Pay Equality at the White House

Posted: April 20, 2012 in analysis

An article on The Free Beacon here makes the simple claim that the White House pays women less than men, according to public records.  They then go on to imply (as others who link to them do more explicitly, like here) that this is demonstrative of an anti-woman attitude in the administration.

So, lets take a look at the numbers, shall we?

The Dataset

The 2011 salaries and titles of all 454 White House staff members are public information, published here.  However, gender is not included.  Converting names to genders is risky and full of ambiguities.  The Free Beacon claims that they researched every name that was not obvious to ascertain the person’s gender; I have done the same.  However, I still don’t know the gender of 17 employees, and I am sure that I am wrong on the gender of some of the ones I am claiming.  Three entries in the list were listed with a salary of $0.00, I removed these as either errors or indicating some sort of volunteer arrangement.  I also make no attempt to distinguish anyone who identifies with or falls into a non-binary gender category.

I do not know how similar my resultant dataset is to the Free Beacon’s on a case by case basis.  They do not indicate if there were any names on the list that they did not assign genders to, or any other data-cleaning steps they took.  I can, however, compare my median salaries with theirs (the only number they published).  I counted 223 men, 211 women, and 17 unknowns in the sample.  The median salary for men was $75,000, and the median for women was $63,240  (the median unknown was $50,000).   This actually differs somewhat from the Free Beacon set; though the proportions are about the same.  I assume that the Free Beacon data assigned a gender to everyone, and left no unknowns.

Analysis

The first question, which I have seen in a few places, is why use median?  The mean values are much closer (78K to 86K, in my data), so is this just cherry picking statistics by the Free Beacon?  Probably not.  Because salaries are not normally distributed (they tend to be clumped up near the low end and spread out more and more as you get higher), the average is often not considered a useful value.  Here, though, since the maximum salary is only 4 times the minimum, this is less important, but there is plenty of precedent to use the median.

Next, looking at $75000 and $63240, one is obviously bigger.  But salaries range from $41k to $170k, so is that difference actually significant, or just a coincidence?  The standard deviation (here just a general estimate of fluctuation, since the distribution isn’t normal) of both gender’s salary distribution is around $40k, so a difference of $12K is less significant in comparison.  But a proper test would be to test the significance of a model which predicts salary by gender.  This model shows a p-value of right around 0.05, depending on how one treats the unknowns, which is on the threshold of traditional “statistical significance”.  But the R^2 of the model is 0.0086.  This means that known the gender explains less than 1% of the difference in salaries between people.

So, the Free Beacon’s mathematical claims are holding up.  The difference is real, and it and probably indicates an underlying fact about the data.

The interesting part comes when you remember that the pay-equality argument is “equal pay for equal work.”  Maybe women just have different sorts of jobs in the White House.  So, perhaps we should consider how men and women are paid for the same job.  For example, there are 19 “Staff Assistants” on the White House payroll (14 women, 4 men, and one unknown).   All but one of these make the same amount; one male makes slightly more.  For the “Analyst” job, things are reversed.  There are more men than women, nearly everyone makes the same, but one woman makes more.

We can make a model that accounts for this.  It models salary based on title, then on gender to try to describe the remaining differences.  The salary gap under these circumstances is reduced to just under $2000, though not eliminated.  However, the chance that that $2k is meaningful decreases significantly, with the p-value climbing past 0.1.  Add the interaction between position and gender (to see if women are being underpaid only in certain positions), and the significance of the model decays further.  The flaw in this model is that while many titles are generic, many of the people in this dataset have unique titles, such as “Special Assistant To The President For Urban Affairs”.  An analysis like this basically doesn’t use those at all.

Conclusions

There are two criticisms that flowed from this article.  The first is the accusation that the White House made a conscious and deliberate decision to pay female employees less than males because they were women.   If this were true, we would expect to see women being paid less than men while doing the same job, and the data do not show that.

The second criticism is that the White House does not employ women as inner-circle trusted advisers to the President.  The data are more supportive of this, but only if you accept many more assumptions, such as that more pay directly maps to a more influential policy role.  To prove this, it would be much better to actually categorize who among the staff are the influential advisers to the President, rather than how much they are paid.

So, my ultimate conclusion is a mixed bag.  I don’t agree with the reasoning used to turn this information into an attack on the President, but the numbers themselves are valid and meaningful.

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