1. "[C]hildless women may be more productive than women with children and their male colleagues (with or without children)." Childless women billed almost 1600 hours, while fathers billed 1541 hours, childless men billed 1491 hours, and mothers billed 1387 hours.
However, the data also show that childless women are less experienced, with an average of 7.13 years of legal experience, compared to 15.3 for fathers, 13.44 for childless men, and 11.06 for mothers. You should picture these firms as employing young childless women, and older men, and older women with children. Are the childless women billing more just because they are younger, that is, your average overworked associate competing for partnership? (In the regressions, the authors control for legal experience, but if mothers tend to be partners, childless women tend to be associates, and partners work less than associates, I don't think that their legal experience control will do the trick.)
2. "[F]amily-friendly benefits appear more advantageous to men than women, even though women with young children would likely gain more from them in balancing work and family." The three variables that measure family-friendly benefits do not actually refer to specific programs such as paid maternity leave; they refer to survey respondents' perceptions of family-friendliness (including such things as whether people at work frown on discussions about child care). The study finds that being in a family-friendly firm does not increase a woman's productivity, but reduces a man's productivity.
The first result is more surprising than the second. To see why, note that one of the measures of family-friendliness is "reasonable workload." It is straightforward that if you are in a firm with a "reasonable workload" you are going to bill fewer hours. The two variables—billable hours and reasonable workload—ought to measure the same thing. So why the different results for women? The only thing I can think of is that maybe women are given more tasks that are not billable, perhaps because they have less legal experience, and it is those tasks that they forgo if they have children while in a family-friendly firm. The authors note that billable hours account for only 2/3 of the time spent by the lawyers at work, so if non-billable hours decline, this will not show up in the regressions and yet may account for a great deal of the underling variation.
But the larger point is that we can't say whether these benefits are more "advantageous" to men or to women without knowing more about how employees are compensated. People don't care only about how many hours they work; they also care about pay. But pay is not in the data set. This leads to a third concern.
3. "[W]e found very little support for ... the costs of working in a family-friendly firm for women's productivity." Emily interprets this statement as follows. "The happy spin from the authors is that the family-friendly policies aren't hurting the firms vis-à-vis their women employees, which makes the policies seem less costly. (Their original hypothesis was that the family-friendly firms would find that mothers were less productive, since these policies are often seen as the path to mommy tracking.)"
Assuming Emily's interpretation is correct (I'm not sure I understand the statement I quoted from the paper), the paper doesn't really provide much support for this idea, or have any normative implications, as far as I can tell. Some firms have family-friendly policies and other firms do not. Women work about the same amount in both firms. But it may be they are paid less in the family-friendly firms, which would suggest that they are being less productive (producing lower-quality work, or producing less work given a fixed investment of the firm's other resources). Or they could be equally productive but receiving some of their compensation in the form of flexibility rather than cash. We just don't know because the study doesn't include salary data or other information (such as the quality of the work) we would need to measure productivity. Also the omitted non-billable hours are troubling.