-stage regression of lnjinshipop:
Statistics robust to heteroskedasticity and clustering on providNumber of obs = 274Number of clusters (provid) = 28------------------------------------------------------------------------------ | Robust lnjinshipop | Coef. Std. Err. t P>|t| [95% Conf. Interval]-------------+---------------------------------------------------------------- bprvdist | -.0846917 .0107633 -7.87 0.000 -.1058948 -.0634886lnnightlight | .183385 .0681077 2.69 0.008 .0492169 .3175531 lncoastdist | .0350333 .0769964 0.45 0.650 -.116645 .1867116 tri | 1.06676 .5625276 1.90 0.059 -.0413849 2.174906 suitability | -.0769726 .0548546 -1.40 0.162 -.1850328 .0310876lnpopdensity | .196144 .084196 2.33 0.021 .030283 .3620051 urbanrates | 3.352916 1.683576 1.99 0.048 .0363742 6.669459 | provid | 12 | .2051006 .0550449 3.73 0.000 .0966656 .3135357 13 | -1.890425 .0949154 -19.92 0.000 -2.077402 -1.703447...... 64 | -1.301895 .157771 -8.25 0.000 -1.612694 -.9910956 | _cons | 2.126233 .9770541 2.18 0.031 .201496 4.050971------------------------------------------------------------------------------第二阶段回归结果
IV (2SLS) estimation
--------------------
Estimates efficient for homoskedasticity only
Statistics robust to heteroskedasticity and clustering on provid
Number of clusters (provid) = 28 Number of obs = 274
F( 34, 27) = 0.34
Prob > F = 0.9984
Total (centered) SS = 3.805186838 Centered R2 = 0.7874
Total (uncentered) SS = 1282.736705 Uncentered R2 = 0.9994
Residual SS = .8089841945 Root MSE = .05434
------------------------------------------------------------------------------
| Robust
lneduyear | Coef. Std. Err. z P>|z| [95% Conf. Interval]
-------------+----------------------------------------------------------------
lnjinshipop | .0834221 .0116773 7.14 0.000 .060535 .1063092
lnnightlight | .0592777 .0102138 5.80 0.000 .0392589 .0792964
lncoastdist | .0093399 .0118791 0.79 0.432 -.0139426 .0326224
tri | -.1044346 .063917 -1.63 0.102 -.2297097 .0208404
suitability | -.0008944 .0125824 -0.07 0.943 -.0255555 .0237666
lnpopdensity | -.0472648 .0115102 -4.11 0.000 -.0698245 -.0247051
urbanrates | -.0353689 .1784687 -0.20 0.843 -.3851612 .3144233
|
provid |
12 | -.10732 .0088755 -12.09 0.000 -.1247157 -.0899243
13 | .0244675 .0276005 0.89 0.375 -.0296284 .0785634
......
64 | -.0740796 .0350354 -2.11 0.034 -.1427477 -.0054116
|
_cons | 2.014146 .1490819 13.51 0.000 1.721951 2.306341
------------------------------------------------------------------------------
弱工具变量检验结果
ivreg2命令会直接报告Cragg-Donald Wald F 统计量和Kleibergen-Paap Wald rk F统计量两个用于弱工具变量检验的统计量，其中Cragg-Donald Wald F 统计量假设扰动项iid（独立同分布），而Kleibergen-Paap Wald rk F统计量没有做扰动项iid的假设。需要注意的是，这里的原假设是所选工具变量是弱工具变量，当两个F统计量大于Stock-Yogo weak ID test critical values中10%偏误的临界值时，可以拒绝原假设，认为不存在弱工具变量问题。Weak identification testHo: equation is weakly identifiedCragg-Donald Wald F statistic 116.42Kleibergen-Paap Wald rk F statistic 61.91
Stock-Yogo weak ID test critical values for K1=1 and L1=1: 10% maximal IV size 16.38 15% maximal IV size 8.96 20% maximal IV size 6.66 25% maximal IV size 5.53Source: Stock-Yogo (2005). Reproduced by permission.NB: Critical values are for Cragg-Donald F statistic and i.i.d. errors.需要本篇推文使用的数据和代码的朋友，请在后台对话框内回复关键词“IV”。
xtivreg和xtivreg2两个命令，语法格式与ivreg2基本类似，大家有兴趣的话可以去看一下这两个命令的help文件。