Chapter 15: Instrumental Variables Estimation and Two Stage Least Squares
with tags instrumental-variables iv -library(AER)
library(wooldridge)Example 15.1
data("mroz")OLS
s.lm.1 <- summary(lm(lwage ~ educ, data = mroz))
s.lm.1##
## Call:
## lm(formula = lwage ~ educ, data = mroz)
##
## Residuals:
## Min 1Q Median 3Q Max
## -3.10256 -0.31473 0.06434 0.40081 2.10029
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) -0.1852 0.1852 -1.000 0.318
## educ 0.1086 0.0144 7.545 2.76e-13 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.68 on 426 degrees of freedom
## (325 observations deleted due to missingness)
## Multiple R-squared: 0.1179, Adjusted R-squared: 0.1158
## F-statistic: 56.93 on 1 and 426 DF, p-value: 2.761e-13fatheduc as IV for educ
s.lm.2 <- summary(lm(educ ~ fatheduc, data = mroz[mroz$inlf !=0 ,]))
s.lm.2##
## Call:
## lm(formula = educ ~ fatheduc, data = mroz[mroz$inlf != 0, ])
##
## Residuals:
## Min 1Q Median 3Q Max
## -8.4704 -1.1231 -0.1231 0.9546 5.9546
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 10.23705 0.27594 37.099 <2e-16 ***
## fatheduc 0.26944 0.02859 9.426 <2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 2.081 on 426 degrees of freedom
## Multiple R-squared: 0.1726, Adjusted R-squared: 0.1706
## F-statistic: 88.84 on 1 and 426 DF, p-value: < 2.2e-16IV estimation
s.iv.1 <- summary(ivreg(lwage ~ educ | fatheduc,
data=mroz))
s.iv.1##
## Call:
## ivreg(formula = lwage ~ educ | fatheduc, data = mroz)
##
## Residuals:
## Min 1Q Median 3Q Max
## -3.0870 -0.3393 0.0525 0.4042 2.0677
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 0.44110 0.44610 0.989 0.3233
## educ 0.05917 0.03514 1.684 0.0929 .
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.6894 on 426 degrees of freedom
## Multiple R-Squared: 0.09344, Adjusted R-squared: 0.09131
## Wald test: 2.835 on 1 and 426 DF, p-value: 0.09294Example 15.2
data("wage2")
s.lm.1 <- summary(lm(educ ~ sibs, data = wage2))
s.lm.1##
## Call:
## lm(formula = educ ~ sibs, data = wage2)
##
## Residuals:
## Min 1Q Median 3Q Max
## -5.139 -1.683 -0.683 1.931 6.140
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 14.13879 0.11314 124.969 < 2e-16 ***
## sibs -0.22792 0.03028 -7.528 1.22e-13 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 2.134 on 933 degrees of freedom
## Multiple R-squared: 0.05726, Adjusted R-squared: 0.05625
## F-statistic: 56.67 on 1 and 933 DF, p-value: 1.215e-13s.iv.1 <- summary(ivreg(lwage ~ educ | sibs, data = wage2))
s.iv.1##
## Call:
## ivreg(formula = lwage ~ educ | sibs, data = wage2)
##
## Residuals:
## Min 1Q Median 3Q Max
## -1.85429 -0.26950 0.04223 0.29276 1.31038
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 5.13003 0.35517 14.444 < 2e-16 ***
## educ 0.12243 0.02635 4.646 3.86e-06 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.4233 on 933 degrees of freedom
## Multiple R-Squared: -0.009174, Adjusted R-squared: -0.01026
## Wald test: 21.59 on 1 and 933 DF, p-value: 3.865e-06Example 15.3
data("bwght")
s.lm.1 <- summary(lm(packs ~ cigprice, data = bwght))
s.lm.1##
## Call:
## lm(formula = packs ~ cigprice, data = bwght)
##
## Residuals:
## Min 1Q Median 3Q Max
## -0.1106 -0.1061 -0.1032 -0.1015 2.4016
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 0.0674257 0.1025384 0.658 0.511
## cigprice 0.0002829 0.0007830 0.361 0.718
##
## Residual standard error: 0.2987 on 1386 degrees of freedom
## Multiple R-squared: 9.417e-05, Adjusted R-squared: -0.0006273
## F-statistic: 0.1305 on 1 and 1386 DF, p-value: 0.7179s.iv.1 <- summary(ivreg(lbwght ~ packs | cigprice,
data = bwght))
s.iv.1##
## Call:
## ivreg(formula = lbwght ~ packs | cigprice, data = bwght)
##
## Residuals:
## Min 1Q Median 3Q Max
## -7.4200 0.1368 0.3055 0.4194 1.1540
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 4.4481 0.9082 4.898 1.08e-06 ***
## packs 2.9887 8.6989 0.344 0.731
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.9389 on 1386 degrees of freedom
## Multiple R-Squared: -23.23, Adjusted R-squared: -23.25
## Wald test: 0.118 on 1 and 1386 DF, p-value: 0.7312Example 15.4
data("card")
s.lm.1 <- summary(lm(educ ~ nearc4 + exper + expersq + black + smsa + south +
smsa66 + reg662 + reg663 + reg664 + reg665 + reg666 + reg667 +
reg668 + reg669,
data = card))
s.lm.1##
## Call:
## lm(formula = educ ~ nearc4 + exper + expersq + black + smsa +
## south + smsa66 + reg662 + reg663 + reg664 + reg665 + reg666 +
## reg667 + reg668 + reg669, data = card)
##
## Residuals:
## Min 1Q Median 3Q Max
## -7.545 -1.370 -0.091 1.278 6.239
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 16.6382529 0.2406297 69.145 < 2e-16 ***
## nearc4 0.3198989 0.0878638 3.641 0.000276 ***
## exper -0.4125334 0.0336996 -12.241 < 2e-16 ***
## expersq 0.0008686 0.0016504 0.526 0.598728
## black -0.9355287 0.0937348 -9.981 < 2e-16 ***
## smsa 0.4021825 0.1048112 3.837 0.000127 ***
## south -0.0516126 0.1354284 -0.381 0.703152
## smsa66 0.0254805 0.1057692 0.241 0.809644
## reg662 -0.0786363 0.1871154 -0.420 0.674329
## reg663 -0.0279390 0.1833745 -0.152 0.878913
## reg664 0.1171820 0.2172531 0.539 0.589665
## reg665 -0.2726165 0.2184204 -1.248 0.212082
## reg666 -0.3028147 0.2370712 -1.277 0.201590
## reg667 -0.2168177 0.2343879 -0.925 0.355021
## reg668 0.5238914 0.2674749 1.959 0.050246 .
## reg669 0.2102710 0.2024568 1.039 0.299076
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 1.941 on 2994 degrees of freedom
## Multiple R-squared: 0.4771, Adjusted R-squared: 0.4745
## F-statistic: 182.1 on 15 and 2994 DF, p-value: < 2.2e-16s.lm.2 <- summary(lm.2 <- lm(lwage ~ educ + exper + expersq + black + smsa + south +
smsa66 + reg662 + reg663 + reg664 + reg665 + reg666 + reg667 +
reg668 + reg669,
data = card))
s.lm.2##
## Call:
## lm(formula = lwage ~ educ + exper + expersq + black + smsa +
## south + smsa66 + reg662 + reg663 + reg664 + reg665 + reg666 +
## reg667 + reg668 + reg669, data = card)
##
## Residuals:
## Min 1Q Median 3Q Max
## -1.62326 -0.22141 0.02001 0.23932 1.33340
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 4.6208068 0.0742327 62.248 < 2e-16 ***
## educ 0.0746933 0.0034983 21.351 < 2e-16 ***
## exper 0.0848320 0.0066242 12.806 < 2e-16 ***
## expersq -0.0022870 0.0003166 -7.223 6.41e-13 ***
## black -0.1990123 0.0182483 -10.906 < 2e-16 ***
## smsa 0.1363845 0.0201005 6.785 1.39e-11 ***
## south -0.1479550 0.0259799 -5.695 1.35e-08 ***
## smsa66 0.0262417 0.0194477 1.349 0.17733
## reg662 0.0963672 0.0358979 2.684 0.00730 **
## reg663 0.1445400 0.0351244 4.115 3.97e-05 ***
## reg664 0.0550756 0.0416573 1.322 0.18623
## reg665 0.1280248 0.0418395 3.060 0.00223 **
## reg666 0.1405174 0.0452469 3.106 0.00192 **
## reg667 0.1179810 0.0448025 2.633 0.00850 **
## reg668 -0.0564361 0.0512579 -1.101 0.27098
## reg669 0.1185698 0.0388301 3.054 0.00228 **
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.3723 on 2994 degrees of freedom
## Multiple R-squared: 0.2998, Adjusted R-squared: 0.2963
## F-statistic: 85.48 on 15 and 2994 DF, p-value: < 2.2e-16s.iv.1 <- summary(ivreg(lwage ~ educ + exper + expersq + black + smsa + south +
smsa66 + reg662 + reg663 + reg664 + reg665 + reg666 + reg667 +
reg668 + reg669 | nearc4 + exper + expersq + black + smsa + south +
smsa66 + reg662 + reg663 + reg664 + reg665 + reg666 + reg667 +
reg668 + reg669,
data = card))
s.iv.1##
## Call:
## ivreg(formula = lwage ~ educ + exper + expersq + black + smsa +
## south + smsa66 + reg662 + reg663 + reg664 + reg665 + reg666 +
## reg667 + reg668 + reg669 | nearc4 + exper + expersq + black +
## smsa + south + smsa66 + reg662 + reg663 + reg664 + reg665 +
## reg666 + reg667 + reg668 + reg669, data = card)
##
## Residuals:
## Min 1Q Median 3Q Max
## -1.83164 -0.24075 0.02428 0.25208 1.42760
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 3.6661509 0.9248295 3.964 7.54e-05 ***
## educ 0.1315038 0.0549637 2.393 0.01679 *
## exper 0.1082711 0.0236586 4.576 4.92e-06 ***
## expersq -0.0023349 0.0003335 -7.001 3.12e-12 ***
## black -0.1467757 0.0538999 -2.723 0.00650 **
## smsa 0.1118083 0.0316620 3.531 0.00042 ***
## south -0.1446715 0.0272846 -5.302 1.23e-07 ***
## smsa66 0.0185311 0.0216086 0.858 0.39119
## reg662 0.1007678 0.0376857 2.674 0.00754 **
## reg663 0.1482588 0.0368141 4.027 5.78e-05 ***
## reg664 0.0498971 0.0437398 1.141 0.25406
## reg665 0.1462719 0.0470639 3.108 0.00190 **
## reg666 0.1629029 0.0519096 3.138 0.00172 **
## reg667 0.1345722 0.0494023 2.724 0.00649 **
## reg668 -0.0830770 0.0593314 -1.400 0.16155
## reg669 0.1078142 0.0418137 2.578 0.00997 **
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.3883 on 2994 degrees of freedom
## Multiple R-Squared: 0.2382, Adjusted R-squared: 0.2343
## Wald test: 51.01 on 15 and 2994 DF, p-value: < 2.2e-16Example 15.5
data("mroz")
s.lm.1 <- summary(lm.1 <- lm(lwage ~ educ + exper + expersq, data = mroz))
s.lm.1##
## Call:
## lm(formula = lwage ~ educ + exper + expersq, data = mroz)
##
## Residuals:
## Min 1Q Median 3Q Max
## -3.08404 -0.30627 0.04952 0.37498 2.37115
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) -0.5220406 0.1986321 -2.628 0.00890 **
## educ 0.1074896 0.0141465 7.598 1.94e-13 ***
## exper 0.0415665 0.0131752 3.155 0.00172 **
## expersq -0.0008112 0.0003932 -2.063 0.03974 *
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.6664 on 424 degrees of freedom
## (325 observations deleted due to missingness)
## Multiple R-squared: 0.1568, Adjusted R-squared: 0.1509
## F-statistic: 26.29 on 3 and 424 DF, p-value: 1.302e-15s.lm.2a <- summary(lm.2a <- lm(educ ~ exper + expersq + motheduc + fatheduc,
data = mroz[mroz$inlf > 0,]))
s.lm.2b <- summary(lm.2b <- lm(educ ~ exper + expersq,data=mroz[mroz$inlf > 0,]))
anova(lm.2a, lm.2b)## Analysis of Variance Table
##
## Model 1: educ ~ exper + expersq + motheduc + fatheduc
## Model 2: educ ~ exper + expersq
## Res.Df RSS Df Sum of Sq F Pr(>F)
## 1 423 1758.6
## 2 425 2219.2 -2 -460.64 55.4 < 2.2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1s.iv.1 <- summary(ivreg(lwage ~ educ + exper + expersq | exper +
expersq + motheduc + fatheduc, data = mroz))
s.iv.1##
## Call:
## ivreg(formula = lwage ~ educ + exper + expersq | exper + expersq +
## motheduc + fatheduc, data = mroz)
##
## Residuals:
## Min 1Q Median 3Q Max
## -3.0986 -0.3196 0.0551 0.3689 2.3493
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 0.0481003 0.4003281 0.120 0.90442
## educ 0.0613966 0.0314367 1.953 0.05147 .
## exper 0.0441704 0.0134325 3.288 0.00109 **
## expersq -0.0008990 0.0004017 -2.238 0.02574 *
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.6747 on 424 degrees of freedom
## Multiple R-Squared: 0.1357, Adjusted R-squared: 0.1296
## Wald test: 8.141 on 3 and 424 DF, p-value: 2.787e-05Example 15.6
data("wage2")
s.iv.1 <- summary(ivreg(lwage ~ educ + exper + tenure + married + south + urban + black +
IQ | KWW + educ + exper + tenure + married + south + urban + black,
data = wage2))
s.iv.1##
## Call:
## ivreg(formula = lwage ~ educ + exper + tenure + married + south +
## urban + black + IQ | KWW + educ + exper + tenure + married +
## south + urban + black, data = wage2)
##
## Residuals:
## Min 1Q Median 3Q Max
## -2.095561 -0.224017 0.006572 0.234495 1.398914
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 4.592453 0.325781 14.097 < 2e-16 ***
## educ 0.025032 0.016607 1.507 0.13206
## exper 0.014420 0.003321 4.342 1.56e-05 ***
## tenure 0.010456 0.002601 4.020 6.30e-05 ***
## married 0.200690 0.040678 4.934 9.56e-07 ***
## south -0.051553 0.031128 -1.656 0.09803 .
## urban 0.176706 0.028212 6.264 5.75e-10 ***
## black -0.022561 0.073960 -0.305 0.76040
## IQ 0.013047 0.004934 2.644 0.00832 **
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.3807 on 926 degrees of freedom
## Multiple R-Squared: 0.19, Adjusted R-squared: 0.183
## Wald test: 36.96 on 8 and 926 DF, p-value: < 2.2e-16Example 15.7
data("mroz")
s.lm.1 <- summary(lm.1 <- lm(lwage ~ educ + exper + expersq, data = mroz))
s.lm.1##
## Call:
## lm(formula = lwage ~ educ + exper + expersq, data = mroz)
##
## Residuals:
## Min 1Q Median 3Q Max
## -3.08404 -0.30627 0.04952 0.37498 2.37115
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) -0.5220406 0.1986321 -2.628 0.00890 **
## educ 0.1074896 0.0141465 7.598 1.94e-13 ***
## exper 0.0415665 0.0131752 3.155 0.00172 **
## expersq -0.0008112 0.0003932 -2.063 0.03974 *
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.6664 on 424 degrees of freedom
## (325 observations deleted due to missingness)
## Multiple R-squared: 0.1568, Adjusted R-squared: 0.1509
## F-statistic: 26.29 on 3 and 424 DF, p-value: 1.302e-15s.lm.2 <- summary(lm.2 <- lm(educ ~ exper + expersq + motheduc + fatheduc,
data = mroz[mroz$inlf != 0,]))
s.lm.3 <- summary(lm.3 <- lm(lwage ~ educ + exper + expersq + lm.2$resid,
data = mroz[mroz$inlf != 0,]))
s.lm.3##
## Call:
## lm(formula = lwage ~ educ + exper + expersq + lm.2$resid, data = mroz[mroz$inlf !=
## 0, ])
##
## Residuals:
## Min 1Q Median 3Q Max
## -3.03743 -0.30775 0.04191 0.40361 2.33303
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 0.0481003 0.3945753 0.122 0.903033
## educ 0.0613966 0.0309849 1.981 0.048182 *
## exper 0.0441704 0.0132394 3.336 0.000924 ***
## expersq -0.0008990 0.0003959 -2.271 0.023672 *
## lm.2$resid 0.0581666 0.0348073 1.671 0.095441 .
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.665 on 423 degrees of freedom
## Multiple R-squared: 0.1624, Adjusted R-squared: 0.1544
## F-statistic: 20.5 on 4 and 423 DF, p-value: 1.888e-15Example 15.8
data("mroz")
s.iv.1 <- summary(iv.1 <- ivreg(lwage ~ educ + exper + expersq |
exper + expersq + motheduc + fatheduc,
data = mroz[mroz$inlf!=0,]))
s.lm.1 <- summary(lm(iv.1$resid ~ exper + expersq + motheduc + fatheduc,
data=mroz[mroz$inlf!=0,]))
s.lm.1##
## Call:
## lm(formula = iv.1$resid ~ exper + expersq + motheduc + fatheduc,
## data = mroz[mroz$inlf != 0, ])
##
## Residuals:
## Min 1Q Median 3Q Max
## -3.1012 -0.3124 0.0478 0.3602 2.3441
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 1.096e-02 1.413e-01 0.078 0.938
## exper -1.833e-05 1.333e-02 -0.001 0.999
## expersq 7.341e-07 3.985e-04 0.002 0.999
## motheduc -6.607e-03 1.189e-02 -0.556 0.579
## fatheduc 5.782e-03 1.118e-02 0.517 0.605
##
## Residual standard error: 0.6752 on 423 degrees of freedom
## Multiple R-squared: 0.0008833, Adjusted R-squared: -0.008565
## F-statistic: 0.0935 on 4 and 423 DF, p-value: 0.9845428 * .0009## [1] 0.3852s.iv.2 <- summary(iv.2 <- ivreg(lwage ~ educ + exper + expersq |
exper + expersq + motheduc + fatheduc + huseduc,
data = mroz[mroz$inlf!=0,]))
s.lm.2 <- summary(lm(iv.2$resid ~ exper + expersq + motheduc + fatheduc + huseduc,
data = mroz[mroz$inlf!=0,]))
s.lm.2##
## Call:
## lm(formula = iv.2$resid ~ exper + expersq + motheduc + fatheduc +
## huseduc, data = mroz[mroz$inlf != 0, ])
##
## Residuals:
## Min 1Q Median 3Q Max
## -3.07503 -0.32777 0.04156 0.37759 2.33621
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 8.606e-03 1.773e-01 0.049 0.961
## exper 5.603e-05 1.323e-02 0.004 0.997
## expersq -8.882e-06 3.956e-04 -0.022 0.982
## motheduc -1.039e-02 1.187e-02 -0.875 0.382
## fatheduc 6.734e-04 1.138e-02 0.059 0.953
## huseduc 6.781e-03 1.143e-02 0.593 0.553
##
## Residual standard error: 0.67 on 422 degrees of freedom
## Multiple R-squared: 0.002605, Adjusted R-squared: -0.009212
## F-statistic: 0.2205 on 5 and 422 DF, p-value: 0.9537428 * .0026## [1] 1.1128s.iv.2##
## Call:
## ivreg(formula = lwage ~ educ + exper + expersq | exper + expersq +
## motheduc + fatheduc + huseduc, data = mroz[mroz$inlf != 0,
## ])
##
## Residuals:
## Min 1Q Median 3Q Max
## -3.08378 -0.32135 0.03538 0.36934 2.35829
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) -0.1868572 0.2853959 -0.655 0.512997
## educ 0.0803918 0.0217740 3.692 0.000251 ***
## exper 0.0430973 0.0132649 3.249 0.001250 **
## expersq -0.0008628 0.0003962 -2.178 0.029976 *
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.6693 on 424 degrees of freedom
## Multiple R-Squared: 0.1495, Adjusted R-squared: 0.1435
## Wald test: 11.52 on 3 and 424 DF, p-value: 2.817e-07Example 15.9
data("fertil1")
s.iv.1 <- summary(iv.1 <- ivreg(kids ~ educ + age + agesq + black + east + northcen +
west + farm + othrural + town + smcity + y74 + y76 +
y78 + y80 + y82 + y84 |
meduc + feduc + age + agesq + black + east +
northcen + west + farm + othrural + town + smcity +
y74 + y76 + y78 + y80 + y82 + y84,
data = fertil1))
s.iv.1##
## Call:
## ivreg(formula = kids ~ educ + age + agesq + black + east + northcen +
## west + farm + othrural + town + smcity + y74 + y76 + y78 +
## y80 + y82 + y84 | meduc + feduc + age + agesq + black + east +
## northcen + west + farm + othrural + town + smcity + y74 +
## y76 + y78 + y80 + y82 + y84, data = fertil1)
##
## Residuals:
## Min 1Q Median 3Q Max
## -4.2345 -1.0206 -0.0746 0.9552 4.7457
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) -7.241244 3.136642 -2.309 0.021149 *
## educ -0.152739 0.039223 -3.894 0.000104 ***
## age 0.523554 0.139035 3.766 0.000175 ***
## agesq -0.005716 0.001571 -3.640 0.000286 ***
## black 1.072952 0.173715 6.176 9.18e-10 ***
## east 0.228555 0.133854 1.708 0.088008 .
## northcen 0.374419 0.122061 3.067 0.002211 **
## west 0.207640 0.167657 1.238 0.215799
## farm -0.077002 0.151372 -0.509 0.611069
## othrural -0.195245 0.181551 -1.075 0.282416
## town 0.081810 0.124682 0.656 0.511864
## smcity 0.212500 0.160425 1.325 0.185575
## y74 0.272129 0.172944 1.574 0.115885
## y76 -0.094548 0.179232 -0.528 0.597939
## y78 -0.057254 0.182554 -0.314 0.753861
## y80 -0.053248 0.184718 -0.288 0.773196
## y82 -0.496215 0.176589 -2.810 0.005041 **
## y84 -0.521360 0.177921 -2.930 0.003456 **
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 1.556 on 1111 degrees of freedom
## Multiple R-Squared: 0.1281, Adjusted R-squared: 0.1148
## Wald test: 7.723 on 17 and 1111 DF, p-value: < 2.2e-16lm.r <- lm(educ ~ meduc + feduc + age + agesq + black + east + northcen +
west + farm + othrural + town + smcity + y74 + y76 + y78 + y80 + y82 + y84,
data = fertil1)
lm.1 <- lm(kids ~ educ + age + agesq + black + east + northcen + west + farm +
othrural + town + smcity + y74 + y76 + y78 + y80 + y82 + y84 + lm.r$resid,
data = fertil1)
summary(lm.1)##
## Call:
## lm(formula = kids ~ educ + age + agesq + black + east + northcen +
## west + farm + othrural + town + smcity + y74 + y76 + y78 +
## y80 + y82 + y84 + lm.r$resid, data = fertil1)
##
## Residuals:
## Min 1Q Median 3Q Max
## -3.9816 -1.0100 -0.0601 0.9181 4.6688
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) -7.241244 3.134883 -2.310 0.021077 *
## educ -0.152739 0.039201 -3.896 0.000104 ***
## age 0.523554 0.138957 3.768 0.000173 ***
## agesq -0.005716 0.001570 -3.642 0.000283 ***
## black 1.072952 0.173618 6.180 8.99e-10 ***
## east 0.228555 0.133779 1.708 0.087831 .
## northcen 0.374419 0.121992 3.069 0.002198 **
## west 0.207640 0.167563 1.239 0.215542
## farm -0.077002 0.151287 -0.509 0.610869
## othrural -0.195245 0.181449 -1.076 0.282147
## town 0.081810 0.124612 0.657 0.511628
## smcity 0.212500 0.160335 1.325 0.185329
## y74 0.272129 0.172847 1.574 0.115681
## y76 -0.094548 0.179132 -0.528 0.597734
## y78 -0.057254 0.182451 -0.314 0.753727
## y80 -0.053248 0.184614 -0.288 0.773072
## y82 -0.496215 0.176490 -2.812 0.005017 **
## y84 -0.521360 0.177821 -2.932 0.003438 **
## lm.r$resid 0.031137 0.044363 0.702 0.482906
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 1.555 on 1110 degrees of freedom
## Multiple R-squared: 0.1299, Adjusted R-squared: 0.1158
## F-statistic: 9.206 on 18 and 1110 DF, p-value: < 2.2e-16Example 15.10
data("jtrain")
d.lscrap <- with(jtrain, lscrap[year == 1988] - lscrap[year == 1987])
d.hrsemp <- with(jtrain, hrsemp[year == 1988] - hrsemp[year == 1987])
d.grant <- with(jtrain, grant[year == 1988] - grant[year == 1987])
s.iv.1 <- summary(ivreg(d.lscrap ~ d.hrsemp | d.grant))
s.iv.1##
## Call:
## ivreg(formula = d.lscrap ~ d.hrsemp | d.grant)
##
## Residuals:
## Min 1Q Median 3Q Max
## -2.308829 -0.218885 -0.008926 0.267436 2.430564
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) -0.032668 0.126951 -0.257 0.7982
## d.hrsemp -0.014153 0.007915 -1.788 0.0808 .
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.629 on 43 degrees of freedom
## Multiple R-Squared: 0.0159, Adjusted R-squared: -0.006984
## Wald test: 3.198 on 1 and 43 DF, p-value: 0.08079