Inexpert tax experts

Richard Murphy, the "tax expert", is strongly in favour of retaining the 50% top income tax rate in the UK:

About 300,000 people will be affected by this tax in HMRC’s estimate. They have taxable income after allowances and reliefs of £150,000 a year. They represent about 1.0% of all taxpayers.

They’re expected to have total taxable income between them of about £47 billion. So the tax - which is an extra 10% over and above the 40% rate previously applying should raise nearly £5 billion a year. It may, because of the disallowance of personal allowances and pension contributions for this group for which we have no real impact data as yet, be higher than that in my opinion – closer to £6 billion in fact, but I stress that’s an estimate.

This is higher than HMRC have estimated – they’ve never gone above £3 billion. It is very obviously radically different from the claims made by opponents that this tax will cost the government money...

He doesn't explain where he gets "nearly £5 billion" from, but the way he presents it makes it look very much  as if he's taking 10% of £47 billion.

Ryan Bourne of the Centre for Policy Studies seizes on this:

I accessed HMRC’s income tax liabilities by taxpayer marginal rate table for 2011-12. Sure enough, it says that additional rate taxpayers (the top 1% earning over £150,000) are liable for a total of £47 billion in tax (28% of total income tax revenues). Therefore it seems that Richard has just assumed that lowering the tax rate from 50% to 40% would be equivalent to reducing their tax liability by 10 percentage points, or £4.7 billion.

This is not how our tax system works. In fact, people earning over £150k don’t pay 50% of their income in tax. The 50% rate means that any income you earn over £150,000 is taxed at 50% - it’s what economists call a marginal rate...

...This means that Richard has overestimated the revenue that the 50p rate brings in, because it doesn’t apply to the first £150,000 of any one of these people’s income. In other words, all income revenue tax paid by those in the 50% rate band below £150,000 is completely unaffected by the change in rate. Given that there are 308,000 additional rate payers and each pays £53,000 in tax before reaching the £150,000 threshold where the 50% rate kicks in, £16.3 billion of the revenues collected from the richest 1% have nothing to do with the 50% rate.

So what would happen if the rate were lowered to 50% to 40% in terms of the remaining revenues actually collected from the 50% tax rate bit? Helpfully, HMRC provides a ready reckoner which estimates this very thing. It estimates that for every 1p drop in the rate, revenue would drop by £70m this year and £120m next year. So, dropping the rate by 10 percentage points, or 10p, would cost between £700m and £1.2 billion – even less than the Treasury’s own predictions. This is likely to take into account behavioural changes: if more people leave the country or find legal ways to avoid paying the 50% rate then revenue will not increase from a higher rate on a straight line basis.

Bourne is right about the £16.3bn (you can read the £53,000 he mentions off this chart).  But he's quite wrong in taking 10% of what's left.  The £47bn is a tax liability, not a taxable income.  So that minus £16.3bn is the tax collected by the 50% rate.  If it were reduced to 40%, then others things being equal a fifth less would be collected: the difference would be £6.1bn.

It's intriguing that Murphy has guessed something very close to that number.  I wonder whether someone who does understand this not very difficult calculation has told him the right number, and he's tried and failed to reproduce it.

£6.1bn is of course vastly more than what Bourne comes up with using Treasury estimates  of the effect of  changing the rate.  The Treasury figure is their best guess, taking into consideration that cutting the top rate will considerably increase taxable incomes of more than £150,000.  These effects are notoriously difficult to estimate.

Murphy reports triumphantly that the number he gets is much more than the estimates given by opponents of the tax.  He goes on to predict that there will be very little elasticity: he is confident that he knows better than the Treasury how people react to changes in income tax rates.

I'm in favour of giving it a couple of years and finding out whose predictions are closer to the truth.


Update 6th March:
Murphy has published a new post in which he sort-of denies making the error Bourne accuses him of:

...if I’d done what [Bourne had] suggested I’d have said that the extra tax would be 25% extra on the £47 billion – which is the proportionate increase on the tax yield of £47 billion that would have been due if all the income that had previously been due at the same fixed 40% marginal rate had now been due at 50%. That’s because 10% is 25% of 40%. And so the extra tax would have actually been, if I’d committed such an error, a whopping £11.75 billion. In that context it’s clear that £4.7 billion more than adequately compensates for the fact that not all the tax on anyone’s income is due at the 50% rate...
...As you’ll see tomorrow my actual estimate of potential tax yield is higher than £4.7 billion – I just used that as a headline last week whilst waiting for my full report to come out...

But the way he phrases all this it does seem that 10% of £47 billion is exactly the "headline" calculation he did.  And if he had been aware of the correct calculation, he wouldn't now be writing "10% is 25% of 40%" when he should be saying "10% is 20% of 50%".

However, Bourne is more credulous than I am, and has apologized and withdrawn his post.