Economic Astronomy: Gender Gaps in Lifetime Earnings

There are two recent studies of gender disparities in science and technology (referred to by the faintly awful acronym "STEM") getting a lot of play over the last few days. As is often the case with social-science results, the data they have aren't quite the data you would really like to have, and I think it's worth poking at them a little, not to deny the validity of the results, but to point out the inherent limitations of the process.

The first is a study of lifetime earnings in various fields that includes this graph showing that women with a Ph.D. earn about the same amount as men with a BA:

That's pretty damning. But also a little deceptive, because this is a plot of "lifetime earnings," which means that they are necessarily doing a social-science analogue of astronomy to make this graph.

What I mean by that is that this is necessarily a retrospective study, looking back at how things were, in the same way that astronomers are looking at distant galaxies as they were back when the light was emitted, millions of years ago. The authors of the current study are following the procedure used by the Census Bureau for similar work, which they describe thusly:

Specifically, the Census approach looks at 5-year age groups -- 25-29, 30-34, etc. -- to get an average for each age group and then sums each of these 5-year averages of a particular demographic and/or educational group to estimate the average 40-year degree for that group.

What that means is that they're taking a cross-section back through time. In order to get the average salary for people at age 40, they are looking at the average salary of people who are 40 now (well, who were 40 in 2007-2009, but you get the idea). That means that you're looking at the salary of a 40-year-old Ph.D. who was hired somewhere in the 1995-2000 range, which is not necessarily the salary someone hired today should expect to be making when they are 40.

This is important for these kind of gap studies, because the data presented necessarily average over many years of changing conditions. To get the last few years of their hypothetical 40-year working life, they're looking at the salaries of Ph.D.'s who were hired in 1970(-ish). And I hope everybody will agree that the working environment was significantly different in 1970 than it is today, particularly when it comes to differential treatment of gender and race.

This makes interpreting this graph a little trickier than is being presented by most of the links to it I've seen. That is, even in the hypothetical fantasy-world case where gender disparities in salary and promotion have magically been fixed today, you would still expect to see a significant gap in this sort of lifetime earnings calculation due to the gender disparities that existed in the past.

If you want to really figure out what's going on with the earnings of different groups from this kind of study, you would need two such studies, preferably separated by a substantial interval in time. And, in fact, we have just that, in the 2002 Census Bureau report referenced in the current study (PDF), which includes this graph:

Aside from trivial differences in formatting, this is the same figure as above. The absolute numbers are different, but what really matters for this discussion is the size of the gaps, which you can measure in percentage terms. Defining the percentage difference as the difference between the two salaries (M-F) divided by the smaller of the two (i.e., the women's salary), we have the following:

In other words, in the 2002 report (based on data from the late '90s), a man with a Ph.D. earned 52% more than a woman with a Ph.D., while in the 2011 report (based on data from the late '00's) the gap in lifetime earnings was 21%. Which is a very different sort of picture, suggesting that the job climate has improved substantially over the last decade (or, more likely, over the decade between 1960 and 1970).

(Interestingly, the current study's gap for Ph.D.'s is smaller than any other category, and dramatically so. The same pattern holds for the older report, though the difference is probably not significant. I'm not sure what this means, but it's interesting.)

Does this mean that everything's rosy? No, not at all. There is one thing that remains the same in the two reports, namely that a woman with a Ph.D. earned about the same amount as a man with a B.A. (slightly more in the newer data, but the difference is about a third of the gap). Which means there's still work to do, but the outlook for a new Ph.D. going forward is not nearly as dire as the top graph alone seems to suggest.

(One other note, not as directly relevant to this: the current study assumes an "ideal" trajectory with no gaps in employment. As one of the usual explanations of gender gaps in lifetime earnings is that women tend to be more likely to take time off for family reasons, this is obviously not perfectly realistic. However, as they note in their discussion, the method they have used would, if anything, tend to understate the difference for those women who do take time off. So, while a more detailed investigation would be nice (if kind of impractical), that's not a killer flaw in their results. It is something to be aware of, though.)