Numerical illiteracy strikes yet again

A news item this morning explained that local authorities had been introducing lie detectors in an effort to reduce benefit fraud and it had already saved 100,000s of pounds ie 10 to the power of 5 - a figure followed by five naughts. That is the price of a few terrace houses.

Benefit fraud it was said, is estimated to cost the government £400,000,000 a year, though this can only be a guesstimate. That is 4 x 10 to the power of 8 ie three orders of magnitude more than the amount saved. In other words the saving is trivial. Not worth a mention in a news programme when tens of thousands have just been killed in a natural disaster.

Total government expenditure is just under £500 billion a year, that is 5 x 10 to the power of 11 so is three orders of magnitude more than the fraud. Now although the cost of the fraud would purchase a tram system for a medium sized town, it too becomes trivial in within the overall picture.

But now look at some other figures. The cost of running the tax system is £25 billion a year, which makes it about 5% of the total. That is serious. It would pay for a High Speed Rail line from London to Scotland and still leave some change over. Then there is legal avoidance of tax. Various figures are bandied about but the concensus is that this is also around £25 billion - again, roughly 5% of the total. But there is no need to get fixated on the exact amounts because all of these are dwarfed by the deadweight cost to the UK economy caused by the tax system - that is economic activity that would take place were it not for tax. This is an astonishing £136 billion (IEA figures for 2006) - which is about 12% of Gross Domestic Product. Now that really is something to get concerned about. That means that everyone who actually is working is doing a day's more work every week just for nothing.

The table below, in very round figures, shows the relative scales of the problem.

Benefit fraud saved by lie detectors........£500,000
Cost of benefit fraud...................£400,000,000
Cost of running the tax system.......£25,000,000,000
Loss due to tax avoidance............£25,000,000,000
Deadweight loss due to tax system...£136,000,000,000
Gross Domestic Product............£1,000,000,000,000