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.

Photo: Getty Images
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There are risks as well as opportunities ahead for George Osborne

The Chancellor is in a tight spot, but expect his political wiles to be on full display, says Spencer Thompson.

The most significant fiscal event of this parliament will take place in late November, when the Chancellor presents the spending review setting out his plans for funding government departments over the next four years. This week, across Whitehall and up and down the country, ministers, lobbyists, advocacy groups and town halls are busily finalising their pitches ahead of Friday’s deadline for submissions to the review

It is difficult to overstate the challenge faced by the Chancellor. Under his current spending forecast and planned protections for the NHS, schools, defence and international aid spending, other areas of government will need to be cut by 16.4 per cent in real terms between 2015/16 and 2019/20. Focusing on services spending outside of protected areas, the cumulative cut will reach 26.5 per cent. Despite this, the Chancellor nonetheless has significant room for manoeuvre.

Firstly, under plans unveiled at the budget, the government intends to expand capital investment significantly in both 2018-19 and 2019-20. Over the last parliament capital spending was cut by around a quarter, but between now and 2019-20 it will grow by almost 20 per cent. How this growth in spending should be distributed across departments and between investment projects should be at the heart of the spending review.

In a paper published on Monday, we highlighted three urgent priorities for any additional capital spending: re-balancing transport investment away from London and the greater South East towards the North of England, a £2bn per year boost in public spending on housebuilding, and £1bn of extra investment per year in energy efficiency improvements for fuel-poor households.

Secondly, despite the tough fiscal environment, the Chancellor has the scope to fund a range of areas of policy in dire need of extra resources. These include social care, where rising costs at a time of falling resources are set to generate a severe funding squeeze for local government, 16-19 education, where many 6th-form and FE colleges are at risk of great financial difficulty, and funding a guaranteed paid job for young people in long-term unemployment. Our paper suggests a range of options for how to put these and other areas of policy on a sustainable funding footing.

There is a political angle to this as well. The Conservatives are keen to be seen as a party representing all working people, as shown by the "blue-collar Conservatism" agenda. In addition, the spending review offers the Conservative party the opportunity to return to ‘Compassionate Conservatism’ as a going concern.  If they are truly serious about being seen in this light, this should be reflected in a social investment agenda pursued through the spending review that promotes employment and secures a future for public services outside the NHS and schools.

This will come at a cost, however. In our paper, we show how the Chancellor could fund our package of proposed policies without increasing the pain on other areas of government, while remaining consistent with the government’s fiscal rules that require him to reach a surplus on overall government borrowing by 2019-20. We do not agree that the Government needs to reach a surplus in that year. But given this target wont be scrapped ahead of the spending review, we suggest that he should target a slightly lower surplus in 2019/20 of £7bn, with the deficit the year before being £2bn higher. In addition, we propose several revenue-raising measures in line with recent government tax policy that together would unlock an additional £5bn of resource for government departments.

Make no mistake, this will be a tough settlement for government departments and for public services. But the Chancellor does have a range of options open as he plans the upcoming spending review. Expect his reputation as a highly political Chancellor to be on full display.

Spencer Thompson is economic analyst at IPPR