# Load required libraries
library(wooldridge)
library(lmtest)
## Loading required package: zoo
##
## Attaching package: 'zoo'
## The following objects are masked from 'package:base':
##
## as.Date, as.Date.numeric
library(car)
## Loading required package: carData
# Load the data
data(wage2)
—- Part (i): Original Model —-
cat("\n=== Part (i): Original Model Analysis ===\n")
##
## === Part (i): Original Model Analysis ===
model1 <- lm(log(wage) ~ educ + exper + tenure + married +
black + south + urban, data = wage2)
# Display results
summary_model1 <- summary(model1)
cat("\nOriginal Model Results:\n")
##
## Original Model Results:
print(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
# Calculate the approximate percentage difference in wages for blacks
black_coef <- coef(model1)["black"]
black_effect <- (exp(black_coef) - 1) * 100
cat("\nWage Differential Analysis for Blacks vs Non-blacks:\n")
##
## Wage Differential Analysis for Blacks vs Non-blacks:
cat("Coefficient:", round(black_coef, 4), "\n")
## Coefficient: -0.1883
cat("Standard Error:", round(summary_model1$coefficients["black", "Std. Error"], 4), "\n")
## Standard Error: 0.0377
cat("t-statistic:", round(summary_model1$coefficients["black", "t value"], 4), "\n")
## t-statistic: -5.0004
cat("p-value:", round(summary_model1$coefficients["black", "Pr(>|t|)"], 4), "\n")
## p-value: 0
cat("Percentage difference in wages:", round(black_effect, 2), "%\n")
## Percentage difference in wages: -17.17 %
—- Part (ii): Adding Squared Terms —-
cat("\n=== Part (ii): Analysis with Squared Terms ===\n")
##
## === Part (ii): Analysis with Squared Terms ===
model2 <- lm(log(wage) ~ educ + exper + I(exper^2) + tenure +
I(tenure^2) + married + black + south + urban,
data = wage2)
# Test joint significance of exper^2 and tenure^2
squared_test <- linearHypothesis(model2,
c("I(exper^2) = 0", "I(tenure^2) = 0"))
cat("\nJoint Test Results for Squared Terms:\n")
##
## Joint Test Results for Squared Terms:
print(squared_test)
##
## 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
—- Part (iii): Education Returns by Race —-
cat("\n=== Part (iii): Education Returns by Race ===\n")
##
## === Part (iii): Education Returns by Race ===
model3 <- lm(log(wage) ~ educ + exper + tenure + married +
black + south + urban + educ:black,
data = wage2)
# Display results
summary_model3 <- summary(model3)
cat("\nModel with Race-Education Interaction:\n")
##
## Model with Race-Education Interaction:
print(summary_model3)
##
## Call:
## lm(formula = log(wage) ~ educ + exper + tenure + married + black +
## south + urban + educ:black, 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 ***
## 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 ***
## black 0.094809 0.255399 0.371 0.710561
## 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
# Calculate return to education for blacks and non-blacks
educ_nonblack <- coef(model3)["educ"]
educ_interaction <- coef(model3)["educ:black"]
educ_black <- educ_nonblack + educ_interaction
cat("\nReturn to Education Analysis:\n")
##
## Return to Education Analysis:
cat("For non-blacks:", round(educ_nonblack * 100, 2), "% per year of education\n")
## For non-blacks: 6.71 % per year of education
cat("For blacks:", round(educ_black * 100, 2), "% per year of education\n")
## For blacks: 4.45 % per year of education
cat("Difference:", round(educ_interaction * 100, 2), "% per year of education\n")
## Difference: -2.26 % per year of education
cat("P-value for difference:", round(summary_model3$coefficients["educ:black", "Pr(>|t|)"], 4), "\n")
## P-value for difference: 0.2626
—- Part (iv): Four Groups Analysis —-
cat("\n=== Part (iv): Four Groups Analysis ===\n")
##
## === Part (iv): Four Groups Analysis ===
# Create interaction variable
wage2$married_black <- wage2$married * wage2$black
model4 <- lm(log(wage) ~ black + married + married_black +
educ + exper + tenure + south + urban,
data = wage2)
# Display results
summary_model4 <- summary(model4)
cat("\nFour Groups Model Results:\n")
##
## Four Groups Model Results:
print(summary_model4)
##
## Call:
## lm(formula = log(wage) ~ black + married + 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 ***
## black -0.240820 0.096023 -2.508 0.012314 *
## married 0.188915 0.042878 4.406 1.18e-05 ***
## married_black 0.061354 0.103275 0.594 0.552602
## 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 ***
## ---
## 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
# Calculate wage differential between married blacks and married nonblacks
married_black_coef <- coef(model4)["black"] + coef(model4)["married_black"]
married_black_diff <- (exp(married_black_coef) - 1) * 100
cat("\nWage Differential for Married Blacks vs Married Non-blacks:\n")
##
## Wage Differential for Married Blacks vs Married Non-blacks:
cat("Coefficient sum:", round(married_black_coef, 4), "\n")
## Coefficient sum: -0.1795
cat("Percentage difference:", round(married_black_diff, 2), "%\n")
## Percentage difference: -16.43 %
# Save all results to a file (optional)
sink("wage_analysis_results.txt")
cat("=== Complete Wage Analysis Results ===\n")
cat("\n=== Part (i) Results ===\n")
print(summary_model1)
cat("\n=== Part (ii) Results ===\n")
print(squared_test)
cat("\n=== Part (iii) Results ===\n")
print(summary_model3)
cat("\n=== Part (iv) Results ===\n")
print(summary_model4)
sink()