Friday, June 02, 2006

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).


maria said...

It's just Polly delivering a load of Government propaganda. She is a total throwback. New Labour isn't Labour and it's about time she addressed some real issues - like why non-representative MPs from elsewhere in the UK foist legislation on to every person in England, non-representative "English regional assemblies" sap money post devolution, Blair's cabinet is made up of so many MPs from his homeland of Scotland (there are around 60 million people in the UK; only 5 million of them live in Scotland) and public spending in England is so much lower than elsewhere in the so-called "UK", despite the fact that certain areas of England are financially worse off than any in Scotland now.

Traditional Labour voters in England are turning to the hateful BNP. Why is this happening?

Polly is a patronising 1960s era throwback. She should be looking at this government's discrimination against the people of England. Yes, whatever your race, colour or creed, if you live in England you are a second class UK citizen. But in Polly's aged brain, "England" is a dirty word.

The modern day people of England, scapegoats for the exploits of the BRITISH during the time of Empire, deserve all they get, apparently. There are no issues there for Polly and her ilk.

And by the way - I used to vote Labour. When the party actually WAS Labour.

Neil Harding said...

The Tax Freedom day will be based on tax payers on the mean average wage which is over £30,000. In fact only 15% of the population get this, so Polly is right, it is only the very rich that have to wait until this day. The median average wage is £21,000.

FactcheckingPollyanna said...

Neil --

No-one denies that for an individual who pays less tax, typically those earning less, the "day" will fall sooner. However, the day represents an average. It is not based just on the rich, but on the total tax take in the economy.

It is therefore wrong to imply that it will fall precisely on 3 June for both Cameron and Osborne.

And no, it is not based on the mean wage -- it is based on total tax take. It includes tax on investment income, VAT, corporation tax, etc... But, you know, nice try.

Neil Harding said...

The tax freedom will be based on adding up all the tax and taking a mean average.

As all statisticians know, the median is the middle position of the range. The mean in this case will be very near the top tax payers - tax paid by those earning over 30,000, the top 15% of earners. So Polly is right to say it is only the very rich that have to wait until this day.

FactcheckingPollyanna said...

Neil --

I do understand the difference between a mean and a median (and even a mode, which is why I referred to the average number of legs in my post).

Two things -- calculating when the day falls is not "based on the mean average wage", as you claimed. You take the total of all tax takes, and do not use the mean wage at all in the calculation. The second point is to do with the mode, as opposed to mean or median -- June 3rd is probably "tax freedom day" for a tiny proportion of the population. For some (many) it will fall sooner. For some (far fewer) it will fall later. But the chance of it occurring on June 3rd for both Cameron and Osborne are vanishingly small.

As all statisticians know.

FactcheckingPollyanna said...

Neil --

As a minor aside, according to HMRC's estimates, 21% of taxpayers earned over £30,000 in 2005/6 (see Social Trends 36, p.74).

The Pedant-General in Ordinary said...

But, but, but, but...

Neil: Are you saying that the rich pay a substantially greater proportion of their income in tax?

Quelle Horreur! How can this be? I thought the rich were supposed to be blood suckers of the first water who are ruthlessly and deliberately exploiting the system for their own ends?