Douglas Clement interviews David Card:

Results: of 677 respondents, 66% have an academic or college educated parent and around 26 are first gens. Only 11% have academic parents, which is admittedly a bit lower than I expected. Results surprisingly very stable as the N went from around 100 upwards.

First of all, the presumption that unions might have an effect on men is based on the observation that within the union sector, wages are more compressed than outside the union sector. There are several institutional reasons for this. For one thing, unions try to equalize wages for people doing similar jobs. They also try to lower the differences between higher-wage and lower-wage people, largely for political reasons. Both features tend to lower inequality in the union sector.

The same thing is not as true for women, largely because unionized women work in sectors where there is already a lot of institutional wage setting, like teaching. In these settings, whether or not there is a union involved makes less difference. In any case, you don’t see much difference in the variability of wages among women who are unionized, or not once you control for education.

What I had done was look at the decline of unionization and how that has affected overall inequality for men. One thing that countervails the equalizing effect of trade unions for men is that unions raise wages. If they raise pay for one group and leave it the same for another, that in itself increases dispersion. The starting point for any analysis is to measure how the equalizing tendency within the union sector plays off against the fact that wages are now higher for an arbitrary group of workers.
The answer for men has always been that the equalizing effect is bigger. Actually, this wasn’t really understood in the literature until the early 1970s when Richard Freeman conducted the first detailed empirical studies of unions and inequality. Prior to his work people didn’t realize the equalizing effect was so much bigger.
My results suggest that the decline in unionization is a small but noticeable part of the overall increase in inequality for men over the past 30 years—maybe 10 to 20 percent of the total. It was most important for workers at the middle of the wage distribution. Typically, a unionized worker is not somebody at the bottom of the distribution, but somebody at the middle. In the 1970s, unionization was pushing this group a little closer to the top and narrowing the degree of wage variability across jobs. As unionization has gone away, there has been some downward drift in the level of wages (relative to the top skill groups) and an opening up of wage inequality in sectors like trucking and manufacturing. Both effects are important, but they’re only a small part of the overall trend.

And within the female labor force, there’s really no effect because unions don’t really equalize wages much for women.