It costs more to fly solo. That’s according to the Good Housekeeping Institute, which last week released a study claiming single life can cost people up to £2,000 a year more. Even as someone who’s spent a good chunk of time single, and felt the occasional sting of shelling out more for hotels, it was hard not to raise an eyebrow at the figures: the extra costs of luxury gym memberships and Med cruises feel very much like a first-world problem.

But part of me was still glad to see this undoubtedly superficial take. As a society, we barely discuss the realities and implications of singledom. In pop culture singledom is almost invariably represented as an easily fixed unhappy state, a step along the way to getting happily hitched. We know little about the long-term singles: how many relish their freedom and independence, and how many feel burdened with loneliness and hope to meet the love of their life? To what extent is singledom driving social infertility – not having children because you haven’t met Mr or Ms Right? And if so, what does it mean for an ageing society in which we expect family members to care for their older relatives?

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The single stereotypes abound. For men, it’s the dysfunctional fortysomething still living with his parents. For women, the callous career woman – who could forget former Australian prime minister Julia Gillard being accused of being “deliberately barren”? Or the crazy cat lady living alone, slowly losing her mind. There’s shame and stigma attached to fessing up to being either happily or unhappily single: would I have written this column a couple of years ago when I was on my own?

Beyond the stereotypes come the pop dating theories. In Date-onomics, Jon Birger posits that a new gender imbalance is set to affect who we settle down with. Studies show that we are likely to couple up with people who broadly resemble ourselves in terms of class and education. But they also suggest men seem less keen to “marry up” and women to “marry down”. With female university graduates now outnumbering men in many countries – women in the UK are a third more likely to go to university than men -unless we see more of the “mixed-collar” partnerships Birger predicts will become more common, more blue-collar men and more female graduates may struggle to find romance. Cue an industry of self-help books and coaching for professional women in their early 30s struggling to meet Mr Right.”

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Pop theories aside, there’s been remarkably little robust research on singledom and social infertility. (There are endless pieces on the theme, but few identify just how many people are unable to find partners.)

While the data may not be great, there are clues. For men, there’s a sharp socioeconomic gradient to being single. Men from disadvantaged backgrounds are twice as likely to live alone in their early 40s than those from rich families, which puts them at further financial disadvantage. Some of that is due to higher levels of relationship breakdown, but there is also a significant minority of men from disadvantaged backgrounds who find it difficult to meet a partner in the first place.

For women, the trend runs the other way. University-educated women born in 1970 were almost twice as likely as women with low levels of education to be childless at the age of 42. As women have become more educated, the proportion of women remaining childless has increased from one in 10 of those born in 1946 to just under one in five of those born in 1970. Cue the Daily Mail stereotypes of career-driven women too selfish and picky to settle down and have kids.

So far, so in line with the pop theories. But what’s surprising is that social infertility – not having children because of a failure to meet the right partner – appears to be almost as big a problem for educated men as it is women.

Similar proportions of male and female university graduates are childless at age 42 – around one in four; and similar proportions of those – around one in three – say it was because they hadn’t met the right person. (Incidentally, just 3% of childless female graduates said it was down to their career.) “I can’t help but wonder what it would be like if that little girl were my little girl.” Heartbreaking words you’d expect to hear from a woman desperate to be a mother? They’re in fact penned by a man who would have loved to have been a father but whose chance passed him by.

Love, family and relationships only feature in policy debates about how we live to the extent that they concern children’s lives. Our attitude has always been that – outside medical infertility – finding love and family life in the first place is an entirely private matter; and if you don’t, well, so what.

But social infertility exists, and we should be talking about it more, from whether there should be publicly funded fertility advice for women looking to conceive alone, to the realities of ageing without children, to whether we should be investing in research into how to extend women’s fertility spans in the first place. To do so, though, we need to be able to have healthy conversations about singledom that go beyond the painful, shaming stereotypes of the undateable, the unloveable and the “deliberately barren”.

• This article was amended on 12 September 2018. An earlier version misconstrued the views posited by Jon Birger’s in Dateonomics.

• Sonia Sodha is an Observer columnist