Also available in Stata and Python versions
Load libraries
library(wooldridge)
library(stargazer)
library(AER)
library(lmtest)
library(haven)Wage equation for married working women
lwage_hetr <- lm(lwage ~ exper + expersq + educ + age + kidslt6 + kidsge6, data=mroz)
lwage_robust <- coeftest(lwage_hetr, vcovHC(lwage_hetr, type = "HC1") )
stargazer(lwage_hetr, lwage_robust, column.labels=c("Hetrosced.", "Robust SE"), no.space=TRUE, type="text")##
## =======================================================
## Dependent variable:
## -----------------------------------
## lwage
## OLS coefficient
## test
## Hetrosced. Robust SE
## (1) (2)
## -------------------------------------------------------
## exper 0.040*** 0.040***
## (0.013) (0.015)
## expersq -0.001* -0.001*
## (0.0004) (0.0004)
## educ 0.108*** 0.108***
## (0.014) (0.014)
## age -0.001 -0.001
## (0.005) (0.006)
## kidslt6 -0.061 -0.061
## (0.089) (0.106)
## kidsge6 -0.015 -0.015
## (0.028) (0.029)
## Constant -0.421 -0.421
## (0.317) (0.318)
## -------------------------------------------------------
## Observations 428
## R2 0.158
## Adjusted R2 0.146
## Residual Std. Error 0.668 (df = 421)
## F Statistic 13.191*** (df = 6; 421)
## =======================================================
## Note: *p<0.1; **p<0.05; ***p<0.01linearHypothesis(lwage_hetr, c("kidslt6=0", "kidsge6=0", "age=0"))## Linear hypothesis test
##
## Hypothesis:
## kidslt6 = 0
## kidsge6 = 0
## age = 0
##
## Model 1: restricted model
## Model 2: lwage ~ exper + expersq + educ + age + kidslt6 + kidsge6
##
## Res.Df RSS Df Sum of Sq F Pr(>F)
## 1 424 188.31
## 2 421 187.99 3 0.31751 0.237 0.8705LM1 pp.64
uhat_rst <- resid(lm(lwage ~ exper + expersq + educ, data=mroz))
summary(uhat_reg <- lm(uhat_rst ~ exper + expersq + educ + age + kidslt6 + kidsge6, data=subset(mroz, !is.na(wage))))##
## Call:
## lm(formula = uhat_rst ~ exper + expersq + educ + age + kidslt6 +
## kidsge6, data = subset(mroz, !is.na(wage)))
##
## Residuals:
## Min 1Q Median 3Q Max
## -3.08183 -0.30631 0.04606 0.37161 2.35708
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 1.011e-01 3.169e-01 0.319 0.750
## exper -1.747e-03 1.339e-02 -0.130 0.896
## expersq 2.996e-05 4.022e-04 0.074 0.941
## educ 3.423e-04 1.440e-02 0.024 0.981
## age -1.465e-03 5.292e-03 -0.277 0.782
## kidslt6 -6.071e-02 8.876e-02 -0.684 0.494
## kidsge6 -1.459e-02 2.790e-02 -0.523 0.601
##
## Residual standard error: 0.6682 on 421 degrees of freedom
## Multiple R-squared: 0.001686, Adjusted R-squared: -0.01254
## F-statistic: 0.1185 on 6 and 421 DF, p-value: 0.9942LM <- (summary(uhat_reg)$r.squared) * (nobs(uhat_reg))
LM ## [1] 0.7216757pchisq(LM, df=3, lower.tail = FALSE)## [1] 0.8680941LM2 Continued on pp.65
uhat_rst <- resid(lm(lwage ~ exper + expersq + educ, data=mroz)) #u from the restricted model
u_age <- resid(lm(age~educ+exper+expersq, data=subset(mroz, !is.na(wage))))*uhat_rst
u_kidslt6 <- resid(lm(kidslt6~educ+exper+expersq, data=subset(mroz, !is.na(wage))))*uhat_rst
u_kidsge6 <- resid(lm(kidsge6~educ+exper+expersq, data=subset(mroz, !is.na(wage))))*uhat_rst
udata <- data.frame(cbind(u_age, u_kidslt6, u_kidsge6))
udata['one'] = 1 #Generates a vector of 1s.
summary(one_r <- lm(one ~ u_age + u_kidslt6 + u_kidsge6 + 0, data=udata))##
## Call:
## lm(formula = one ~ u_age + u_kidslt6 + u_kidsge6 + 0, data = udata)
##
## Residuals:
## Min 1Q Median 3Q Max
## 0.7818 0.9926 0.9996 1.0055 1.2620
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## u_age -0.002512 0.010715 -0.234 0.815
## u_kidslt6 -0.090505 0.169209 -0.535 0.593
## u_kidsge6 -0.026719 0.060337 -0.443 0.658
##
## Residual standard error: 1.003 on 425 degrees of freedom
## Multiple R-squared: 0.001196, Adjusted R-squared: -0.005854
## F-statistic: 0.1696 on 3 and 425 DF, p-value: 0.9169LM <- (summary(one_r)$r.squared) * (nobs(one_r))
LM ## [1] 0.5118801pchisq(LM, df=3, lower.tail = FALSE)## [1] 0.9162738Using IQ as a Proxy for Ability
nls80 <- read_dta("nls80.dta") #Data From working directory or using the bcuse command in Stata
summary(lm(lwage ~ exper + tenure + married + south + urban + black + educ, data=nls80))##
## Call:
## lm(formula = lwage ~ exper + tenure + married + south + urban +
## black + educ, data = nls80)
##
## Residuals:
## Min 1Q Median 3Q Max
## -1.98069 -0.21996 0.00707 0.24288 1.22822
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 5.395497 0.113225 47.653 < 2e-16 ***
## exper 0.014043 0.003185 4.409 1.16e-05 ***
## tenure 0.011747 0.002453 4.789 1.95e-06 ***
## married 0.199417 0.039050 5.107 3.98e-07 ***
## south -0.090904 0.026249 -3.463 0.000558 ***
## urban 0.183912 0.026958 6.822 1.62e-11 ***
## black -0.188350 0.037667 -5.000 6.84e-07 ***
## educ 0.065431 0.006250 10.468 < 2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.3655 on 927 degrees of freedom
## Multiple R-squared: 0.2526, Adjusted R-squared: 0.2469
## F-statistic: 44.75 on 7 and 927 DF, p-value: < 2.2e-16summary(lm(lwage ~ exper + tenure + married + south + urban + black + educ + iq, data=nls80))##
## Call:
## lm(formula = lwage ~ exper + tenure + married + south + urban +
## black + educ + iq, data = nls80)
##
## Residuals:
## Min 1Q Median 3Q Max
## -2.01203 -0.22244 0.01017 0.22951 1.27478
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 5.1764392 0.1280006 40.441 < 2e-16 ***
## exper 0.0141458 0.0031651 4.469 8.82e-06 ***
## tenure 0.0113951 0.0024394 4.671 3.44e-06 ***
## married 0.1997644 0.0388025 5.148 3.21e-07 ***
## south -0.0801695 0.0262529 -3.054 0.002325 **
## urban 0.1819463 0.0267929 6.791 1.99e-11 ***
## black -0.1431253 0.0394925 -3.624 0.000306 ***
## educ 0.0544106 0.0069285 7.853 1.12e-14 ***
## iq 0.0035591 0.0009918 3.589 0.000350 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.3632 on 926 degrees of freedom
## Multiple R-squared: 0.2628, Adjusted R-squared: 0.2564
## F-statistic: 41.27 on 8 and 926 DF, p-value: < 2.2e-16Effects of Job Training Grants on Worker Productivity
summary(lm(lscrap ~ grant, data=subset(jtrain, jtrain$year==1988)))##
## Call:
## lm(formula = lscrap ~ grant, data = subset(jtrain, jtrain$year ==
## 1988))
##
## Residuals:
## Min 1Q Median 3Q Max
## -3.4043 -0.9536 -0.0465 0.9636 2.8103
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 0.4085 0.2406 1.698 0.0954 .
## grant 0.0566 0.4056 0.140 0.8895
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 1.423 on 52 degrees of freedom
## (103 observations deleted due to missingness)
## Multiple R-squared: 0.0003744, Adjusted R-squared: -0.01885
## F-statistic: 0.01948 on 1 and 52 DF, p-value: 0.8895summary(lm(lscrap ~ grant + lscrap_1, data=subset(jtrain, jtrain$year==1988)))##
## Call:
## lm(formula = lscrap ~ grant + lscrap_1, data = subset(jtrain,
## jtrain$year == 1988))
##
## Residuals:
## Min 1Q Median 3Q Max
## -1.9146 -0.1763 0.0057 0.2308 1.5991
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 0.02124 0.08910 0.238 0.8126
## grant -0.25397 0.14703 -1.727 0.0902 .
## lscrap_1 0.83116 0.04444 18.701 <2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.5127 on 51 degrees of freedom
## (103 observations deleted due to missingness)
## Multiple R-squared: 0.8728, Adjusted R-squared: 0.8678
## F-statistic: 174.9 on 2 and 51 DF, p-value: < 2.2e-16Return to Education Depends on Ability
summary(lwage_rg <- lm(lwage ~ exper + tenure + married + south + urban + black + educ*iq, data=nls80) )##
## Call:
## lm(formula = lwage ~ exper + tenure + married + south + urban +
## black + educ * iq, data = nls80)
##
## Residuals:
## Min 1Q Median 3Q Max
## -2.00733 -0.21715 0.01177 0.23456 1.27305
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 5.6482483 0.5462963 10.339 < 2e-16 ***
## exper 0.0139072 0.0031768 4.378 1.34e-05 ***
## tenure 0.0113929 0.0024397 4.670 3.46e-06 ***
## married 0.2008658 0.0388267 5.173 2.82e-07 ***
## south -0.0802354 0.0262560 -3.056 0.002308 **
## urban 0.1835758 0.0268586 6.835 1.49e-11 ***
## black -0.1466989 0.0397013 -3.695 0.000233 ***
## educ 0.0184559 0.0410608 0.449 0.653192
## iq -0.0009418 0.0051625 -0.182 0.855289
## educ:iq 0.0003399 0.0003826 0.888 0.374564
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.3632 on 925 degrees of freedom
## Multiple R-squared: 0.2634, Adjusted R-squared: 0.2563
## F-statistic: 36.76 on 9 and 925 DF, p-value: < 2.2e-16linearHypothesis(lwage_rg, c("educ:iq =0", "iq=0"))## Linear hypothesis test
##
## Hypothesis:
## educ:iq = 0
## iq = 0
##
## Model 1: restricted model
## Model 2: lwage ~ exper + tenure + married + south + urban + black + educ *
## iq
##
## Res.Df RSS Df Sum of Sq F Pr(>F)
## 1 927 123.82
## 2 925 122.02 2 1.8024 6.8318 0.001134 **
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1