Universities are asked to be many things, and are accused of being many more.

We want them to be social mobility machines, drivers of productivity and centres of culture and learning. We accuse them of being elitist, left-wing madrasas that saddle the young with debt.

They are, depending on your point of view, ruthless neoliberal employers, or rest homes for a cosseted class who seem not to know how good they have it.

Universities don¡¯t always help themselves. At a recent gathering of academic leaders held by Times Higher Education at Palack? University Olomouc in the Czech Republic, 200 or so delegates were asked what they considered the primary duty of a university to be.

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Not one person said that it was to land their graduates high-paying jobs ¨C understandable in a part of the world facing the spectre of authoritarianism that it thought had been banished for ever.

Back in the UK, meanwhile, the Russell Group plonked out declaring proudly that ¡°#RussellGroup graduates can expect to earn an average of ?3,000 a year more than their peers¡­¡±. Stay classy, as they say these days.

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Contradictions, then, are just as likely to come from within the sector as from outside. But there are some fundamentals that are common to all universities worthy of the title.

Improving opportunity is one of them, and in our cover story we assess whether higher education is fulfilling this responsibility in relation to young men in particular.

Female participation is growing faster than male across the world. The reasons vary, but the result is the same: young men are too often being left behind in the educational stakes.

And as is pointed out, it¡¯s hard to whip up a strong lobby to try to do something about it.

The answer, of course, is not to dampen or curtail the phenomenal success story of young women¡¯s educational empowerment. This is real and impactful and worthy of wild celebration. I was talking recently to an academic at an Indian university about different forms of social impact. In parts of India, he explained, the gender mix is skewed because of sex-selective abortion. But look closely at the area immediately around a women¡¯s university he was familiar with, and this is not the case.

Just having this beacon in the community has wiped out an ingrained cultural practice that devalues female life, he suggested. How¡¯s that for impact? Does it beat a ?3,000-a-year graduate premium?

Another area of contention for universities has been their role in globalisation, which has swung in the popular mind from the key to a brighter future to a dirty word.

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On the one hand, there is little evidence that those who oppose migration extend this to overseas students and faculty; on the other, many governments ¨C including the UK¡¯s ¨C have, whether explicitly or not, included such scholars in the hostile environments they have fostered to curtail immigration.

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This is not the case everywhere. As we report in our news pages, India is now opening up its huge university sector to international students. In time, this could change the global dynamics, although India is unlikely to be fishing in the same pool as the established markets in the foreseeable future.

But attitudes to incoming students, and whether or not they should be allowed to stay on to work, are highly relevant to that other fundamental role of a university: as a driver of economic prosperity.

This is demonstrated once again in a forthcoming study in the Economic Journal that examines data on international migration and trade between more than 100 countries during a 20-year period.

It finds a direct link between migration from a country with a particular export profile and a subsequent boost in the receiving country¡¯s economic activity and competitiveness in the same areas.

The effect is particularly strong when migration is highly skilled ¨C the authors suggest that the impact of a skilled immigrant is about 10 times greater than that of an unskilled one.

It is unfortunate that stories of this kind fail to capture the public imagination, and that competition has encouraged the small-minded one-upmanship demonstrated by that Russell Group tweet.

Universities are not perfect, should not be immune from criticism, and must work harder to reach groups they are currently missing.

But fundamentally, they remain what they always have been: powerful forces for good that shape the societies in which we all live ¨C almost always for the better.

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john.gill@timeshighereducation.com