There are not 120,000 "troubled families"

This zombie statistic refuses to die.

The Department for Communities and Local Government has released a report focusing on so-called "troubled families", which presents a compelling case that the worst of these families have problems which need urgent intervention. But it also takes the opportunity to revive one of the department's favourite zombie statistics. A report which is based on formal interviews with 16 families ("although she met and talked with many more") is generalised out to cover 120,000.

This six-figure number is one of the DCLG's favourites. It has been pushing it since at least February, when NIESR's Jonathan Portes first drew attention to the problems with the definition of "troubled". When the Prime Minister quoted the figure, he called these families:

The source of a large proportion of the problems in society. Drug addiction. Alcohol abuse. Crime. A culture of disruption and irresponsibility that cascades through generations.

As Portes pointed out, the actual definition of troubled families focuses far more on them being families with troubles, rather than families causing trouble. The DCLG has an explanatory note on the topic, which defines the families as any holding five or more of the following characteristics:

a) no parent in work
b) poor quality housing,
c) no parent with qualifications,
d) mother with mental health problems
e) one parent with longstanding disability/illness
f) family has low income,
g) Family cannot afford some food/clothing items                                                        

So back in February, the overarching problem with the statistic was how it was used, rather than the number itself. Whether or not there were 120,000 of them, these troubled families are in no way "irresponsible".

But last month, the dishonesty became clearer. Perhaps realising that the rhetoric didn't match up with the definition, the department published a new explanatory note, which claimed that troubled families were:

Characterised by there being no adult in the family working, children not being in school and family members being involved in crime and anti-social behaviour.

That definition does sound much more like one of a family suffering "a culture of disruption and irresponsibility", certainly. But normally, when one changes a definition of something, the number of cases falling under that definition also changes. Not so with the troubled families. The department continued – and continues – to refer to "120,000" of them.

Even worse, when the Prime Minister first referred to the families (using the kinder definition), he did so with an extraordinary level of granularity, saying:

There are an estimated 4,500 of these families in Birmingham, 2,500 in Manchester, and 1,115 here in Sandwell.

Once the definition changed, had the location? Like hell.

As Jonathan Portes concluded his post:

It is difficult to conclude anything except that the Department, and the governnment, have become hung up on the 120,000 number despite the fact that they are well aware that it is now completely discredited, either as a national estimate of the number of "troubled families" or as a sensible guide to local policy.

The release of today's report just confirms that feeling. The figure of 120,000 is mentioned exactly twice in the 30,000 word report (pdf), once in author Louise Casey's foreword and once in the introduction. It is also mentioned twice in the 600 word press release, and twice in each of the Guardian and Mail's reports on the topic. It seems like something which has little to do with the content of the report (an admirable qualititative study of what it's like to live in an incredibly disfunctional household, but one which offers little guidance as to how widespread the problems are) and everything to do with a need to push a continuing narrative.

People like to put numbers on things, so here's one: with the actual information the DCLG has put out, we know of just 16 troubled families, the ones interviewed by Casey. Pick a number any higher than that and you're getting into the same voodoo mathematics the government has been performing for the last six months.

Syringes lie on the floor. But are they from a "troubled family"? 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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Q&A: What are tax credits and how do they work?

All you need to know about the government's plan to cut tax credits.

What are tax credits?

Tax credits are payments made regularly by the state into bank accounts to support families with children, or those who are in low-paid jobs. There are two types of tax credit: the working tax credit and the child tax credit.

What are they for?

To redistribute income to those less able to get by, or to provide for their children, on what they earn.

Are they similar to tax relief?

No. They don’t have much to do with tax. They’re more of a welfare thing. You don’t need to be a taxpayer to receive tax credits. It’s just that, unlike other benefits, they are based on the tax year and paid via the tax office.

Who is eligible?

Anyone aged over 16 (for child tax credits) and over 25 (for working tax credits) who normally lives in the UK can apply for them, depending on their income, the hours they work, whether they have a disability, and whether they pay for childcare.

What are their circumstances?

The more you earn, the less you are likely to receive. Single claimants must work at least 16 hours a week. Let’s take a full-time worker: if you work at least 30 hours a week, you are generally eligible for working tax credits if you earn less than £13,253 a year (if you’re single and don’t have children), or less than £18,023 (jointly as part of a couple without children but working at least 30 hours a week).

And for families?

A family with children and an income below about £32,200 can claim child tax credit. It used to be that the more children you have, the more you are eligible to receive – but George Osborne in his most recent Budget has limited child tax credit to two children.

How much money do you receive?

Again, this depends on your circumstances. The basic payment for a single claimant, or a joint claim by a couple, of working tax credits is £1,940 for the tax year. You can then receive extra, depending on your circumstances. For example, single parents can receive up to an additional £2,010, on top of the basic £1,940 payment; people who work more than 30 hours a week can receive up to an extra £810; and disabled workers up to £2,970. The average award of tax credit is £6,340 per year. Child tax credit claimants get £545 per year as a flat payment, plus £2,780 per child.

How many people claim tax credits?

About 4.5m people – the vast majority of these people (around 4m) have children.

How much does it cost the taxpayer?

The estimation is that they will cost the government £30bn in April 2015/16. That’s around 14 per cent of the £220bn welfare budget, which the Tories have pledged to cut by £12bn.

Who introduced this system?

New Labour. Gordon Brown, when he was Chancellor, developed tax credits in his first term. The system as we know it was established in April 2003.

Why did they do this?

To lift working people out of poverty, and to remove the disincentives to work believed to have been inculcated by welfare. The tax credit system made it more attractive for people depending on benefits to work, and gave those in low-paid jobs a helping hand.

Did it work?

Yes. Tax credits’ biggest achievement was lifting a record number of children out of poverty since the war. The proportion of children living below the poverty line fell from 35 per cent in 1998/9 to 19 per cent in 2012/13.

So what’s the problem?

Well, it’s a bit of a weird system in that it lets companies pay wages that are too low to live on without the state supplementing them. Many also criticise tax credits for allowing the minimum wage – also brought in by New Labour – to stagnate (ie. not keep up with the rate of inflation). David Cameron has called the system of taxing low earners and then handing them some money back via tax credits a “ridiculous merry-go-round”.

Then it’s a good thing to scrap them?

It would be fine if all those low earners and families struggling to get by would be given support in place of tax credits – a living wage, for example.

And that’s why the Tories are introducing a living wage...

That’s what they call it. But it’s not. The Chancellor announced in his most recent Budget a new minimum wage of £7.20 an hour for over-25s, rising to £9 by 2020. He called this the “national living wage” – it’s not, because the current living wage (which is calculated by the Living Wage Foundation, and currently non-compulsory) is already £9.15 in London and £7.85 in the rest of the country.

Will people be better off?

No. Quite the reverse. The IFS has said this slightly higher national minimum wage will not compensate working families who will be subjected to tax credit cuts; it is arithmetically impossible. The IFS director, Paul Johnson, commented: “Unequivocally, tax credit recipients in work will be made worse off by the measures in the Budget on average.” It has been calculated that 3.2m low-paid workers will have their pay packets cut by an average of £1,350 a year.

Could the government change its policy to avoid this?

The Prime Minister and his frontbenchers have been pretty stubborn about pushing on with the plan. In spite of criticism from all angles – the IFS, campaigners, Labour, The Sun – Cameron has ruled out a review of the policy in the Autumn Statement, which is on 25 November. But there is an alternative. The chair of parliament’s Work & Pensions Select Committee and Labour MP Frank Field has proposed what he calls a “cost neutral” tweak to the tax credit cuts.

How would this alternative work?

Currently, if your income is less than £6,420, you will receive the maximum amount of tax credits. That threshold is called the gross income threshold. Field wants to introduce a second gross income threshold of £13,100 (what you earn if you work 35 hours a week on minimum wage). Those earning a salary between those two thresholds would have their tax credits reduced at a slower rate on whatever they earn above £6,420 up to £13,100. The percentage of what you earn above the basic threshold that is deducted from your tax credits is called the taper rate, and it is currently at 41 per cent. In contrast to this plan, the Tories want to halve the income threshold to £3,850 a year and increase the taper rate to 48 per cent once you hit that threshold, which basically means you lose more tax credits, faster, the more you earn.

When will the tax credit cuts come in?

They will be imposed from April next year, barring a u-turn.

Anoosh Chakelian is deputy web editor at the New Statesman.