The pressure for gender diversity in public positions and private companies has never been greater, with countries such as France, Sweden, and Germany even bringing in quotas for company boards.

Indeed, Norway has required boards to be 40 per cent women since 2003. But this push for women in the boardroom has not filtered down to the C-suite.

The German Institute for Economic Research found just eight per cent of executive positions were taken by women in the top 200 non-financial companies in the country in 2018.

According to the European Institute for Gender Equality women amount to 17.6 per cent of executive positions of the largest listed companies in the EU, with Cranfield University reporting just 10.9 per cent of executive roles in the UK’s FTSE 100 were female.

And yet it is in the C-suite where women create the greatest value for companies.

My research with Jacob Lyngsie, of Southern Denmark University, has found that if companies want more innovation then they should increase the number of women on their senior management team and not just by one or two, but by many.

In fact, in larger and more complex organisations our research shows that women may be the X factor for firm innovation to succeed.

That’s because after combining a survey of nearly 400 Danish firms with national data from the Danish Integrated Database for Labour Market Research (IDA) we found a positive relationship between the proportion of women in top management teams and that firm’s innovation.

Even more interestingly we found there was no limit to this effect, so the more women the better the firm’s ability to produce innovations. In fact, if a company really wants to boost its innovation it is best to have just women in its top management team.

There is a critical mass though. It is not enough to have just one woman on the executive team, the study revealed 1.7 was the magic number for any impact to be made on innovation – so you need at least two women.

We speculate that the more women in the top management team then the negative stereotypes and biases dissipate, allowing them to be effective members of senior decision-makers.

However, there is one caveat to this. A third finding is that this positive relationship between women and innovation is negatively influenced by the proportion of women in the company’s labour force, so if there are a lot of women in the company’s workforce under the senior management team then the effect is diluted to the point where it doesn’t make any difference.

But in companies dominated by men who have a very feminine top management team, then the effect is strengthened.

Why this happens is difficult to speculate on. Indeed, we found a negative relationship between the proportion of women in the executive team and female’s wages below them.

Is more senior women in the C-suite always good?

While there is the untested assumption that solidarity exists among women inside a company, it may be in companies dominated by women that this no longer exists. Indeed, there is research highlighting the “queen bee” phenomenon where women who have succeeded in reaching the executive team are particularly hostile to lower-ranked female workers to protect their position.

When women below the senior team experience this it de-motivates and harms openness, knowledge sharing and communication, and so dampens innovation.

These findings are based on two huge sets of data. We combined the company register data of Denmark, the IDA, which reveals the gender, wages, education and more of all employees at every company in the country, with our own survey on 392 firms’ innovation habits.

We used the IDA’s data from 2007 to 2009 while our survey questioned CEOs on their entrepreneurial activities and asked the HR department about the company’s organisational structure and HR practices over the same three-year period.

By using basic statistical analysis while controlling for such variables as firm size and age, whether the company is based in a municipality that is pro-women, and industry affiliation, we were able to unearth this positive relationship between women in the executive team and a firm’s innovation.

We started this study to try to see if diversity really does have an affect as there is research suggesting that an executive team with varied educational backgrounds, tenure and gender promote entrepreneurial thinking, while the media is abuzz with the positive idea of diversity.

But there has never been any hard statistical facts to back this up – until now.

And so the positive relationship between women and innovation could well be evidence of the diversity argument, where true creativity comes from a diverse group of people and adding women to a male-dominated C-suite untaps this.

But if that is really the case then we would expect the highest level of innovation to occur when there is the perfect gender mix of 50:50, but we didn’t.

Another theory is that those women who get to the top in companies are likely to be particularly talented because the selection environment and criteria for females is tougher, they have to overcome more hurdles and navigate a largely male-dominated business world to get there.

Thus, having more of them, means they are more skilled managers and so are better at creating the environment and processes needed to successfully launch new products or services.

Are women leaders better at fostering innovation?

A third theory is that innovation is encouraged because of the leadership style of women. There is a lot of research around this, and it is found women are more inclusive, more trusting, and share knowledge to a greater extent.

These are all things that may be helpful when trying to build an innovative environment by facilitating greater communication and openness to ideas from outside the company.

With this evidence we hope companies will reappraise the glacial pace of advancing women into senior management positions. But having seen their record on it, governments may want to take things into their own hands, especially if it means they will be boosting innovation - one of the main drivers of economic growth in a country.

However, my latest research with Peggy Lee, of Arizona State University, Samuele Murtinu, of the University of Groningen, and Vittoria Scalera, of the University of Amsterdam, adds some caution to this.

We found that in those countries where the government has imposed quotas for the number of women in senior management positions the effect of women producing more innovation is weaker, while in those countries without legislation the positive relationship between more women on senior management teams and innovation remains strong.

We used the data from the Management, Organisation and Innovation (MOI) survey developed by the World Bank and the European Bank for Reconstruction and Development (EBRD), which looked at 1,777 manufacturing companies across 12 countries.

Among them, India and Uzbekistan have legally-binding quotas to raise the number of females in parliament. This, research has found, sends a signal to business to do the same and promote women to senior positions.

Germany, Lithuania and Romania have voluntary quotas for business, while Belarus, Kazakhstan, where 53 per cent of senior management positions are taken by women, Bulgaria, Poland, Russia, Serbia and Ukraine have no voluntary or legal system of promoting female bosses.

The results suggests that legally-binding quotas promoting women into senior positions does indeed produce ‘tokenism’ and the selection of unqualified female managers, producing potentially negative effects for the firm.

This might mean that the pool of qualified women just isn’t big enough despite more women now in the labour market than ever before.

When promoting women is purely voluntary for companies we find that female managers are able to maximise their influence on the decision-making process despite being in a minority on the senior management team, and the positive relationship with innovation continues.

So our research shows that instead of dragging their feet companies should be clamouring to get more women into executive roles. But the fact they are not does not mean Governments should push them to do it – having more women within firms’ management team, it seems, is only half the equation.

Nicolai Foss is Distinguished Research Environment Professor at Warwick Business School.