Slipped into yesterday's PBR releases were two reports from HMRC - one called Measuring Indirect Tax Losses and the other called Methodologies for Measuring Direct Tax Losses.

Now the titles may not be gripping, but these are important. Lets take the first. The highlights are this:

- 14.2% of VAT is not collected. Current cost (my estimate based on HMRC data) - £13.24 billion

- £400 million of duty on spirits is not collected

- 13% of cigarettes are smuggled - cost £1.65 billion

- 56% of hand rolled tobacco is black market - cost £750 million

- £350 mill ion of diesel duty is evaded in the UK

- 43% of all diesel duty is evaded in Northern Ireland (people cross the border) - cost £210 million

The overall rate of weighted loss on indirect taxes excluding VAT is, I estimate about 9.4% based on this data.

Then let's look at Direct Taxes. Here HMRC show very muddled thinking, They admit they should do a 'top down' analysis of tax lost, which is what they do on indirect taxes. But they then say they can't do it. So they do a 'bottom up analysis' instead, which works solely on the basis of the returns made and the tax estimated to be unpaid by those submitting them based on investigation work. But as they admit this means they do not really measure tax lost by:

- non-payment;
- large business;
- the use of avoidance schemes/devices to reduce liability;
- the informal economy; and
- individuals who are not issued a return.

Which means that as a measure what comes out is not that useful.

Even so they note that:

- 13% of tax due by those subject to self assessment is lost

- 1.2% of PAYE and NI due on small and medium sized payrolls is lost

- About 14% of tax due by small and medium sized companies is lost.

The losses on that lot come to £5 billion - but their data is up to 5 years out of date - amazingly.

I've reflected on this data. Extrapolating the average tax lost on direct taxes and those taxes that probably behave like them and applying this to 2007/08 HMRC data then total direct tax losses might be £17.6 billion, VAT might be £13.2 billion and other indirect taxes £4.8 billion - a loss of £35.6 billion.

Now that's big. But it's wrong. It understates the loss. That's because:

- The direct tax losses are understated for the reasons noted above;

- The Revenue themselves fail to take into account the fact that if VAT is lost then the income related to it is almost certain to be suppressed as well, meaning that there are direct losses resulting from this evasion. These would not be counted in the above figure as this would be in the informal economy. In other words, only a top down approach works.

Now, £13.24 billion of lost VAT suggests an undeclared turnover net of costs of £75.6 billion. It's this sum that has not been taxed or not been declared for direct tax purposes. This is a measure of the 'informal' economy missed out of the direct tax loss calculations noted above.

What's the right tax rate on this?

- It's fair to assume that this is additional income - so no personal and other allowances for income tax need be given.

- It's fair to assume that this activity is not being done through many companies, or if it is that they are not complying with legal requirements, so the cash is being paid straight on to owners.

- This is earned income. NIC should apply.

- Some of this will be organised and give rise to high income. A lot will not be. It will be living wage abuse.

- So, let's take the likely situation that the tax due will be at basic rate for income tax or the broadly similar small company corporation tax rate and call that 22%. And then apply employer and employee NIC rates at a combined figure of, say 20% (which is less than the maximum). That's a 42% loss.

On £75 billion that's £31.7 billion.

So the combined loss is now £67.3 billion.

Now lets add the loss amongst large companies. I calculated that as £4.6 billion in Mind the Tax Gap for 2004/05. But Corporation Tax yields have risen since then, and so will this gap have done. Pro rata the figure should be £6.8 billion now.

That brings us to £74.1 billion.

No lets assume that tax planning by individuals increases the gap. I have shown that the domicile rule costs £4.3 billion. Let's very modestly assume that all otter planning contributes no more (and this is very generous).

Now the Tax Gap is not less than £82.7 billion. Which happens to exceed the amount of VAT collected this year. Or the cost of education in the UK, with almost £5 billion over.

Sobering, isn't it?