Child benefit withdrawal will make it better to work less for families with over seven children

And come 2076, that will be the case for every family in the nation.

The child tax credit withdrawal, taking effect on Monday, will lead to marginal tax rates of over 100 per cent on families with more than eight children earning between £50,000 and £60,000.

The IFS explains how the marginal rates are calculated:

Affected taxpayers will pay back one per cent of their family’s Child Benefit for every £100 by which taxable income exceeds £50,000. One per cent of Child Benefit is £10.56 per year for a 1-child family, and an additional £6.97 per child for larger families. Hence the marginal tax rate between £50,000 and £60,000 is increased by about 11 percentage points for the first child and by an additional 7 percentage points for each subsequent one. So, for example, while about 320,000 people will find that their marginal income tax rate increases to more than 50%, about 40,000 of them - those with three or more children - will find that it jumps to at least 65%.

They offer a chart with the rate calculated up to four children:

By seven children, the marginal rate rises to 99.35 per cent, and by eight, it breaks 100 per cent (106.32 per cent, to be exact). This means that any individual with a family of eight kids earning between £50,000 and £60,000 would be better off if they reduced their salary back down to £50,000. In fact, for that individual, they would have to earn £61,105 before their post-tax income was the same as it was at £50,000.

It's unclear whether any families actually exist matching that criterion - rather wonderfully, my back-of-the-envelope maths (which assumes that the exponential decrease in the number of families of each size continues: e.g., there are 1/8th the number of families with three or more kids as there are with two or more, so I'm assuming that there are correspondingly 1/8th the number of families with four or more as there are with three or more, and so on) suggests that there may be exactly one – but even if there are none at the moment, there's no reason why there won't be one in the future. Families with eight children do, after all, exist.

In fact, as time goes on, this problem will get worse. The IFS points out that child benefit is uprated with inflation, while tax bands aren't. Currently, each extra child after the first increases your "marginal tax rate" by around seven per cent, but suppose child benefit is uprated by two per cent a year. In that case, the marginal tax would exceed one hundred per cent for families with seven children next year; for six children in the year 2020; for five children in the year 2028; and, eventually, for families with just one child – i.e., every family – in the year 2076.

Hopefully the law will be changed before then, of course. But as a rule of thumb, laws which become ridiculously damaging unless you actively intervene ought not be signed in the first place. Oops.

Children. Photograph: Getty Images

Alex Hern is a technology reporter for the Guardian. He was formerly staff writer at the New Statesman. You should follow Alex on Twitter.

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Owen Smith is naïve if he thinks misogynist abuse in Labour started with Jeremy Corbyn

“We didn’t have this sort of abuse before Jeremy Corbyn became the leader.”

Owen Smith, the MP challenging Jeremy Corbyn in the Labour leadership contest, has told BBC News that the party’s nastier side is a result of its leader.

He said:

“I think Jeremy should take a little more responsibility for what’s going on in the Labour party. After all, we didn’t have this sort of abuse and intolerance, misogyny, antisemitism in the Labour party before Jeremy Corbyn became the leader.

“It’s now become something that is being talked about on television, on radio, and in newspapers. And Angela is right, it has been effectively licenced within the last nine months.

“We’re the Labour party. We’ve got to be about fairness, and tolerance, and equality. It’s in our DNA. So for us to be reduced to this infighting is awful. Now, I understand why people feel passionately about the future of our party – I feel passionately about that. I feel we’re in danger of splitting and being destroyed.

“But we can’t tolerate it. And it isn’t good enough for Jeremy simply to say he has threats too. Well, I’ve had death threats, I’ve had threats too, but I’m telling him, it’s got to be stamped out. We’ve got to have zero tolerance of this in the Labour party.”

While Smith’s conclusion is correct, his analysis is worryingly wrong.

Whether it is out of incompetence or an unwillingness to see the extent of the situation, Corbyn has done very little to stamp out abuse in his party, which has thus been allowed to escalate. It is fair enough of Smith to criticise him for his failure to stem the flow and punish the perpetrators.

It is also reasonable to condemn Corbyn's inability to stop allies like Chancellor John McDonnell and Unite leader Len McCluskey using violent language (“lynch mob”, “fucking useless”, etc) about their opponents, which feeds into the aggressive atmosphere. Though, as I’ve written before, Labour politicians on all sides have a duty to watch their words.

But it’s when we see how Smith came to the point of urging Corbyn to take more responsibility that we should worry. Smith confidently argues that there wasn’t “this sort of abuse and intolerance, misogyny, antisemitism” in the party before Corbyn was voted in. (I assume when he says “this sort”, he means online, death threats, letters, and abuse at protests. The sort that has been high-profile recently).

This is naïve. Anyone involved in Labour politics – or anything close to it – for longer than Corbyn’s leadership could tell Smith that misogyny and antisemitism have been around for a pretty long time. Perhaps because Smith isn’t the prime target, he hasn’t been paying close enough attention. Sexism wasn’t just invented nine months ago, and we shouldn’t let the belief set in that it did – then it simply becomes a useful tool for Corbyn’s detractors to bash him with, rather than a longstanding, structural problem to solve.

Smith's lament that “it’s now become something that is being talked about” is also jarring. Isnt it a good thing that such abuse is now being called out so publicly, and closely scrutinised by the media?

In my eyes, this is a bit like the argument that Corbyn has lost Labour’s heartlands. No, he hasn’t. They have been slowly slipping away for years – and we all noticed when Labour took a beating in the last general election (way before Corbyn had anything to do with the Labour leadership). As with the abuse, Corbyn hasn’t done much to address this, and his inaction has therefore exacerbated it. But if we tell ourselves that it started with him, then we’re grasping for a very, very simple solution (remove Corbyn = automatic win in the North, and immediate erasure of misogyny and antisemitism) to a problem we have catastrophically failed to analyse.

Anoosh Chakelian is deputy web editor at the New Statesman.