From a study (Breaking the Glass Ceiling? The Effect of Board Quotas on Female Labor Market Outcomes in Norway) by Marianne Bertrand, Sandra E. Black, Sissel Jensen and Adriana Lleras-Muney:
We document that the women appointed to these boards post-reform were observably more qualified than their female predecessors along many dimensions, and that the gender gap in earnings within boards fell substantially. On the other hand, we see no robust evidence that the reform benefited the larger set of women employed in the companies subject to the quota. Moreover, the reform had no clear impact on highly qualified women whose qualifications mirror those of board members but who were not appointed to boards. Finally, we find mixed support for the view that the reform affected the decisions of young women: while the reform was not accompanied by any change in female enrollment in business education programs, we do see some improvements in labor market outcomes for young women with graduate business degrees in their early career stages; however, we observe similar improvements for young women with graduate science degrees, suggesting this may not be due to the reform. Overall, seven years after the board quota policy fully came into effect, we conclude that it had very little discernible impact on women in business beyond its direct effect on the women who made it into boardrooms.The case for quotas (other than the 'it's fair' argument) is that they provide for positive female role models and, therefore, act over time to improve the lot of women in the workforce. This would appear to be a questionable assertion - indeed when Nima Sanandaji looked at The Economist's 'Glass Ceiling Index' he found:
...that the rise of the welfare state created jobs for women as well as aided their labor market participation by offering various family-related services. Yet this same system contains disincentives for female ascension in business. One example is high taxes that make it costly to purchase household services (a strategy otherwise used by parents to “buy” time so that they can take care of children as well as focus on their careers); generous benefit systems combined with high taxes that reduce economic incentives for both parents to work full-time and public sector monopolies/oligopolies in female-dominated sectors and parental policies that give women incentive to take long breaks from the working life.The Nordic welfare state is very good for female participation in the workforce but seems less good at improving female power in that workforce - here's Nima Sanandaji again:
Based on the Economist index, the United States has unusually women-unfriendly work policies while the Nordics have the most women-friendly work policies in the world. However, it is the United States which has the highest rate of women managers amongst all countries included in the Index, while the Nordic countries have a lower share.Again the findings suggest that open market economies with fewer state monopolies are better for female power even when they are less good for participation. Sanandaji confirms this in showing how within the Nordic countries the levels of female empowerment (indicated by numbers of women managers) vary depending on the extent to which services operate in a competitive market.