Ben Hayes

The Gender Income Gap

How do factors (besides gender) affect the gender income gap?

Feb 11, 2018 20 min read Ben Hayes

Is there a significant difference in income between men and women? Does the difference vary depending on other factors (e.g., education, marital status, criminal history, drug use, childhood household factors, profession, etc.)?

The issue of gender-income disparity is not new - it is nuanced. In order to answer these questions, we will rely on the National Longitudinal Survey of Youth, 1979 cohort, data set (abbreviated ‘NLSY79’). To draw strong conclusions, we must evaluate the data set provided - is it accurate, relevant, and useful for drawing statistical conclusions? Once we summarize the data, we can discuss methodology - how should we approach the data, what variables should we consider, what techniques are appropriate? Third, we openly discuss findings about the sampled individuals and attempt to infer relationships about the income difference (if any) between men and women in the larger population based on other factors. Lastly, we end with a discussion of the relevancy and signicance of our findings given the context of the survey data available and the methodology used.

Table of Contents:

1. Data Summary
2. Methodology
3. Findings
4. Closing Discussion

1. Data Summary

In the boxplot to the below, you can see the distribution of incomes for men and women. Notice that the median income for men is higher than the median income for women and in general, the variability in income of men is higher than the variability in the income of women. Also, notice the outliers for both men and women at the top of the income scale.

The income data from the National Longitudinal Survey of Youth, 1979 cohort, data set is top-coded. The income values for the top 2% of earners are set to the average income of the top 2% of earners (to obscure the actual values). While this change seems harmless, and would be when calculating simple averages, it does have potential to affect our analysis. By setting values of the top earners to the average of that group, the standard deviation for the top 2% has been eliminated. This subtle change will be further examined when we determine and discuss significance of our results later.

But first, let’s examine the data available and begin to hone in on a few key variables.

Gender:

As can be seen in the bar chart:

• The average salary of men in our dataset is approximately $24961 more than that of women.
• The 95% confidence intervals do not overlap so the probability that this difference is significant is extremely high (>99.99%).

This depiction of the gap indicates that there certainly may be a problem, but how can we confidently conclude that there is an income gap? Do men work more? Have Higher Education? What happens when we include other variables?

Individual’s Race:

• The race with the highest difference in average income is the non-hispanic/non-black group.
• The income difference in race, when holding race constant by using sub-groups, is significant for all 3 races.
• Note that women in the non-hispanic/non-black group, on average, earn more income than men who are black (although we can show that any difference is not significant).

Geographic Region:

• You can see the average income in the northeast is higher than in the other 3 regions but the gap between men and women remains relatively similar.
• Most of the respondents are from the south or north central regions.
• All differences in income by gender and region appear to be significant atthe 95% confidence level.

Marital Status:

• The majority of respondents are either married, never married, or divorced:
• The first observation for this chart must be the interesting fact that men who are married earn more income than men who are never married, separated, divorced, or widowed - and that there is no corresponding spike (at least proportional to the spike for men) in income for women who are married.
• The differences in income by gender only appear to be significant for married and divorced individuals.

Country of Origin:

• The majority of individuals who are included in the NLSY79 survey are originally from the United States.
• Regardless of the country, it appears that the income difference between men and women is significant.
• Based on the data, men from outside of the U.S. see a small bump in pay relative to their counterpart from the United States - women however do not appear to experience the same bump.

Education Level:

• The education variable, coupled with the gender variable, shows an interesting relationship:
• Once the 10th grade education level is attained, we begin to see a significant difference in the incomes between men and women.
• As education level increases, the gap in income between the genders also increases.
• Note that the sample sizes for indivdiuals 11th grade and lower have smaller samples.

Industry/Business:

• Notice the 95% confidence interval is large for several subgroups. For example, women in the Armed Forces make up 3 of the remaining respondents. The standard deviation for this group is very high causing the confidence interval to dip noticeably below $0.
• The income gap between men and women is statistically significant at the 95% confidence level in several industries: Manufacturing, Wholesale/Resale Trade, Information, Finance/Insurance, Professional Services, Educational Services, and Healthcare/Social Assistance.

Due to the granularity of this variable and the lack of surveyed individuals for some of the industry~gender sub-groupings, this variable and may not be helpful later when we perform regression analysis.

2. Methodology

Missing Values

R provides ways to account for missing values (encode as NA and use rm.na = True) but for the purpose of this analysis the missing values were removed.

Inappropriate Values

The following categories of values were removed from the corresponding variable (these data cleanup changes are reflected in the plots shown in the Data Summary section above):

• ‘Unknown’ from Country of Origin
• ‘Non-interview’, ‘Invalid Skip’ from Marital Status (2000)
• ‘Refusal’, ‘Do not know’ from Region of Current Residence
• ‘Ungraded’ from Education Level
• ‘Error’, ‘Not in Labor Force’ from Industry/Business

Top-Coded Income Variable

Selecting Variables

• Income
• Gender
• Race
• Education Level
• Geographic Region
• Marital Status

Variables that were previously evaluated but since removed from the analysis include:

• Country of Origin - This value is suspected to not affect the income gap based on the bar chart above.
• Industry/Business - This value subdivides the data to levels that are too small to draw statistically significant conclusions from when performing regression analysis.

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3.Findings

We can perform regression analysis (including a range of variables) to help isolate the effect of each variable on income. If we attempt to regress income on gender, you will see familiar results:

To interpret the regression output, pay close attention to the GenderFemale estimated value. This value represents the amount that women can expect to earn less than a man (while considering no other variables) and is statistically significant. You will notice that the value is the same as when we compared the simple averages!

As mentioned in this section’s preface, we want to develop a more satisfying model for evaluating the effect of other variables on income. Let’s see what happens when we account for other variables:

Main Effects

Income ~ Gender + Race + Education Level + Geographic Region + Marital Status

Additionally, living in the Northeast typically leads to an increase in income of $6748 more than someone similar living in North Central US, $5968 more than someone similar living in the south, and $5976 more than someone similar living in the west.

But we want to compare how these variables affect the gap in income between men and women… Then let’s do it!

Interaction Effects

Income ~ Gender + … + Gender * Race

Regression Comparison

## Analysis of Variance Table
## 
## Model 1: TotalIncome_2012 ~ Gender + Race + GradeCompleted_2012 + RegionOfCurrentResidence_2012 + 
##     MaritalStatus_2000
## Model 2: TotalIncome_2012 ~ Gender + Race + GradeCompleted_2012 + RegionOfCurrentResidence_2012 + 
##     MaritalStatus_2000 + Gender * Race
##   Res.Df        RSS Df  Sum of Sq      F    Pr(>F)    
## 1   6152 1.5352e+13                                   
## 2   6150 1.5173e+13  2 1.7834e+11 36.142 2.484e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

Interaction Effects

Income ~ Gender + … + Gender * Education Level

Regression Comparison

## Analysis of Variance Table
## 
## Model 1: TotalIncome_2012 ~ Gender + Race + GradeCompleted_2012 + RegionOfCurrentResidence_2012 + 
##     MaritalStatus_2000
## Model 2: TotalIncome_2012 ~ Gender + Race + GradeCompleted_2012 + RegionOfCurrentResidence_2012 + 
##     MaritalStatus_2000 + Gender * GradeCompleted_2012
##   Res.Df        RSS Df  Sum of Sq      F    Pr(>F)    
## 1   6152 1.5352e+13                                   
## 2   6143 1.4851e+13  9 5.0049e+11 23.003 < 2.2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

Interaction Effects

Income ~ Gender + … + Gender * Geographic Region

Note the t-statistics are varying in their significance.

Regression Comparison

## Analysis of Variance Table
## 
## Model 1: TotalIncome_2012 ~ Gender + Race + GradeCompleted_2012 + RegionOfCurrentResidence_2012 + 
##     MaritalStatus_2000
## Model 2: TotalIncome_2012 ~ Gender + Race + GradeCompleted_2012 + RegionOfCurrentResidence_2012 + 
##     MaritalStatus_2000 + Gender * RegionOfCurrentResidence_2012
##   Res.Df        RSS Df  Sum of Sq      F  Pr(>F)  
## 1   6152 1.5352e+13                               
## 2   6149 1.5332e+13  3 1.9761e+10 2.6418 0.04767 *
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

Interaction Effects

Income ~ Gender + … + Gender * Marital Status

Regression Comparison

## Analysis of Variance Table
## 
## Model 1: TotalIncome_2012 ~ Gender + Race + GradeCompleted_2012 + RegionOfCurrentResidence_2012 + 
##     MaritalStatus_2000
## Model 2: TotalIncome_2012 ~ Gender + Race + GradeCompleted_2012 + RegionOfCurrentResidence_2012 + 
##     MaritalStatus_2000 + Gender * MaritalStatus_2000
##   Res.Df        RSS Df  Sum of Sq      F    Pr(>F)    
## 1   6152 1.5352e+13                                   
## 2   6148 1.5083e+13  4 2.6906e+11 27.419 < 2.2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

How ‘good’ is our initial (interaction-less) regression model?

Residuals vs. Fitted

Second, above the primary band of plotted points, there is a second band that exists. This separation indicates there is a second influence on the residuals produced by our regression model.

Normal Q-Q

Scale-Location

Residuals vs Leverage

How ‘good’ is one of our interactive regression models?

4. Closing Discussion

How confident are we in the results?

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