# Math Geek Mom: Seventy Seven Cents?

Women are paid, on average, only seventy seven cents for every dollar earned by men. As can be seen at the site of “moms rising”, even larger differentials exist for women who are mothers, and these are most extreme for women who are single mothers. But where do these numbers come from? How are they calculated, and, more importantly, what assumptions are made in performing those calculations? I will discuss how these wage differentials, which many of us have encountered in our own professional careers, are calculated.

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October 30, 2008

Women are paid, on average, only seventy seven cents for every dollar earned by men. As can be seen at the site of “moms rising”, even larger differentials exist for women who are mothers, and these are most extreme for women who are single mothers. But where do these numbers come from? How are they calculated, and, more importantly, what assumptions are made in performing those calculations? I will discuss how these wage differentials, which many of us have encountered in our own professional careers, are calculated. If you want to learn more about the techniques discussed here, consult a good labor economics text, such as that written by George Borjas and published by Irwin McGraw-Hill.

To calculate this differential, we need to get beyond asking what the average woman is paid and comparing it to what the average man is paid. Instead, we ask the question “what would the average woman be paid, if she were paid according to the same criteria as men.” For example, if a man gets paid an extra \$10,000 for each year of schooling, then so would this average woman. This analysis is done for each labor market characteristic that we believe influences a person’s pay scale, such as education, experience, and number of young children at home.

To find how each variable influences men and women, separate regressions are run for both men and women. This statistical technique looks for the effect of each characteristic, while holding the other characteristics constant. The effect of each is found, assuming that the other characteristics are not changing and therefore are not affecting the pay scale themselves. Of course, we all know this is never the way things work; we might pursue additional education just as our children arrive and we may drop out of the labor force for a while when they do arrive, so nothing is ever really “held constant”. But this technique allows us to imagine what would happen IF everything else could be held constant. The result is information on how a change in each characteristic affects the pay of men and of women.

We then look at the average woman, an imaginary woman who has the same education, experience, etc. as the average value from our data set for each characteristic for women. We calculate what her average pay would be if she were to be paid as a woman, using the mean values for women and the pay scale information we found from our regression for women. We then ask what she would be paid, if she were paid according to the pay scale for men. The difference between what she would be paid as a woman and what she would be paid as a man is unexplained, and is often attributed to discrimination.

Note that, since this looks at the effect of a change in an input variable, simply changing the level of that variable, such as education, for the average woman will not necessarily have any effect on the wage differential. When people talk about lowering the wage differential between men and women, they need to look beyond increasing the level of education or training for women. Instead, they must look at the reasons why men and women are often rewarded differently in the labor market for the same characteristics.

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