THE Nordic countries have done more than anywhere else to provide women with equal opportunities. Maternity leave is generous. State provision of child care is first-rate. Female university graduates outnumber males by six to four. Half of Finland’s cabinet ministers and 57% of Sweden’s are female. The latest Global Gender Gap Index, compiled by the World Economic Forum (WEF), awards the first five places to the Vikings: Iceland comes top, followed by Finland, Norway, Sweden and Denmark. The region has also led the world in introducing quotas for corporate boards. Norway started the trend, and now requires stockmarket-listed companies to allot at least 40% of board seats to women. Iceland, Finland and some other European countries have introduced similar requirements.

But such rules cover only board seats, and only at listed firms. Visit a typical Nordic company headquarters and you will notice something striking among the standing desks and modernist furniture: the senior managers are still mostly men, and most of the women are PAs. The egalitarian flame that burns so brightly at the bottom of society splutters at the top of business. The WEF ranked Denmark 72nd in terms of the gender gap among senior managers and officials. There may be more women sitting round the table at board meetings, but the person who runs the show is almost always a man: only 6% of Norwegian listed firms had a female chief executive in 2013, little better than the 5% of American companies on the Fortune 500 list that have a woman as CEO.

There is much discussion about why Viking women have failed to crack the glass ceiling. The left reckons they must still be suffering from unconscious prejudice. The right maintains it is a matter of individual women choosing to give priority to their children. The Nordics can hardly be faulted for spending too little money: as a share of GDP their public spending on child care is between seven and nine times America’s (where the proportion is a measly 0.1%). But there is no simple relationship between providing equality of opportunity and securing equality of results.

Indeed, it is possible that generous social policies can backfire. Studies by Nina Smith, an economist at Aarhus University in Denmark, and others raise two striking possibilities. First, Nordic women may suffer lower earnings later in their careers because generous maternity leave encourages them to take long breaks to raise children earlier on, when male competitors are gaining valuable experience. Second, women trying to climb the career ladder seem to find it harder to afford domestic help than their American equivalents, because those generous social policies have to be paid for with high taxes. And, when chores cannot be offloaded to domestic staff, working women still get lumbered with the time-inflexible household tasks, such as picking up children from school, whereas men do “their” chores at the weekend. Public-sector employers are more inclined to provide female staff with child-friendly hours, ample family leave and so on; and they have a larger proportion of women bosses than private firms. But the wage structure in such workplaces is much more compressed than in the predominantly male-led private sector.

Overall, then, policies that reduce the gender gap for the mass of workers may be increasing it at the upper levels of management. Ms Smith calculates that in Denmark and Sweden the gap between men and women at the upper end of the pay scale has actually increased in recent decades.

Supporters of board quotas argue that they are a useful response to the failure of equal opportunities: by putting women into board seats by fiat, you will break up old-boy networks and create old-girl networks. Certainly, the policy has transformed the boardrooms of Norway’s listed companies: female directors have closed the pay gap with male ones, even as their numbers have surged. But look beyond those “golden skirts” and the picture is more complex. Companies fled the stockmarket as quotas were phased in: Norway’s stock of listed firms fell from 563 in 2003 to 179 in 2008. And even among those that remain on the stockmarket, Norway’s 6% figure for female CEOs in 2013 is an improvement on the 2% in 2001, but no more of an increase than Denmark, which has no quotas, achieved over the same period.

Furthermore, in the first substantial study of the Norwegian reforms, Marianne Bertrand of the University of Chicago’s Booth business school and three colleagues conclude that “there is no evidence that these gains at the very top trickled down.” They have done nothing to improve the career prospects of highly qualified women below board level. They have not helped close the gender gap in the incomes of recent business-school graduates. Nor have they done anything to encourage younger women to go to business school in the first place.

Too vague, or too prescriptive

The two main ways to advance women’s business careers that have been tried so far—female-friendly social policies and board quotas—suffer from opposite problems. The first is too vague: it makes life easier for women but does not encourage them to aim higher. The second is too prescriptive: it provides guaranteed places for a select group in a specific role, without strengthening the career ladder for women as a whole.

However, there is plenty more that can be done. Companies should make sure they include plenty of women among the high-flyers selected for challenging assignments. Senior women should take their role as mentors seriously. Employers should encourage, not penalise, fathers who take parenting breaks, and let them work flexible hours so they can do the school run. Selection committees should stop putting so much emphasis on continuity of service, and penalising women who take career breaks to care for young children. Winston Churchill spent years away from the front line of politics in the 1930s but showed, when Britain needed it, that he had what it takes to be a leader.