Numerical fragility

Today's Polly Toynbee column says of the tax credit system:

That means 20% will be overpaid and 10% will be underpaid. How bad is that? Not all that bad. The standard error rate of the social security system for means-tested benefits under all governments has always been around 10%.

Actually, if you are overpaying 20% and underpaying 10%, that means an error rate of 30%, considerably higher than the already generous 10% error rate Polly cites.

She then goes on to say:

But most of these over- and underpayments are not errors. The whole point of the system is to make sure families can keep on an even keel when their incomes change. Overpayment happens if they fail to declare when their household incomes rise, when earning more, moving in with an earning partner or stopping childcare, or when a child reaches 18. Families are underpaid if they fail to claim when their income drops or they have another child.

Overpayments also happen because of government error, of course. The IFS, cited approvingly later on the article in a different context, has some interesting research here on this. To save you reading the entire thing, consider just the headline:

Government paying tax credits and benefits to 200,000 more lone parents than live in the UK

When Polly does cite the IFS, she says:

according to the Institute for Fiscal Studies, tax credits have delivered "the longest sustained fall in child poverty since records began" - 700,000 fewer children now live below the poverty line, back to levels of 20 years ago

I think a reasonable person would think from this inaccurate précis that the IFS were claiming that the fall of 700,000 children in child poverty was due to the tax credits. In fact, their research (pdf link here) says on page 46 that:

The size of the population effect depends on the overall change in the number of children and on the average poverty risk. The table shows that the fall in the number of children reduced child poverty by around 42,000

On page 49, they go on to say that:

To summarise a complicated set of changes, child poverty fell primarily because

• there were large falls in the risk of poverty for children in workless families, those with part-time working lone parents and those in couple families with one full-time parent and one non-working parent

• there was a substantial decline in the proportion of children living in workless families.

So part of the fall was attributable to a fall in the number of children, and part was due to a 'substantial decline' in children living in workless families. Which is not to say that the tax credits haven't helped, or that a fall in unemployment is a bad thing. It is to say that there is more at work than the tax credit system.

And finally, in the very paragraph where she talk of Oborne's "numerical fragility", she misses the point of an average, as represented by the idea of the so-called 'Tax Freedom Day'. In a nutshell, it represents the proportion of total national income which is paid to the government in the form of tax as a day on the calendar. This is an average. Polly rightly implies that the day will occur sooner for people earning less, however she wrongly states that it will occur on that precise day for the "very.very rich, of course -- the Notting Hill people." Averages rarely represent the true figure for individuals (the old cliché is that no-one has the average number of legs).