The Post has an interesting summary of some recent research:

American women earn substantially more money and narrow the long-standing gender gap in income if other women in their workplaces reach the ranks of senior management, according to a new national study presented here.

By contrast, the study found, increasing the number of women managers in junior positions makes no difference to the gender gap -- women on average continue to earn about 20 percent less than men.

Surprisingly, men who work for women managers seem to do slightly worse in income than men who work for men, irrespective of whether the women managers are in senior positions.

The study answers for the first time what happens to workers when women break through the glass ceiling, and is based on 1.3 million American workers in nearly 30,000 jobs and 79 metropolitan areas...

Cohen and University of California at Irvine sociologist Matt L. Huffman found that women earn about 81 percent of what men make, and that figure remains unchanged when the number of junior-level women managers rises from 2 percent to more than 50 percent. But when women become senior managers, female workers earn 91 percent of men's salaries.

The sociologists used data from the 2000 census that asked Americans about their professional lives, including the industry they work in and their incomes. The sociologists then compared the information against what was known about the ratio of male and female managers in particular industries, and how senior the female managers were in each of those local industries. They accounted for dozens of other variables, including race, geographic location, size of workers' families, education and experience.

For example, the sociologists found 1,887 restaurant managers in the Los Angeles area and 10,422 restaurant workers. There were far more female restaurant managers in Los Angeles than in New York, but the Los Angeles female managers were more likely to be low-level. Consistent with the study's findings, women restaurant workers in New York earned 95 percent of the pay of their male counterparts, while workers in Los Angeles earned 92 percent of what men made.

I have not seen the paper. I do wonder, though, how solid the conclusion is.

There are two immediate theories that would explain the data described in this report. One is that the presence of female managers lessens anti-women discrimination in the workplace, thereby increasing earnings by women. Another is that the success of women in the workplace - both in terms of earnings and chance of making the senior management - is positively correlated with some cultural factors which differ from city to city in the US - it may be just my prejudices, but I think women are more succesful relative to men in San Francisco than in Wichita, Kansas.

Both of the above explanations, if true, would produce a correlation between number of female managers and earnings by women. The first explanation though would imply a causation from the former to the latter, while the second would not. So I wonder whether Cohen and Huffman managed to rule out alternative explanations.