Iain Duncan Smith was right to weep when he visited Easterhouse, all those years ago – although he would not have known the reason.

It turns out there are probably drug dealers on that estate with a better grasp of mathematics than anybody in his Department for Work and Pensions – or, let’s be honest, the entire Coalition government.

This week it emerged that the National Audit Office has refused to sign off the DWP’s accounts – for the 25th year running. While this indicates that the problem is not limited to the Coalition, it should be noted that David Cameron’s crew has done nothing to rectify it.

The NAO has instead delivered a “qualified” audit opinion, in respect of fraud and error which is considered to be unacceptably high. It seems the department overpaid £3.5 billion or 2.1 per cent of total benefit expenditure due to fraud and error – and also underpaid £1.4 billion to claimants.

Of this, fraud remained static at £1.2 billion (the same as in 2011-12), while underpayments due to official error increased from £400 million to £500 million.

Official error has increased while fraud has not.

An interesting sidebar to this is the fact that fraud has not decreased either, despite all Mr Duncan Smith’s apparent efforts to hammer it. Next year’s accounts – due after April 2014, although your guess on the actual date is as good as anyone’s – should make interesting reading, as they should show the effect of the major regressions (not reforms) he introduced this year.

Further evidence of government incompetence with the figures came in a chart from Conservative Central HQ’s press office, flagged up by Jonathan Portes and the immeasurably cleverer people at NIESR (National Institute of Economic and Social Research).

The chart’s claim was that 28,500 households had been receiving more than £500 per week in benefits, despite containing people who could work but weren’t – until the £26,000 per year Benefit Cap was brought in and reduced it to nothing.

Mr Portes told us the chart was based on DWP statistics published last week that show that 28,500 households have had their benefit capped at £500 per week, “however, the interpretation – and the chart – is utterly wrong in every respect.

“It just is not the case that every one of those 28,500 households contains someone who “can work”.  As the DWP publication clearly states, the cap applies to households in receipt of key out of work benefits – including both those in the Employment and Support Allowance (ESA) Work-Related Activity Group (WRAG) and those on Income Support (IS).  For people in the WRAG, the position is quite clear. As the DWP itself puts it… they are ‘currently too ill or disabled to work’.

“DWP makes clear that there is no assumption that Income Support claimants ‘can work’, but quite the opposite. As a general rule, most people who ‘can work’ should be on Jobseekers Allowance (JSA), not IS. In practice, most of those on IS are single mothers with young children, who are not expected to work.

“Overall, although we don’t have precise numbers from the DWP statistics, it seems quite likely that in fact less than half of the households affected by the cap contain ‘people who can work but aren’t’.”

Mr Portes went on to analyse the second assumption in the chart – that there are now no households receiving more than £500 per week in benefits that include “people who can work but aren’t” – and found it “just as wrong,” – because DWP guidance exempts households with anyone on DLA, PIP, Attendance Allowance, the support component of ESA or Industrial Injuries Benefits, and those receiving War Disablement Pension and equivalent payments from the Armed Forces Compensation Payments Scheme.

“Of course it’s perfectly possible for such households to contain ‘people who can work but aren’t’ – most obviously households with a child receiving DLA, but there are lots of other possible cases. Moreover, even this excludes couple households where one person is working but the other could work, but is not, who are also exempt. Given enough children and/or high enough housing costs, such households can receive more than £500 per week in benefits,” wrote Mr Portes.

“Again, we don’t know the exact numbers, but we are certainly talking about thousands of households, not zero.”

Only on Monday, Mr Duncan Smith assured the Commons Work and Pensions Select Committee that he had warned CCHQ and Tory chairman Grant Shapps against such jiggery-pokery with his departmental stats: “I have had conversations with him and others about being careful to check with the department.”

So did the chart go out with his department’s full endorsement, in which case this is even more proof that the DWP can’t get its facts right – or did CCHQ ignore Mr Duncan Smith’s words and make its own mistake?

For this government, and Mr “In Deep Sh…ambles”, the result is the same.

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