Private schooling in Britain is unaffordable for the majority of families, but for those that can afford it what do their children get out of paying for education? There are some who say, not much, and that it all depends on family background, but most of the evidence finds that this is not true: private school pupils achieve better GCSEs and A-levels (England’s school-leaving exams) – on average – even when we allow for their background. The crucial point for those interested in social mobility, however, is that later in life it is those that have been to private school who are found – again on average – to get on especially well in the labour market and in public life.

So the next big question is: why?

Many private schools, especially those at secondary level and including the well-known “public schools” with ancient traditions and very high fees, aspire to offer much more than just academic development. They want to educate the “whole child” and often their marketing focuses explicitly on leadership and team working skills which may be developed, not in the classroom but on the playing fields, in school theatres, concert halls, and in other extra-curricular activities.

To study the possible long-term outcomes of this emphasis, together with co-researchers Anna Vignoles from Cambridge University and Golo Henseke from UCL, I looked at the sorts of jobs that people do in later life. We focused not just on the salaries that people earned but also on some important characteristics involved in the jobs: leadership, participation in decision-making and the requirement to put in hard work.

‘We found some stark differences between the jobs being done by privately-educated and state-educated people’

And just as the schools have claimed, we found some stark differences between the jobs being done by privately-educated and state-educated people. We looked at representative samples of workers across the country, and then specifically at a cohort of people born in 1970 when they had reached the age of 42 in 2012. Privately-educated workers have jobs where they exercise significantly greater leadership, and are more likely to participate in work organisation matters. From the perspective of their job quality, however, their jobs require somewhat greater work intensity.

At the same time, we found the same large earnings “premium” that other studies have found. Among those aged 42 with similar social backgrounds, the privately educated men earned 35% more than state-educated men; while privately-educated women earn 21% more than state-educated women.

Looking more closely, we found that educational level was by a long chalk the most important factor explaining the private-state gaps. Indeed, even though jobs requiring leadership are better paid, we found along with other studies that the earnings premium for privately educated women is almost all accounted for by their educational achievements.

But a big social-scientific puzzle remains: privately educated men gain a premium of somewhere between 8% and 15% in the labour market, even when compared with state school men having the same educational achievements, social background and job requirements. Some writers have held that this is evidence of a continuing class bias in recruitment, with graduates having the sort of “public school values” that sometimes find favour in interviews. In other words, an “old boys network”, which used to be rampant for much of the last century, might still be operating, albeit in more subtle ways now that recruitment is typically more professionally organised than fifty years ago. However, there is not a lot of solid evidence to confirm or refute any such bias.

We did find one clue, however. Much of the remaining premium for men is associated with the particular industries where men are concentrated – most notably, the business and financial services industries. These are the high-paying industries of old, and it seems that the privately-educated do especially well in this part of the economy. Maybe this is a matter of preferences but, if there were a private-school bias in recruitment, this is where we should be looking for it.