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
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Will the House of Lords block Brexit?

Process, and a desire to say "I told you so" will be the real battle lines. 

It’s the people versus the peers, at least as far as some overly-excited Brexiteers are concerned. The bill to trigger Article 50 starts its passage through the House of Lords today, and with it, a row about the unelected chamber and how it ought to behave as far as Brexit is concerned.

This week will, largely, be sound and fury. More peers have signed up to speak than since Tony Blair got rid of the bulk of hereditary peers, triggering a 200-peer long queue of parliamentarians there to rage against the dying of the light, before, inevitably, the Commons prevailed over the Lords.

And to be frank, the same is ultimately going to happen with Article 50. From former SDPers, now either Labour peers or Liberal Democrat peers, who risked their careers over Europe, to the last of the impeccably pro-European Conservatives, to committed Labour and Liberal politicians, there are a number of pro-Europeans who will want to make their voices heard before bowing to the inevitable. Others, too, will want to have their “I told you so” on record should it all go belly-up.

The real battle starts next week, when the bill enters committee stage, and it is then that peers will hope to extract concessions from the government, either through defeat in the Lords or the threat of defeat in the Lords. Opposition peers will aim to secure concessions on the process of the talks, rather than to frustrate the exit.

But there are some areas where the government may be forced to give way. The Lords will seek to codify the government’s promise of a vote on the deal and to enshrine greater parliamentary scrutiny of the process, which is hard to argue against, and the government may concede that quarterly statements to the House on the process of Brexit are a price worth paying, and will, in any case, be a concession they end up making further down the line anyway.

But the big prize is the rights of EU citizens already resident here.  The Lords has the advantage of having the overwhelming majority of the public – and the promises of every senior Leaver during the referendum campaign – behind them on that issue. When the unelected chamber faces down the elected, they like to have the weight of public opinion behind them so this is a well-chosen battleground.

But as Alex Barker explains in today’s FT, the rights of citizens aren’t as easy to guarantee as they look. Do pensions count? What about the children of EU citizens? What about access to social security and health? Rights that are easy to protect in the UK are more fraught in Spain, for instance. What about a British expat, working in, say, Italy, married to an Italian, who divorces, but wishes to remain in Italy afterwards? There is general agreement on all sides that the rights of Brits living in the rest of the EU and citizens of the EU27 living here need to be respected and guaranteed. But that even areas of broad agreement are the subject of fraught negotiation shows why those “I told you sos”  may come in handy sooner than we think.

Stephen Bush is special correspondent at the New Statesman. His daily briefing, Morning Call, provides a quick and essential guide to British politics.