library(ggplot2)
library(dplyr)
library(readxl)
df <- read_excel("Wage_GenderDS.xlsx")
head(df)# A tibble: 6 × 6
Observation Wage Female Age Educ Parttime
<dbl> <dbl> <dbl> <dbl> <dbl> <dbl>
1 119 32 1 31 1 1
2 2 34 1 42 1 1
3 41 37 1 31 1 1
4 65 38 1 33 1 1
5 246 38 1 21 2 1
6 254 38 0 28 2 1ggplot(df, aes(x = Wage)) +
geom_histogram(binwidth = 20, fill = "blue", color = "white") +
labs(title = "Histogram of Raw Hourly Wage", x = "Wage", y = "Frequency") +
theme_minimal()
df$Gender <- ifelse(df$Female == 1, "Women", "Men")
ggplot(df, aes(x = Gender, y = Wage, fill = Gender)) +
geom_boxplot() +
labs(title = "Wage by Gender", x = "", y = "Wage") +
theme_minimal() +
theme(legend.position = "none")
Comparison:
df %>%
group_by(Gender) %>%
summarise(
Mean = round(mean(Wage), 2),
Median = round(median(Wage), 2),
SD = round(sd(Wage), 2),
Min = min(Wage),
Max = max(Wage)
)# A tibble: 2 × 6
Gender Mean Median SD Min Max
<chr> <dbl> <dbl> <dbl> <dbl> <dbl>
1 Men 125. 111 57.3 38 384
2 Women 97.3 83.5 46.3 32 364mean_men <- mean(df$Wage[df$Female == 0])
mean_women <- mean(df$Wage[df$Female == 1])
cat("Raw wage gap (Men - Women):", round(mean_men - mean_women, 2))Raw wage gap (Men - Women): 27.81Raw wage gap: Men earn an average of more per hour, average wage of: **27.81 more than women. This is simply a descriptive number - it does not yet take into consideration variations in education, age and working hours. It informs us that there is a gap but not the reason why there is a gap.
df$l_wage <- log(df$Wage)
ggplot(df, aes(x = l_wage)) +
geom_histogram(binwidth = 0.15, fill = "darkorange", color = "white") +
labs(title = "Histogram of log(Wage)", x = "log(Wage)", y = "Frequency") +
theme_minimal()
Comparison with raw Wage: The histogram, using the log transformation, is far more symmetric and bell-shaped, sharply contrasting with the strong right skew of the raw Wage histogram. The log transformation squeeches the long right tail, moving the high earners nearer to the middle of the distribution. This makes the data much more suitable for statistical analysis.
ggplot(df, aes(x = Gender, y = l_wage, fill = Gender)) +
geom_boxplot() +
labs(title = "log(Wage) by Gender", x = "", y = "log(Wage)") +
theme_minimal() +
theme(legend.position = "none")
Does a log transformation alter the apparent gap?: This difference between men and women is still vivid following the log transformation. The distributions are made more symmetric, and relative extreme outliers are not as dramatic, but the difference between the two groups is retained.
Why economists prefer l_wage:
mean_lw_men <- mean(df$l_wage[df$Female == 0])
mean_lw_women <- mean(df$l_wage[df$Female == 1])
cat("Mean log(Wage) - Men: ", round(mean_lw_men, 4), "\n")Mean log(Wage) - Men: 4.7336 cat("Mean log(Wage) - Women:", round(mean_lw_women, 4), "\n")Mean log(Wage) - Women: 4.483 cat("Approximate % gap: ", round(100 * (mean_lw_men - mean_lw_women), 2), "%")Approximate % gap: 25.06 %Interpretation: The wage gap is approximately 25.1%. This implies that men in this sample have an average of 25 per cent higher wages than women. This is a good approximation with small differences.
table(df$Gender, df$Educ)
1 2 3 4
Men 108 77 72 59
Women 88 57 33 6ggplot(df, aes(x = factor(Educ), fill = Gender)) +
geom_bar(position = "dodge") +
labs(title = "Education Level by Gender", x = "Education Level", y = "Count") +
theme_minimal()
Which education level is most common?
The difference is important since the higher the level of education, the higher the wages are generally. The higher concentration of women in level 1 could be one of the reasons why women earn less.
df %>%
group_by(Gender) %>%
summarise(Parttime_Proportion = round(mean(Parttime), 3))# A tibble: 2 × 2
Gender Parttime_Proportion
<chr> <dbl>
1 Men 0.225
2 Women 0.56 df %>%
group_by(Gender) %>%
summarise(
Mean_Age = round(mean(Age), 2),
Median_Age = median(Age)
)# A tibble: 2 × 3
Gender Mean_Age Median_Age
<chr> <dbl> <dbl>
1 Men 40.0 39
2 Women 39.9 39Are they similar? Yes — the mean and median age are nearly identical for both groups (both approximately 40 years old). This means age is unlikely to explain the wage gap in this dataset. If men were systematically older, we might attribute part of the wage gap to greater accumulated work experience, but that is not the case here.
Two major motives giving the logarithm of wages importance to economists as compared to raw wages include:
Interpretation of results in percentages. We can directly interpret the coefficient on the female dummy, when we regress log(wage) on gender and control variables, as an approximation to a percentage wage difference (e.g., women earn 15 percent less than men, other things being equal). A regression coefficient of a raw-wage would be in dollars, which is less easily interpreted and compared across wage levels or time.
No, the raw wage gap is not the same as discrimination. The $27.81 hourly gap (approximately 25%) is a descriptive statistic that mixes together many different factors. Our exploration of the data reveals at least two important confounders:
Part-time work: Women are more than twice as likely to work part-time (56% vs. 22.5%). Since part-time workers tend to earn lower wages, this structural difference alone can account for a significant portion of the observed gap — without any discrimination being involved.
Education: Women in this sample are more concentrated in lower education levels (Educ = 1), while men are more evenly spread across levels 1–4. Because education and wages are positively related, this compositional difference also contributes to the raw gap.
To isolate the portion of the wage gap that might reflect discrimination, we would need a multivariate regression that controls for education, age, part-time status, occupation, and other relevant variables. The unexplained residual after such controls is a closer — though still imperfect — measure of discrimination, since unobserved factors like occupational segregation and career interruptions can still bias the estimate.
End of analysis.