library(wooldridge)
data("wage2")
#(i)
model1 <- lm(log(wage) ~ educ + exper + tenure + married + black + south + urban, data = wage2)
summary(model1)
##
## Call:
## lm(formula = log(wage) ~ educ + exper + tenure + married + black +
## south + urban, data = wage2)
##
## 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 ***
## educ 0.065431 0.006250 10.468 < 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 ***
## black -0.188350 0.037667 -5.000 6.84e-07 ***
## south -0.090904 0.026249 -3.463 0.000558 ***
## urban 0.183912 0.026958 6.822 1.62e-11 ***
## ---
## 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-16
#The coefficient for black is -0.1884.This suggests that, on average, Black individuals earn about 18.84% less than non-Black individuals, holding other factors (such as education, experience, tenure, marital status, region, and urban status) constant.
#The p-value for the black variable is below the 0.05 threshold. This means that the wage difference between Black and non-Black individuals is statistically significant.
#(ii)
model2 <- lm(log(wage) ~ educ + exper + I(exper^2) + tenure + I(tenure^2) + married + black + south + urban, data = wage2)
summary(model2)
##
## Call:
## lm(formula = log(wage) ~ educ + exper + I(exper^2) + tenure +
## I(tenure^2) + married + black + south + urban, data = wage2)
##
## Residuals:
## Min 1Q Median 3Q Max
## -1.98236 -0.21972 -0.00036 0.24078 1.25127
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 5.3586756 0.1259143 42.558 < 2e-16 ***
## educ 0.0642761 0.0063115 10.184 < 2e-16 ***
## exper 0.0172146 0.0126138 1.365 0.172665
## I(exper^2) -0.0001138 0.0005319 -0.214 0.830622
## tenure 0.0249291 0.0081297 3.066 0.002229 **
## I(tenure^2) -0.0007964 0.0004710 -1.691 0.091188 .
## married 0.1985470 0.0391103 5.077 4.65e-07 ***
## black -0.1906636 0.0377011 -5.057 5.13e-07 ***
## south -0.0912153 0.0262356 -3.477 0.000531 ***
## urban 0.1854241 0.0269585 6.878 1.12e-11 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.3653 on 925 degrees of freedom
## Multiple R-squared: 0.255, Adjusted R-squared: 0.2477
## F-statistic: 35.17 on 9 and 925 DF, p-value: < 2.2e-16
library(car)
## Loading required package: carData
library(carData)
linearHypothesis(model2, c("I(exper^2) = 0", "I(tenure^2) = 0"))
##
## Linear hypothesis test:
## I(exper^2) = 0
## I(tenure^2) = 0
##
## Model 1: restricted model
## Model 2: log(wage) ~ educ + exper + I(exper^2) + tenure + I(tenure^2) +
## married + black + south + urban
##
## Res.Df RSS Df Sum of Sq F Pr(>F)
## 1 927 123.82
## 2 925 123.42 2 0.39756 1.4898 0.226
#At the 20% significance level, exper^2 and tenure^2 are jointly insignificant, meaning there is no strong evidence that including these squared terms improves the model's explanatory power.
#(iii)
model3 <- lm(log(wage) ~ educ * black + exper + tenure + married + south + urban, data = wage2)
summary(model3)
##
## Call:
## lm(formula = log(wage) ~ educ * black + exper + tenure + married +
## south + urban, data = wage2)
##
## Residuals:
## Min 1Q Median 3Q Max
## -1.97782 -0.21832 0.00475 0.24136 1.23226
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 5.374817 0.114703 46.859 < 2e-16 ***
## educ 0.067115 0.006428 10.442 < 2e-16 ***
## black 0.094809 0.255399 0.371 0.710561
## exper 0.013826 0.003191 4.333 1.63e-05 ***
## tenure 0.011787 0.002453 4.805 1.80e-06 ***
## married 0.198908 0.039047 5.094 4.25e-07 ***
## south -0.089450 0.026277 -3.404 0.000692 ***
## urban 0.183852 0.026955 6.821 1.63e-11 ***
## educ:black -0.022624 0.020183 -1.121 0.262603
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.3654 on 926 degrees of freedom
## Multiple R-squared: 0.2536, Adjusted R-squared: 0.2471
## F-statistic: 39.32 on 8 and 926 DF, p-value: < 2.2e-16
#p-value is 0.263, which is not statistically significant. Thus, based on the results, there is no evidence to suggest that the return to education depends on race.
#(iv)
model4 <- lm(log(wage) ~ married * black + educ + exper + tenure + south + urban, data = wage2)
summary(model4)
##
## Call:
## lm(formula = log(wage) ~ married * black + educ + exper + tenure +
## south + urban, data = wage2)
##
## Residuals:
## Min 1Q Median 3Q Max
## -1.98013 -0.21780 0.01057 0.24219 1.22889
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 5.403793 0.114122 47.351 < 2e-16 ***
## married 0.188915 0.042878 4.406 1.18e-05 ***
## black -0.240820 0.096023 -2.508 0.012314 *
## educ 0.065475 0.006253 10.471 < 2e-16 ***
## exper 0.014146 0.003191 4.433 1.04e-05 ***
## tenure 0.011663 0.002458 4.745 2.41e-06 ***
## south -0.091989 0.026321 -3.495 0.000497 ***
## urban 0.184350 0.026978 6.833 1.50e-11 ***
## married:black 0.061354 0.103275 0.594 0.552602
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.3656 on 926 degrees of freedom
## Multiple R-squared: 0.2528, Adjusted R-squared: 0.2464
## F-statistic: 39.17 on 8 and 926 DF, p-value: < 2.2e-16
#The wage differential between married Black and married non-Black individuals is approximately -0.18 (18% lower), but this difference is not statistically significant.Thus, it won't make strong evidence that marriage affects wages differently based on race.