This creates two problems, say the consultants. Companies whose employees aren’t engaged have weaker financial performance and if promising women leave, companies pay an additional financial penalty for having a less diverse leadership team. The good news is: by making leaders accountable for results, companies can create a more engaging environment - not only for senior-level women but for all employees.

BCG's data shows that companies with the highest overall engagement scores do not have a gender gap. Women and men at all levels are equally engaged. Yet companies with lower overall engagement show a notable gender gap In other words, when companies get engagement right, everyone benefits. When they don’t, senior women feel the pain disproportionately.

Here is BCG's take on the situation:

1. Appreciation. Women cite appreciation for their work from their superiors as the top criterion they look for in a job - as do men. In lower-engagement companies, senior women report feeling less appreciated.

2. Work-life balance. Work-life balance or flexibility is the second-most-important factor for both women and men. As men rise in seniority, they report more support from their colleagues for their non-work obligations, while women report the opposite. Flexible working hours and paid time off rate relatively high on employee's wish list; other work-life-balance programmes - such as maternity and adoptive leave, family growth support, and wellness initiatives - rate lower.

3. Cooperation and relations with colleagues. Women and men alike cite a strong relationship with colleagues as the third-most-important factor. Again, we see troubling results for senior women in the lower-engagement companies. They are more sceptical about whether their managers behave honestly with them and with others.

4. Mentorship, sponsorship. Junior women in all companies report a positive experience with mentoring. Senior women at lower-engagement companies are less satisfied. In terms of receiving help with their professional growth, women’s scores remain flat as they increase in seniority, even as men’s scores rise steadily. When asked whether “my manager is a good mentor to me,” men’s positive responses increase with rising seniority twice as fast as women’s do.

5. Compensation and promotion. Junior women are as confident as their male peers that their compensation accurately reflects performance. But this confidence rises less quickly for women as their seniority increases than it does for men. Even more concerning, men’s scores on the topic of “teams that perform well are recognized for it” rise three times as fast with seniority as women’s do.

6. Job attributes. On average, senior women report feeling underleveraged as leaders, as demonstrated by their scores on the topic of “getting the chance to use my skills and abilities”, while senior men are less likely to feel that way.

7. Company objectives. Among non-managers, junior women tend to feel positive about their connection to their company’s objectives and aspirations, but senior women are less positive than their male counterparts on this critical dimension. Similarly, junior women give comparatively high scores to questions about whether they “know what’s going on at the company”, “understand the company values” and feel that there are “clear consequences for people who act against them”. Senior women are less convinced.

Read more at BCG.Perspectives