这篇文章主要是：R语言中工具变量的使用、涉及到的数据处理以及模型含义。

两个例题：例题一涉及6个问题，使用的数据集为R语言自带的fertil2。例题二涉及3个问题，使用的数据集为stata格式的eitc.dta。本文介绍例题一。例题二见上篇。

例题一

1.1 问题

使用数据集fertil2，因变量为children，educ为自变量（是否为内生在问题1-6中会讨论），还有其他自变量如age等。

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1.2 我的解答

解答

1.3 R语言代码

> library(wooldridge) # To download database
> library(tidyverse) # Tidyverse packages
> library(stargazer) # To draw output tables 
> library(lmtest)
> library(AER) # applied econometrics in R
> data("fertil2")
> view(fertil2)
> head(fertil2,6)  #看数据前6行
  mnthborn yearborn age electric radio tv bicycle educ ceb agefbrth children knowmeth usemeth monthfm yearfm agefm
1        5       64  24        1     1  1       1   12   0       NA        0        1       0      NA     NA    NA
2        1       56  32        1     1  1       1   13   3       25        3        1       1      11     80    24
3        7       58  30        1     0  0       0    5   1       27        1        1       0       6     83    24
4       11       45  42        1     0  1       0    4   3       17        2        1       0       1     61    15
5        5       45  43        1     1  1       1   11   2       24        2        1       1       3     66    20
6        8       52  36        1     0  0       0    7   1       26        1        1       1      11     76    24
  idlnchld heduc agesq urban urb_educ spirit protest catholic frsthalf educ0 evermarr
1        2    NA   576     1       12      0       0        0        1     0        0
2        3    12  1024     1       13      0       0        0        1     0        1
3        5     7   900     1        5      1       0        0        0     0        1
4        3    11  1764     1        4      0       0        0        0     0        1
5        2    14  1849     1       11      0       1        0        1     0        1
6        4     9  1296     1        7      0       0        0        0     0        1

#问题1
> model_1 = lm(children~ educ + age + agesq,data = fertil2)
> summary(model_1)
Call:
lm(formula = children ~ educ + age + agesq, data = fertil2)

Coefficients:
              Estimate Std. Error t value Pr(>|t|)    
(Intercept) -4.1383066  0.2405942 -17.200   <2e-16 ***
educ        -0.0905755  0.0059207 -15.298   <2e-16 ***
age          0.3324486  0.0165495  20.088   <2e-16 ***
agesq       -0.0026308  0.0002726  -9.651   <2e-16 ***

#问题4
> model_2 = lm(educ~ frsthalf,data = fertil2)
> summary(model_2)
Call:
lm(formula = educ ~ frsthalf, data = fertil2)

Coefficients:
            Estimate Std. Error t value Pr(>|t|)    
(Intercept)  6.36277    0.08711  73.042  < 2e-16 ***
frsthalf    -0.93766    0.11849  -7.913 3.15e-15 ***

#问题5
> model_3 = lm(children~ frsthalf + age + agesq,data = fertil2)
> summary(model_3)

Call:
lm(formula = children ~ frsthalf + age + agesq, data = fertil2)

Coefficients:
              Estimate Std. Error t value Pr(>|t|)    
(Intercept) -5.0501211  0.2412071 -20.937  < 2e-16 ***
frsthalf     0.1461660  0.0455053   3.212  0.00133 ** 
age          0.3421186  0.0169552  20.178  < 2e-16 ***
agesq       -0.0025856  0.0002795  -9.252  < 2e-16 ***

#问题5
> model_4 = lm(children~ educ + age + agesq + electric + tv + bicycle,
+              data = fertil2)
> summary(model_4)

Call:
lm(formula = children ~ educ + age + agesq + electric + tv + 
    bicycle, data = fertil2)

Coefficients:
              Estimate Std. Error t value Pr(>|t|)    
(Intercept) -4.3897837  0.2403173 -18.267  < 2e-16 ***
educ        -0.0767093  0.0063526 -12.075  < 2e-16 ***
age          0.3402038  0.0164417  20.692  < 2e-16 ***
agesq       -0.0027081  0.0002706 -10.010  < 2e-16 ***
electric    -0.3027293  0.0761869  -3.974 7.20e-05 ***
tv          -0.2531443  0.0914374  -2.768  0.00566 ** 
bicycle      0.3178950  0.0493661   6.440 1.33e-10 ***

> model_5 = ivreg(children~educ + age + agesq + electric + tv + bicycle|
+                frsthalf + age + agesq + electric + tv + bicycle,
+              data = fertil2)
> summary(model_5)

Call:
ivreg(formula = children ~ educ + age + agesq + electric + tv + 
    bicycle | frsthalf + age + agesq + electric + tv + bicycle, 
    data = fertil2)

Coefficients:
              Estimate Std. Error t value Pr(>|t|)    
(Intercept) -3.5913324  0.6450889  -5.567 2.74e-08 ***
educ        -0.1639814  0.0655269  -2.503   0.0124 *  
age          0.3281451  0.0190587  17.218  < 2e-16 ***
agesq       -0.0027222  0.0002766  -9.843  < 2e-16 ***
electric    -0.1065314  0.1659650  -0.642   0.5210    
tv          -0.0025550  0.2092301  -0.012   0.9903    
bicycle      0.3320724  0.0515264   6.445 1.28e-10 ***

以上是我自己做的答案，也不知道正确答案如何，如果有会的同学来点评帮助一下，小编将感激不尽。共勉。