Hate crimes have more than doubled in the past five years, new figures showed earlier this week – no surprise there. But if you search the list for the motivating factor recorded in these crimes, there is one notable omission: age. According to the Crown Prosecution Service, there is no such thing as age-related hate crime. Facebook’s definition of hate speech is longer – you are not allowed to attack people because of their race, ethnicity, national origin, religious affiliation, sexual orientation, caste, sex, gender, gender identity or serious disease or disability. Age? Absent again.

So this week’s announcement that the Law Commission is examining whether age should be added to hate crime legislation is timely and welcome. It is evident that open expressions of hostility to older people have become more common since the EU referendum – the “old people screwing millennials” trope. Indeed, the idea that how you voted was determined chiefly by your age has been repeated so often that it has acquired the patina of truth. But it is based on a fundamental misreading of the data.

The British Social Attitudes survey last year found that the crucial factor in shaping how people voted was not age, but education: 80% of 18- to 34-year-olds with a degree voted remain, but so did 70% of those aged over 55. It’s not a vast difference – it’s just that fewer of this cohort went to university. The stereotype is of older, wealthy people denying young people the privileges they have enjoyed. The reality is that the older leave vote came largely from those who didn’t go to university and who never had that privilege in the first place.

The ‘greedy oldies' narrative has taken hold and has led to a torrent of abuse directed at old people

Nevertheless, the “greedy oldies” narrative has taken hold and has led to a torrent of abuse directed at old people. Young people have repeatedly claimed that old people are “stealing our future”. More than one in four 18- to 34-year-old remainers have professed themselves willing to see pensions reduced if it stopped Brexit. “I’m never giving up my seat on the train for an old person again,” one tweet warned in the days after the vote. A common refrain directed at older people has been “you’ve had your life”. Bizarre, I know, but as an old person I believe – perhaps deludedly – that I still have one.

A former head of public affairs at Help the Aged UK has suggested that “baby boomer” has almost become a term of abuse. I’ve always hated that term, anyway. Originally, it meant the explosion of births between 1946 and 1964, but “boom” has come to be associated with all the advantages they supposedly amassed, and babies because they are lifelong infants selfishly obliterating everyone else’s needs. The idea was planted by David Willetts, in his 2010 book The Pinch: How the Baby Boomers Took Their Children’s Future – and Why They Should Give It Back. I suppose we also made off with his sense of irony, since Willetts was the minister of state for universities who tripled tuition fees.

After the referendum, the “greedy oldies” line was fanned by columnists such as the Times’s Giles Coren: “From their stairlifts and their Zimmer frames, their electric recliner beds and their walk-in baths,” he wrote, “they reached out with their wizened old writing hands to make their wobbly crosses and screwed their children and their children’s children for a thousand generations.” Then, earlier this year, Jeremy Paxman suggested people over the age of 65 shouldn’t be allowed to vote. (He is 68.)

Analysis shows that areas with a larger proportion of men also had a higher percentage of leave votes. Funny, I must have missed all those articles calling for men to lose the right to vote.

Age shaming an entire generation is not without consequences. In the aftermath of the referendum, Rosa Kornfeld-Matte, the UN’s independent expert on the human rights of old people, deplored the way in which they had been stigmatised as the cause of Brexit and argued that ageism is “intimately linked to violence and abuse against [older people] in public and private spheres”.

Such endless vilification of older people encourages the young to stereotype not only a huge swath of the population but also their future selves. For when it comes to old age, the demonisers eventually become the demonised – as confirmed by recent research by the Royal Society for Public Health, in which young people expressed the conviction that they would eventually become the butt of ageist attitudes and behaviour as they got older, as if it were the natural order of things and somehow intrinsic to the ageing process.

Of course, I don’t blame young people for their outpouring of anger: I’m old but I am also enraged by the situation they face, for this isn’t a zero-sum game. I’m angry for them and us at the same time. I wish, though, that their rage was better targeted. This repetition of the Pinch trope reinforces the absurd, harmful notion that age is the single most important determinant of wealth, whereas in reality great differences exist within each generation and not just between them – inequality is gendered, racialised and shaped by social class, and many old people remain poor. It is political decisions that have landed young people with debt, homelessness and unemployment, not old people. By contrast, in Scandinavian countries, where the state is viewed less as an authoritarian nanny and more as a protective parent meeting (properly funded) basic human needs, the sense of intergenerational inequity is far less pronounced.

It is entirely understandable that young people are furious at their prospects in post-crash, post-Brexit Britain. But those who direct that rage at old people have picked the wrong culprit.

• Anne Karpf is a columnist, writer and sociologist